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Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 212806 11 pageshttpdxdoiorg1011552013212806
Research ArticleLocalization with Single Stationary Anchor for Mobile Node inWireless Sensor Networks
Haipeng Qu1 Guojia Hou1 Ying Guo2 Ning Wang1 and Zhongwen Guo1
1 Department of Computer Science Ocean University of China Qingdao 266100 China2 School of Information Science and Technology Qing Dao University of Science and Technology Qingdao 266100 China
Correspondence should be addressed to Haipeng Qu haipengqugmailcom
Received 16 October 2012 Revised 15 January 2013 Accepted 8 February 2013
Academic Editor Long Cheng
Copyright copy 2013 Haipeng Qu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We proposed a localization algorithm named LSARSSI for mobile node based on RSSI (received signal strength indicator) betweenlocating sensor node with inertia module built-in and the single anchor Instead of directly mapping RSSI values into physicaldistance contrasting RSSI values received from anchor in different visited locations LSARSSI utilizes the geometric relationshipof perpendicular intersection to compute node positions Given that the values of RSSI among two visited locations are equal weregard that their distances to anchor node are equal After obtaining several sets of such visited locations the relative location ofmobile node and anchor node can be calculated Because of the limitations of LSARSSI we put forward an improved algorithmnamed ILSARSSI Our scheme uses only one location-known anchor which is useful in low density environment without usingadditional hardware The simulations show that LSARSSI achieves high accuracy and ILSARSSI performs high stability andfeasibility
1 Introduction
Wireless sensor networks (WSNs) are such popular researchfields that are highly interdisciplinary and state-of-the-art[1] It has emerged as one of the key enablers for a varietyof applications such as military environment monitoringemergency response target detection and tracking and somebusiness fields In recent years a number of research achieve-ments aboutWSNs localization have arisen According to thedeployment of beacon nodes (which is also called anchor)the localization approaches that have been proposed can bedivided into two types one of which is based on multiplestationary beacon nodes [2ndash5] and another is based onmobile beacon node(s) [6ndash10]
But these methods are not suitable for all the applicationsof WSNs In some scenarios however there is only a station-ary beacon node [11] or a seed (reference nodewhich positionis known) For example when we observe WSN on the seadata can be transmitted to the shore or on board throughan aggregation node and only the position of aggregationnode is known Another example is regarding mountaininspection the inspectorwould carry sensormodule tomovetransmitting data collected through the aggregation base
station on the peak and only the position of base station isknown In this situation neither methods based on mobilebeacon nor methods based on multiple beacon nodes couldbe used directly
To address the previous issues in this paper we pro-posed a localization algorithm named LSARSSI an RSSI-based localization scheme using single stationary anchor Toincrease the feasibility of our scheme we further put forwardan improved method called ILSARSSI Major contributionsof this paper are as follows
(i) Our schemes can be used to locatemobile node in lowdensity environment which only need single anchor
(ii) In order to avoid errors from directly mappingabsolute RSSI values to distances we obtain thegeometrical relationship of sensors by contrastingthe measured RSSI values We then design a novellocalization scheme LSARSSI which has a betteraccuracy and low overhead
(iii) The simulation results show that our schemes per-form high accuracy and feasibility even in large-scaleenvironment
2 International Journal of Distributed Sensor Networks
119883
119885
119884
119860(1199090 1199100 1199110)
1198750(119909 119910 119911)
119875119894(119909 + Δ119909 119910 + Δ119910 119911 + Δ119911)
Figure 1 A model assumption in 3D
The rest of this paper is organized as follows Section 2introduces the related works about the localization of WSNsSections 3 and 4 respectively present our algorithm ofLSARSSI and ILSARSSI Section 5 presents our implemen-tation and the simulation results We conclude this paper inSection 6
2 Related Works
According to the deployment of beacon nodes localizationtechnology can be classified into two categories multiple sta-tionary beacon nodes based approaches and mobile beaconnode(s) based approaches
21 Multiple Stationary Beacon Nodes Based ApproachesMeasurement techniques inWSNs based onmultiple station-ary beacon nodes can be broadly classified into two cate-gories range-based approaches and range-free approaches
211 Range-Based Approaches Range-based approaches as-sume that sensor nodes can measure the distance andor therelative directions of neighbor nodes Several mechanismshave been proposed to measure the nodersquos physical distanceFor example time of arrival (TOA) obtains range informationthrough signal propagation times [12] and time differenceof arrival (TDOA) estimates the node location by utilizingthe time differences among signals that are received frommultiple senders [13] As an extension of TOA and TDOAangle of arrival (AOA) allows nodes to estimate the relativedirections between neighbors by setting an antenna array foreach node [14]
All the previous approaches require additional hardwareequipment so as to increase the cost of the sensor nodesgreatly Such TDOA needs at least two signal generators [13]AOA needs antenna arrays and multiple ultrasonic receivers[14]
A popular and widely used ranging technique is thereceived signal strength (RSS) or quantified as the received
signal strength indicator (RSSI) RSSI is utilized to estimatethe distance between two nodes with ordinary hardware[12 15] Various theoretical or empirical models of radiosignal propagation have been constructed to map absoluteRSSI values into estimated distances [16] The accuracy andprecision of such models however are far from perfectbecause of factors such as multipath fading and backgroundinterference [15 17]
212 Range-Free Approaches Given that range-based ap-proaches are limited by hardware limitations and energyconstraints researchers have proposed range-free solutionsas cost-effective alternatives
Range-free approaches rely on the connectivity measure-ments between the measurement sensor nodes and a numberof reference nodes called seeds For example in the centroidalgorithm [18] seeds broadcast their position to all neighbornodes that record all received beacons Each node estimatesits location by calculating the center of the locations of allseeds it hears In Approximate Point-in-Triangulation Test(APIT) [19] each node estimates whether it resides inside oroutside several triangular regions bounded by the seeds that ithears and refines the computed location by overlapping suchregions In ring overlapping based on comparison of receivedsignal strength indicator (ROCRSSI) [20] each sensor nodeuses a series of overlapping rings to narrow down the possiblearea in which it resides
22 Mobile Beacons Approaches Localization algorithmsmentioned previously are in static sensor networks whichare not available in some scenarios Recently mobile-assistedlocalization approaches have been proposed to improve theefficiency of range-based approaches [10 21] The location ofa sensor node can be calculated with the rangemeasurementsfrom themobile beacon to itself the localization accuracy canalso be improved bymultiplemeasurements that are obtainedwhen the mobile beacons are in different positions
Several localization schemes are proposed in this fieldFor example Bergamo and Mazzini propose a scheme toperform localization based on the estimation of the powerreceived by only two beacons placed in known positions [22]By starting from the received powers eventually averaged ona given window to counteract interference and fading theactual distance between the sensor and the beacons is derivedand the position is obtained by means of triangulationIn [10] a localization technique based on a single mobilebeacon aware of its position (eg by being equipped with aGPS receiver) was presented Sensor nodes receiving beaconpackets infer proximity constraints to the mobile beacon anduse them to construct and maintain position estimates InPI algorithm [9] instead of using the absolute RSSI valuesby contrasting the measured RSSI values from the mobilebeacon to a sensor node PI utilizes the geometric relationshipof perpendicular intersection to compute the position of thenode
In recent years more researches are focusing on mobilesensor networks which are mainly based on mobile nodes[23ndash25] Unlike other algorithms the scene of the application
International Journal of Distributed Sensor Networks 3
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
(a) (b)
RSSI(1198751) RSSI(1198751)
RSSI(1198750) RSSI(1198750)
RSSI(1198751000)
RSSI(119875999)RSSI(119875999)
RSSI(119875119894)[minmax]
11987201198720
11987211198721
119872119894
119872999 119872999
1198721000
Figure 2 The 1001th message stored by sensor
of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches
3 LSARSSI Algorithm
In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space
31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module
We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909
0 1199100 1199110) Assume that the
coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875
119894(119894 isin [1 119899]) is a visited location of the mobile
node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875
119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the
coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in
Figure 1Table 1 shows the messages obtained by the locating
node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875
0to 119875999
and if the RSSI value of 119875119894is minimum
(or maximum) the message of 1198751000
will replace it as shownin Figure 2
As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable
Table 1 Messages stored by sensor
Locations Messages (node N)1198750
Δ119909 Δ119910 Δ119911 RSSI(1198750)
1198751
119909 + Δ11990901
119910 + Δ11991001
119911 + Δ11991101
RSSI(1198751)
119875119894
119909 + Δ1199090119894
119910 + Δ1199100119894
119911 + Δ1199110119894
RSSI(119875119894)
119875119899minus1
119909 + Δ1199090119899minus1
119910 + Δ1199100119899minus1
119911 + Δ1199110119899minus1
RSSI(119875119899minus1
)119875119899
119909 + Δ1199090119899
119910 + Δ1199100119899
119911 + Δ1199110119899
RSSI(119875119899)
32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889
minus119899119901 where 119899119901
is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as
[119901119903 (119889)]119889119861119898
= [119901119903(1198890)]119889119861119898
minus 10119899 log 119889
1198890
(1)
where 1198750is the received power (dBm) at short reference
distance 1198890
From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3
Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875
3are the visited locations of locating node
119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875
01198751 11987521198753 and RSSI(119875
0) = RSSI(119875
1) RSSI(119875
2) =
RSSI(1198753)
4 International Journal of Distributed Sensor Networks
1198750
1198752
1198753
1198751
119860
119861
119862
Figure 3 An example of LSARSSI algorithm in 2D
The following are the formulas for calculating the locationof locating node
119860 = (1199090 1199100) 119875
0= (119909 119910)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02)
1198753= (119909 + Δ119909
03 119910 + Δ119910
03)
119861 = (119909 + Δ1199090119861 119910 + Δ119910
0119861)
119862 = (119909 + Δ1199090119862 119910 + Δ119910
0119862)
(2)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001) rarr
11987521198753
= (Δ11990923 Δ11991023)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100)
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090)
+ Δ11991001lowast (119910 + Δ119910
0119861minus 1199100) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090)
+ Δ11991023lowast (119910 + Δ119910
0119862minus 1199100) = 0
dArr
(1) Δ11990901lowast 119909 + Δ119910
01lowast 119910
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
(2) Δ11990923lowast 119909 + Δ119910
23lowast 119910
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
(3)
Assume that119886 = Δ119909
01lowast (1199090minus Δ1199090119861)
+ Δ11991001lowast (1199100minus Δ1199100119861)
119887 = Δ11990923lowast (1199090minus Δ1199090119862)
+ Δ11991023lowast (1199100minus Δ1199100119862)
(4)
then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886
(4) Δ11990923lowast 119909 + Δ119910
23lowast 119910 = 119887
dArr
119909 =1198631
119863 119910 =
1198632
119863
(5)
where
119863 =10038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11990923
Δ11991023
10038161003816100381610038161003816100381610038161003816 119863
1=10038161003816100381610038161003816100381610038161003816
119886 Δ11991001
119887 Δ11991023
10038161003816100381610038161003816100381610038161003816
1198632=10038161003816100381610038161003816100381610038161003816
Δ11990901
119886
Δ11990923
119887
10038161003816100381610038161003816100381610038161003816
(6)
33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect
The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875
0 1198751 119875119899 Their RSSI values
are RSSI(1198750)RSSI(119875
1) RSSI(119875
119899) locations can be divided
into a number of subsets 1198731 1198732 119873119898 based on RSSI val-
ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873
119886| = 2 and
|119873119887| = 2 and |119873
119888| = 2 (as shown in Figure 4(a)) (2) |119873
119886| = 3
and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873
119886| = 4 (as
shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take
|119873119886| = 2 |119873
119887| = 2 and |119873
119888| = 2 as an example to indicate
formulas for calculating the location of locating node119860 is theanchor119875
01198751119875211987531198754 and119875
5are the visited locations of the
mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and
11987541198755 And
119860 = (1199090 1199100 1199110)
1198750= (119909 119910 119911)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01 119911 + Δ119911
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02 119911 + Δ119911
02)
International Journal of Distributed Sensor Networks 5
119860
119861
119862119863
119884
119883
119885
1198755
1198751 1198752
1198753
1198750 1198754
(a)
119884
119883
119885
119860
1198751
1198752
11987531198754
1198750
(b)
119884
119883
119885
119860
1198752
1198753
1198751
1198750
(c)
Figure 4 Examples of LSARSSI algorithm in 3D
119884
119883
119860
119874
119861
119862
119863
119864
119875998400
1
1198711
11987121198713
1198714
119875998400
3
119875998400
2
119875998400
0
1198751
1198752
1198753
1198750
Figure 5 An example of ILSARSSI algorithm in 2D
1198753= (119909 + Δ119909
03 119910 + Δ119910
03 119911 + Δ119911
03)
1198754= (119909 + Δ119909
04 119910 + Δ119910
04 119911 + Δ119911
04)
1198755= (119909 + Δ119909
05 119910 + Δ119910
05 119911 + Δ119911
05)
RSSI (1198750) = RSSI (119875
1)
RSSI (1198752) = RSSI (119875
3)
RSSI (1198754) = RSSI (119875
5)
(7)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001 Δ11991101) rarr
11987521198753
= (Δ11990923 Δ11991023 Δ11991123)
rarr11987541198755
= (Δ11990945 Δ11991045 Δ11991145)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100 119911 + Δ119911
0119861minus 1199110)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100 119911 + Δ119911
0119862minus 1199110)
dArr
rarr119860119863
= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910
0119863minus 1199100 119911 + Δ119911
0119863minus 1199110)
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
2 International Journal of Distributed Sensor Networks
119883
119885
119884
119860(1199090 1199100 1199110)
1198750(119909 119910 119911)
119875119894(119909 + Δ119909 119910 + Δ119910 119911 + Δ119911)
Figure 1 A model assumption in 3D
The rest of this paper is organized as follows Section 2introduces the related works about the localization of WSNsSections 3 and 4 respectively present our algorithm ofLSARSSI and ILSARSSI Section 5 presents our implemen-tation and the simulation results We conclude this paper inSection 6
2 Related Works
According to the deployment of beacon nodes localizationtechnology can be classified into two categories multiple sta-tionary beacon nodes based approaches and mobile beaconnode(s) based approaches
21 Multiple Stationary Beacon Nodes Based ApproachesMeasurement techniques inWSNs based onmultiple station-ary beacon nodes can be broadly classified into two cate-gories range-based approaches and range-free approaches
211 Range-Based Approaches Range-based approaches as-sume that sensor nodes can measure the distance andor therelative directions of neighbor nodes Several mechanismshave been proposed to measure the nodersquos physical distanceFor example time of arrival (TOA) obtains range informationthrough signal propagation times [12] and time differenceof arrival (TDOA) estimates the node location by utilizingthe time differences among signals that are received frommultiple senders [13] As an extension of TOA and TDOAangle of arrival (AOA) allows nodes to estimate the relativedirections between neighbors by setting an antenna array foreach node [14]
All the previous approaches require additional hardwareequipment so as to increase the cost of the sensor nodesgreatly Such TDOA needs at least two signal generators [13]AOA needs antenna arrays and multiple ultrasonic receivers[14]
A popular and widely used ranging technique is thereceived signal strength (RSS) or quantified as the received
signal strength indicator (RSSI) RSSI is utilized to estimatethe distance between two nodes with ordinary hardware[12 15] Various theoretical or empirical models of radiosignal propagation have been constructed to map absoluteRSSI values into estimated distances [16] The accuracy andprecision of such models however are far from perfectbecause of factors such as multipath fading and backgroundinterference [15 17]
212 Range-Free Approaches Given that range-based ap-proaches are limited by hardware limitations and energyconstraints researchers have proposed range-free solutionsas cost-effective alternatives
Range-free approaches rely on the connectivity measure-ments between the measurement sensor nodes and a numberof reference nodes called seeds For example in the centroidalgorithm [18] seeds broadcast their position to all neighbornodes that record all received beacons Each node estimatesits location by calculating the center of the locations of allseeds it hears In Approximate Point-in-Triangulation Test(APIT) [19] each node estimates whether it resides inside oroutside several triangular regions bounded by the seeds that ithears and refines the computed location by overlapping suchregions In ring overlapping based on comparison of receivedsignal strength indicator (ROCRSSI) [20] each sensor nodeuses a series of overlapping rings to narrow down the possiblearea in which it resides
22 Mobile Beacons Approaches Localization algorithmsmentioned previously are in static sensor networks whichare not available in some scenarios Recently mobile-assistedlocalization approaches have been proposed to improve theefficiency of range-based approaches [10 21] The location ofa sensor node can be calculated with the rangemeasurementsfrom themobile beacon to itself the localization accuracy canalso be improved bymultiplemeasurements that are obtainedwhen the mobile beacons are in different positions
Several localization schemes are proposed in this fieldFor example Bergamo and Mazzini propose a scheme toperform localization based on the estimation of the powerreceived by only two beacons placed in known positions [22]By starting from the received powers eventually averaged ona given window to counteract interference and fading theactual distance between the sensor and the beacons is derivedand the position is obtained by means of triangulationIn [10] a localization technique based on a single mobilebeacon aware of its position (eg by being equipped with aGPS receiver) was presented Sensor nodes receiving beaconpackets infer proximity constraints to the mobile beacon anduse them to construct and maintain position estimates InPI algorithm [9] instead of using the absolute RSSI valuesby contrasting the measured RSSI values from the mobilebeacon to a sensor node PI utilizes the geometric relationshipof perpendicular intersection to compute the position of thenode
In recent years more researches are focusing on mobilesensor networks which are mainly based on mobile nodes[23ndash25] Unlike other algorithms the scene of the application
International Journal of Distributed Sensor Networks 3
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
(a) (b)
RSSI(1198751) RSSI(1198751)
RSSI(1198750) RSSI(1198750)
RSSI(1198751000)
RSSI(119875999)RSSI(119875999)
RSSI(119875119894)[minmax]
11987201198720
11987211198721
119872119894
119872999 119872999
1198721000
Figure 2 The 1001th message stored by sensor
of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches
3 LSARSSI Algorithm
In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space
31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module
We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909
0 1199100 1199110) Assume that the
coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875
119894(119894 isin [1 119899]) is a visited location of the mobile
node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875
119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the
coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in
Figure 1Table 1 shows the messages obtained by the locating
node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875
0to 119875999
and if the RSSI value of 119875119894is minimum
(or maximum) the message of 1198751000
will replace it as shownin Figure 2
As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable
Table 1 Messages stored by sensor
Locations Messages (node N)1198750
Δ119909 Δ119910 Δ119911 RSSI(1198750)
1198751
119909 + Δ11990901
119910 + Δ11991001
119911 + Δ11991101
RSSI(1198751)
119875119894
119909 + Δ1199090119894
119910 + Δ1199100119894
119911 + Δ1199110119894
RSSI(119875119894)
119875119899minus1
119909 + Δ1199090119899minus1
119910 + Δ1199100119899minus1
119911 + Δ1199110119899minus1
RSSI(119875119899minus1
)119875119899
119909 + Δ1199090119899
119910 + Δ1199100119899
119911 + Δ1199110119899
RSSI(119875119899)
32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889
minus119899119901 where 119899119901
is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as
[119901119903 (119889)]119889119861119898
= [119901119903(1198890)]119889119861119898
minus 10119899 log 119889
1198890
(1)
where 1198750is the received power (dBm) at short reference
distance 1198890
From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3
Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875
3are the visited locations of locating node
119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875
01198751 11987521198753 and RSSI(119875
0) = RSSI(119875
1) RSSI(119875
2) =
RSSI(1198753)
4 International Journal of Distributed Sensor Networks
1198750
1198752
1198753
1198751
119860
119861
119862
Figure 3 An example of LSARSSI algorithm in 2D
The following are the formulas for calculating the locationof locating node
119860 = (1199090 1199100) 119875
0= (119909 119910)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02)
1198753= (119909 + Δ119909
03 119910 + Δ119910
03)
119861 = (119909 + Δ1199090119861 119910 + Δ119910
0119861)
119862 = (119909 + Δ1199090119862 119910 + Δ119910
0119862)
(2)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001) rarr
11987521198753
= (Δ11990923 Δ11991023)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100)
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090)
+ Δ11991001lowast (119910 + Δ119910
0119861minus 1199100) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090)
+ Δ11991023lowast (119910 + Δ119910
0119862minus 1199100) = 0
dArr
(1) Δ11990901lowast 119909 + Δ119910
01lowast 119910
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
(2) Δ11990923lowast 119909 + Δ119910
23lowast 119910
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
(3)
Assume that119886 = Δ119909
01lowast (1199090minus Δ1199090119861)
+ Δ11991001lowast (1199100minus Δ1199100119861)
119887 = Δ11990923lowast (1199090minus Δ1199090119862)
+ Δ11991023lowast (1199100minus Δ1199100119862)
(4)
then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886
(4) Δ11990923lowast 119909 + Δ119910
23lowast 119910 = 119887
dArr
119909 =1198631
119863 119910 =
1198632
119863
(5)
where
119863 =10038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11990923
Δ11991023
10038161003816100381610038161003816100381610038161003816 119863
1=10038161003816100381610038161003816100381610038161003816
119886 Δ11991001
119887 Δ11991023
10038161003816100381610038161003816100381610038161003816
1198632=10038161003816100381610038161003816100381610038161003816
Δ11990901
119886
Δ11990923
119887
10038161003816100381610038161003816100381610038161003816
(6)
33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect
The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875
0 1198751 119875119899 Their RSSI values
are RSSI(1198750)RSSI(119875
1) RSSI(119875
119899) locations can be divided
into a number of subsets 1198731 1198732 119873119898 based on RSSI val-
ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873
119886| = 2 and
|119873119887| = 2 and |119873
119888| = 2 (as shown in Figure 4(a)) (2) |119873
119886| = 3
and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873
119886| = 4 (as
shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take
|119873119886| = 2 |119873
119887| = 2 and |119873
119888| = 2 as an example to indicate
formulas for calculating the location of locating node119860 is theanchor119875
01198751119875211987531198754 and119875
5are the visited locations of the
mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and
11987541198755 And
119860 = (1199090 1199100 1199110)
1198750= (119909 119910 119911)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01 119911 + Δ119911
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02 119911 + Δ119911
02)
International Journal of Distributed Sensor Networks 5
119860
119861
119862119863
119884
119883
119885
1198755
1198751 1198752
1198753
1198750 1198754
(a)
119884
119883
119885
119860
1198751
1198752
11987531198754
1198750
(b)
119884
119883
119885
119860
1198752
1198753
1198751
1198750
(c)
Figure 4 Examples of LSARSSI algorithm in 3D
119884
119883
119860
119874
119861
119862
119863
119864
119875998400
1
1198711
11987121198713
1198714
119875998400
3
119875998400
2
119875998400
0
1198751
1198752
1198753
1198750
Figure 5 An example of ILSARSSI algorithm in 2D
1198753= (119909 + Δ119909
03 119910 + Δ119910
03 119911 + Δ119911
03)
1198754= (119909 + Δ119909
04 119910 + Δ119910
04 119911 + Δ119911
04)
1198755= (119909 + Δ119909
05 119910 + Δ119910
05 119911 + Δ119911
05)
RSSI (1198750) = RSSI (119875
1)
RSSI (1198752) = RSSI (119875
3)
RSSI (1198754) = RSSI (119875
5)
(7)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001 Δ11991101) rarr
11987521198753
= (Δ11990923 Δ11991023 Δ11991123)
rarr11987541198755
= (Δ11990945 Δ11991045 Δ11991145)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100 119911 + Δ119911
0119861minus 1199110)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100 119911 + Δ119911
0119862minus 1199110)
dArr
rarr119860119863
= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910
0119863minus 1199100 119911 + Δ119911
0119863minus 1199110)
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
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Active and Passive Electronic Components
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 3
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
middot middot middot
(a) (b)
RSSI(1198751) RSSI(1198751)
RSSI(1198750) RSSI(1198750)
RSSI(1198751000)
RSSI(119875999)RSSI(119875999)
RSSI(119875119894)[minmax]
11987201198720
11987211198721
119872119894
119872999 119872999
1198721000
Figure 2 The 1001th message stored by sensor
of ours is locating the mobile node with single stationaryanchor by comparing the measured RSSI values betweenthe locating sensor node with inertia module built-in andthe single anchor In this sense LSARSSI and ILSARSSI areactually range-free approaches
3 LSARSSI Algorithm
In this section we first describe the application model inSection 31 Section 32 presents the design of our localizationscheme in detail Section 33 further presents the localizationalgorithm in 3D space
31 Model Assumptions For better implementing our algo-rithm the hypotheses are as follows (1) an anchor and amobile node with inertial module whose trajectory is notdesignated (2) the environment is an obstacle-free outdoorarea (3) the communication is not continuous and thelocating node receives the RSSI at different time intervals(4) the RSSI values can be measured and the offsets can beobtained and stored by themobile node with inertial module
We can illustrate it by the following model assumptionThe coordinate of anchor 119860 is (119909
0 1199100 1199110) Assume that the
coordinate of initial location of the locating node 119873 is1198750(119909 119910 119911) 119875
119894(119894 isin [1 119899]) is a visited location of the mobile
node 119873 after time 119879 the relative offset of node 119873 among1198750and 119875
119894in the 119883 119884 and 119885 axis is Δ119909 Δ119910 and Δ119911 So the
coordinate of 119875119894is (119909 + Δ119909 119910 + Δ119910 119911 + Δ119911) as shown in
Figure 1Table 1 shows the messages obtained by the locating
node 119873 in different visited locations it contains offsets andRSSI values As the locating node needs to store the relativedistances between locations that it visited as well as the RSSIvalues between those locations to the anchor It may requirelarge memory storage for sensors The issue can be resolvedby the following method assume that sensor can store 1000messages of 119875
0to 119875999
and if the RSSI value of 119875119894is minimum
(or maximum) the message of 1198751000
will replace it as shownin Figure 2
As the communication is not continuous and the visitedlocations for our schemes needed are countable the compu-tation and communication costs are acceptable
Table 1 Messages stored by sensor
Locations Messages (node N)1198750
Δ119909 Δ119910 Δ119911 RSSI(1198750)
1198751
119909 + Δ11990901
119910 + Δ11991001
119911 + Δ11991101
RSSI(1198751)
119875119894
119909 + Δ1199090119894
119910 + Δ1199100119894
119911 + Δ1199110119894
RSSI(119875119894)
119875119899minus1
119909 + Δ1199090119899minus1
119910 + Δ1199100119899minus1
119911 + Δ1199110119899minus1
RSSI(119875119899minus1
)119875119899
119909 + Δ1199090119899
119910 + Δ1199100119899
119911 + Δ1199110119899
RSSI(119875119899)
32 Localization Algorithm Design Typically the ensemblemean received power in a real world obstructed channeldecays proportional to 119889
minus119899119901 where 119899119901
is the path-lossexponent [26] The ensemble mean power at distance 119889 istypically modeled as
[119901119903 (119889)]119889119861119898
= [119901119903(1198890)]119889119861119898
minus 10119899 log 119889
1198890
(1)
where 1198750is the received power (dBm) at short reference
distance 1198890
From (1) we know that ideally the longer the distancebetween sender and receiver the weaker the signal strengthdetected by the receiverThe localization schemewas inspiredby the perpendicular bisector of a chord conjecture [27]Withtwo chords of the same circle the intersection point of twoperpendicular bisectors of the chords will be the center of thecircleThe localization problem can be transformed based onthe conjecture The center of the circle is the position of theanchor the chord is a segment that is a connection of twopositions (the RSSI values of the two positions are equal) ofthe mobile node at a given moment The solution is detailedillustrated in Figure 3
Node 119860 is the anchor 119873 is the mobile locating node1198750 1198751 1198752 and 119875
3are the visited locations of locating node
119873 after the time period of 119894119905 119895119905 119896119905 119897119905 119861 119862 are the midpointsof segments 119875
01198751 11987521198753 and RSSI(119875
0) = RSSI(119875
1) RSSI(119875
2) =
RSSI(1198753)
4 International Journal of Distributed Sensor Networks
1198750
1198752
1198753
1198751
119860
119861
119862
Figure 3 An example of LSARSSI algorithm in 2D
The following are the formulas for calculating the locationof locating node
119860 = (1199090 1199100) 119875
0= (119909 119910)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02)
1198753= (119909 + Δ119909
03 119910 + Δ119910
03)
119861 = (119909 + Δ1199090119861 119910 + Δ119910
0119861)
119862 = (119909 + Δ1199090119862 119910 + Δ119910
0119862)
(2)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001) rarr
11987521198753
= (Δ11990923 Δ11991023)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100)
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090)
+ Δ11991001lowast (119910 + Δ119910
0119861minus 1199100) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090)
+ Δ11991023lowast (119910 + Δ119910
0119862minus 1199100) = 0
dArr
(1) Δ11990901lowast 119909 + Δ119910
01lowast 119910
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
(2) Δ11990923lowast 119909 + Δ119910
23lowast 119910
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
(3)
Assume that119886 = Δ119909
01lowast (1199090minus Δ1199090119861)
+ Δ11991001lowast (1199100minus Δ1199100119861)
119887 = Δ11990923lowast (1199090minus Δ1199090119862)
+ Δ11991023lowast (1199100minus Δ1199100119862)
(4)
then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886
(4) Δ11990923lowast 119909 + Δ119910
23lowast 119910 = 119887
dArr
119909 =1198631
119863 119910 =
1198632
119863
(5)
where
119863 =10038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11990923
Δ11991023
10038161003816100381610038161003816100381610038161003816 119863
1=10038161003816100381610038161003816100381610038161003816
119886 Δ11991001
119887 Δ11991023
10038161003816100381610038161003816100381610038161003816
1198632=10038161003816100381610038161003816100381610038161003816
Δ11990901
119886
Δ11990923
119887
10038161003816100381610038161003816100381610038161003816
(6)
33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect
The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875
0 1198751 119875119899 Their RSSI values
are RSSI(1198750)RSSI(119875
1) RSSI(119875
119899) locations can be divided
into a number of subsets 1198731 1198732 119873119898 based on RSSI val-
ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873
119886| = 2 and
|119873119887| = 2 and |119873
119888| = 2 (as shown in Figure 4(a)) (2) |119873
119886| = 3
and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873
119886| = 4 (as
shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take
|119873119886| = 2 |119873
119887| = 2 and |119873
119888| = 2 as an example to indicate
formulas for calculating the location of locating node119860 is theanchor119875
01198751119875211987531198754 and119875
5are the visited locations of the
mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and
11987541198755 And
119860 = (1199090 1199100 1199110)
1198750= (119909 119910 119911)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01 119911 + Δ119911
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02 119911 + Δ119911
02)
International Journal of Distributed Sensor Networks 5
119860
119861
119862119863
119884
119883
119885
1198755
1198751 1198752
1198753
1198750 1198754
(a)
119884
119883
119885
119860
1198751
1198752
11987531198754
1198750
(b)
119884
119883
119885
119860
1198752
1198753
1198751
1198750
(c)
Figure 4 Examples of LSARSSI algorithm in 3D
119884
119883
119860
119874
119861
119862
119863
119864
119875998400
1
1198711
11987121198713
1198714
119875998400
3
119875998400
2
119875998400
0
1198751
1198752
1198753
1198750
Figure 5 An example of ILSARSSI algorithm in 2D
1198753= (119909 + Δ119909
03 119910 + Δ119910
03 119911 + Δ119911
03)
1198754= (119909 + Δ119909
04 119910 + Δ119910
04 119911 + Δ119911
04)
1198755= (119909 + Δ119909
05 119910 + Δ119910
05 119911 + Δ119911
05)
RSSI (1198750) = RSSI (119875
1)
RSSI (1198752) = RSSI (119875
3)
RSSI (1198754) = RSSI (119875
5)
(7)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001 Δ11991101) rarr
11987521198753
= (Δ11990923 Δ11991023 Δ11991123)
rarr11987541198755
= (Δ11990945 Δ11991045 Δ11991145)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100 119911 + Δ119911
0119861minus 1199110)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100 119911 + Δ119911
0119862minus 1199110)
dArr
rarr119860119863
= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910
0119863minus 1199100 119911 + Δ119911
0119863minus 1199110)
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
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Submit your manuscripts athttpwwwhindawicom
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
4 International Journal of Distributed Sensor Networks
1198750
1198752
1198753
1198751
119860
119861
119862
Figure 3 An example of LSARSSI algorithm in 2D
The following are the formulas for calculating the locationof locating node
119860 = (1199090 1199100) 119875
0= (119909 119910)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02)
1198753= (119909 + Δ119909
03 119910 + Δ119910
03)
119861 = (119909 + Δ1199090119861 119910 + Δ119910
0119861)
119862 = (119909 + Δ1199090119862 119910 + Δ119910
0119862)
(2)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001) rarr
11987521198753
= (Δ11990923 Δ11991023)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100)
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090)
+ Δ11991001lowast (119910 + Δ119910
0119861minus 1199100) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090)
+ Δ11991023lowast (119910 + Δ119910
0119862minus 1199100) = 0
dArr
(1) Δ11990901lowast 119909 + Δ119910
01lowast 119910
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
(2) Δ11990923lowast 119909 + Δ119910
23lowast 119910
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
(3)
Assume that119886 = Δ119909
01lowast (1199090minus Δ1199090119861)
+ Δ11991001lowast (1199100minus Δ1199100119861)
119887 = Δ11990923lowast (1199090minus Δ1199090119862)
+ Δ11991023lowast (1199100minus Δ1199100119862)
(4)
then (1) (2) can be converted into(3) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 = 119886
(4) Δ11990923lowast 119909 + Δ119910
23lowast 119910 = 119887
dArr
119909 =1198631
119863 119910 =
1198632
119863
(5)
where
119863 =10038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11990923
Δ11991023
10038161003816100381610038161003816100381610038161003816 119863
1=10038161003816100381610038161003816100381610038161003816
119886 Δ11991001
119887 Δ11991023
10038161003816100381610038161003816100381610038161003816
1198632=10038161003816100381610038161003816100381610038161003816
Δ11990901
119886
Δ11990923
119887
10038161003816100381610038161003816100381610038161003816
(6)
33 Algorithm in 3D Here we extend our algorithm tothree-dimensional space As we know if there are threenoncoincident chords on the sphere the intersection of threemidvertical planes is the center of the sphere provided thatthese three planes can intersect
The general idea of this algorithm in 3D utilizes theprevious conjecture This problem can be described as fol-lows the locations of locating node 119873 at different timescompose a collection 119875 = 119875
0 1198751 119875119899 Their RSSI values
are RSSI(1198750)RSSI(119875
1) RSSI(119875
119899) locations can be divided
into a number of subsets 1198731 1198732 119873119898 based on RSSI val-
ues and the RSSI values in each subset are equal respectivelyAfter that given that one of the following conditions occursour LSARSSI algorithm can be achieved (1) |119873
119886| = 2 and
|119873119887| = 2 and |119873
119888| = 2 (as shown in Figure 4(a)) (2) |119873
119886| = 3
and |119873119887| = 2 (as shown in Figure 4(b)) (3) |119873
119886| = 4 (as
shown in Figure 4(c)) (119886 119887 119888 isin [1119898])As (2) and (3) are the special cases of (1) here we take
|119873119886| = 2 |119873
119887| = 2 and |119873
119888| = 2 as an example to indicate
formulas for calculating the location of locating node119860 is theanchor119875
01198751119875211987531198754 and119875
5are the visited locations of the
mobile node 119861 119862 and119863 are the midpoint of 11987501198751 11987521198753 and
11987541198755 And
119860 = (1199090 1199100 1199110)
1198750= (119909 119910 119911)
1198751= (119909 + Δ119909
01 119910 + Δ119910
01 119911 + Δ119911
01)
1198752= (119909 + Δ119909
02 119910 + Δ119910
02 119911 + Δ119911
02)
International Journal of Distributed Sensor Networks 5
119860
119861
119862119863
119884
119883
119885
1198755
1198751 1198752
1198753
1198750 1198754
(a)
119884
119883
119885
119860
1198751
1198752
11987531198754
1198750
(b)
119884
119883
119885
119860
1198752
1198753
1198751
1198750
(c)
Figure 4 Examples of LSARSSI algorithm in 3D
119884
119883
119860
119874
119861
119862
119863
119864
119875998400
1
1198711
11987121198713
1198714
119875998400
3
119875998400
2
119875998400
0
1198751
1198752
1198753
1198750
Figure 5 An example of ILSARSSI algorithm in 2D
1198753= (119909 + Δ119909
03 119910 + Δ119910
03 119911 + Δ119911
03)
1198754= (119909 + Δ119909
04 119910 + Δ119910
04 119911 + Δ119911
04)
1198755= (119909 + Δ119909
05 119910 + Δ119910
05 119911 + Δ119911
05)
RSSI (1198750) = RSSI (119875
1)
RSSI (1198752) = RSSI (119875
3)
RSSI (1198754) = RSSI (119875
5)
(7)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001 Δ11991101) rarr
11987521198753
= (Δ11990923 Δ11991023 Δ11991123)
rarr11987541198755
= (Δ11990945 Δ11991045 Δ11991145)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100 119911 + Δ119911
0119861minus 1199110)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100 119911 + Δ119911
0119862minus 1199110)
dArr
rarr119860119863
= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910
0119863minus 1199100 119911 + Δ119911
0119863minus 1199110)
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
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Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 5
119860
119861
119862119863
119884
119883
119885
1198755
1198751 1198752
1198753
1198750 1198754
(a)
119884
119883
119885
119860
1198751
1198752
11987531198754
1198750
(b)
119884
119883
119885
119860
1198752
1198753
1198751
1198750
(c)
Figure 4 Examples of LSARSSI algorithm in 3D
119884
119883
119860
119874
119861
119862
119863
119864
119875998400
1
1198711
11987121198713
1198714
119875998400
3
119875998400
2
119875998400
0
1198751
1198752
1198753
1198750
Figure 5 An example of ILSARSSI algorithm in 2D
1198753= (119909 + Δ119909
03 119910 + Δ119910
03 119911 + Δ119911
03)
1198754= (119909 + Δ119909
04 119910 + Δ119910
04 119911 + Δ119911
04)
1198755= (119909 + Δ119909
05 119910 + Δ119910
05 119911 + Δ119911
05)
RSSI (1198750) = RSSI (119875
1)
RSSI (1198752) = RSSI (119875
3)
RSSI (1198754) = RSSI (119875
5)
(7)
According to the geometry of vector we can obtain that
rarr11987501198751
= (Δ11990901 Δ11991001 Δ11991101) rarr
11987521198753
= (Δ11990923 Δ11991023 Δ11991123)
rarr11987541198755
= (Δ11990945 Δ11991045 Δ11991145)
rarr119860119861
= (119909 + Δ1199090119861minus 1199090 119910 + Δ119910
0119861minus 1199100 119911 + Δ119911
0119861minus 1199110)
rarr119860119862
= (119909 + Δ1199090119862minus 1199090 119910 + Δ119910
0119862minus 1199100 119911 + Δ119911
0119862minus 1199110)
dArr
rarr119860119863
= (119909 + Δ1199090119863minus 1199090 119910 + Δ119910
0119863minus 1199100 119911 + Δ119911
0119863minus 1199110)
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 International Journal of Distributed Sensor Networks
Anchor
Locating mobile node
Trajectory
500 lowast 500m2
Figure 6 A trajectory of the locating mobile node
rarr11987501198751
sdot rarr119860119861
= Δ11990901lowast (119909 + Δ119909
0119861minus 1199090) + Δ119910
01lowast (119910 + Δ119910
0119861minus 1199100)
+ Δ11991101lowast (119911 + Δ119911
0119861minus 1199110) = 0
rarr11987521198753
sdot rarr119860119862
= Δ11990923lowast (119909 + Δ119909
0119862minus 1199090) + Δ119910
23lowast (119910 + Δ119910
0119862minus 1199100)
+ Δ11991123lowast (119911 + Δ119911
0119862minus 1199110) = 0
dArr
rarr11987541198755
sdot rarr119860119863
= Δ11990945lowast (119909 + Δ119909
0119863minus 1199090) + Δ119910
45lowast (119910 + Δ119910
0119863minus 1199100)
+ Δ11991145lowast (119911 + Δ119911
0119863minus 1199110) = 0
(1) Δ11990901 lowast 119909 + Δ11991001 lowast 119910 + Δ11991101 lowast 119911
= Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
(2) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911
= Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
12001000800400 6002000
minus95
minus100
minus105
minus110
minus115
minus120
Time (s)
RSSI
(dBm
)
Figure 7 RSSI values received by locating node after time 119879
(3) Δ11990945 lowast 119909 + Δ11991045 lowast 119910 + Δ11991145 lowast 119911
= Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(8)
Assume that
119886 = Δ11990901lowast (1199090minus Δ1199090119861) + Δ119910
01lowast (1199100minus Δ1199100119861)
+ Δ11991101lowast (1199110minus Δ1199110119861)
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
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Active and Passive Electronic Components
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 7
300
250
200
150
100
50
01 2 3 4 5
Transmission period (s)
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
(a) Impact of packet transmission period
250
200
150
100
50
0
Num
ber o
f loc
atio
ns
LSARSSIILSARSSI
Average LSARSSI numbersAverage ILSARSSI numbers
100 lowast 100 400 lowast 400300 lowast 300 500 lowast 500200 lowast 200
Size of sensor field (m2)
(b) Impact of size of sensor field
Figure 8 Number of locations of LSARSSI and ILSARSSI algorithms
119887 = Δ11990923lowast (1199090minus Δ1199090119862) + Δ119910
23lowast (1199100minus Δ1199100119862)
+ Δ11991123lowast (1199110minus Δ1199110119862)
119888 = Δ11990945lowast (1199090minus Δ1199090119863) + Δ119910
45lowast (1199100minus Δ1199100119863)
+ Δ11991145lowast (1199110minus Δ1199110119863)
(9)
then (1) (2) and (3) can be converted into
(4) Δ11990901lowast 119909 + Δ119910
01lowast 119910 + Δ119911
01lowast 119911 = 119886
(5) Δ11990923 lowast 119909 + Δ11991023 lowast 119910 + Δ11991123 lowast 119911 = 119887
(6) Δ11990945lowast 119909 + Δ119910
45lowast 119910 + Δ119911
45lowast 119911 = 119888
dArr
119909 =1198631
119863 119910 =
1198632
119863 119911 =
1198633
119863
(10)
where
119863 =
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
Δ11991101
Δ11990923
Δ11991023
Δ11991123
Δ11990945
Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198631=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
119886 Δ11991001
Δ11991101
119887 Δ11991023
Δ11991123
119888 Δ11991045
Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198632=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
119886 Δ11991101
Δ11990923
119887 Δ11991123
Δ11990945
119888 Δ11991145
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1198633=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
Δ11990901
Δ11991001
119886
Δ11990923
Δ11991023
119887
Δ11990945
Δ11991045
119888
100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(11)
4 Improved Algorithm ILSARSSI
In real scenarios the measure of the RSS is discontinuousit may be difficult to obtain several groups of locations withthe same RSSI values So the algorithm proposed previously
cannot be successfully used to locate However the locatingnode can be located by comparing the RSSI according to thesignal attenuation model [26]
Figure 5 demonstrates an example of the improved algo-rithm ILSARSSI The RSSI values of node 119873 measuredin 1198750 11987510158400 1198751 11987510158401 1198752 11987510158402 1198753 11987510158403are RSSI(119875
0) RSSI(1198751015840
0)
RSSI(1198751) RSSI(1198751015840
1) RSSI(119875
2) RSSI(1198751015840
2) RSSI(119875
3) RSSI(1198751015840
3)
and RSSI(1198750) lt RSSI(1198751015840
0) RSSI(119875
1) gt RSSI(1198751015840
1) RSSI(119875
2) gt
RSSI(11987510158402) RSSI(119875
3) gt RSSI(1198751015840
3) The anchor is in the enclosed
region BCDE of four perpendicular bisectors of the segment119875011987510158400 119875111987510158401 119875211987510158402 119875311987510158403 After finding a sufficient number of
locations that meet such condictions we can further narrowthe area where the anchor node is We take the centroid ofthe enclosed area as the position of the anchor and then thecoordinates of visited locations can be obtained
The following are the formulas for calculating the locationof locating node
119860 (1199090 1199100) 119875
0= (1199091 1199101) 119875
1015840
0= (1199091015840
1 1199101015840
1)
1198751= (1199092 1199102) 119875
1015840
1= (1199091015840
2 1199101015840
2)
1198752= (1199093 1199103) 119875
1015840
2= (1199091015840
3 1199101015840
3)
1198753= (1199094 1199104) 119875
1015840
3= (1199091015840
4 1199101015840
4)
(12)
As 1198711 1198712 1198713 and 119871
4are the perpendicular bisector of
119875011987510158400 119875111987510158401 119875211987510158402 and 119875
311987510158403 according to the geometry of
vector we can obtain that1198711 (1199091minus 1199091015840
1) lowast 119909 + (119910
1minus 1199101015840
1) lowast 119910
= (1199091+ 11990910158401
2) lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1)
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
8 International Journal of Distributed Sensor Networks
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
Transmission period (s)
(a) Impact of packet transmission period
0
2
4
6
8
10
12
14
16
LSARSSI algorithmSsursquos algorithmBT algorithm
Aver
age l
ocal
izat
ion
erro
r (m
)
400 lowast 400300 lowast 300 500 lowast 500
Size of sensor field (m2)
100 lowast 100 200 lowast 200
(b) Impact of size of sensor field
Figure 9 Localization error of our LSARSSI algorithm
1198712 (1199092minus 1199091015840
2) lowast 119909 + (119910
2minus 1199101015840
2) lowast 119910
= (1199092+ 11990910158402
2) lowast (119909
2minus 1199091015840
2) + (
1199102+ 11991010158402
2) lowast (119910
2minus 1199101015840
2)
1198713 (1199093minus 1199091015840
3) lowast 119909 + (119910
3minus 1199101015840
3) lowast 119910
= (1199093+ 11990910158403
2) lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2) lowast (119910
3minus 1199101015840
3)
1198714 (1199094minus 1199091015840
4) lowast 119909 + (119910
4minus 1199101015840
4) lowast 119910
= (1199094+ 11990910158404
2) lowast (119909
4minus 1199091015840
4) + (
1199104+ 11991010158404
2) lowast (119910
4minus 1199101015840
4)
As 1198711cap 1198714= 119861 119871
3cap 1198714= 119862
1198712cap 1198713= 119863 119871
1cap 1198712= 119864
dArr
(13)
119909119861=
100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 1199091015840
1
2)lowast(1199091minus 1199091015840
1) + (
1199101+ 1199101015840
1
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2) lowast (119910
4minus 1199101015840
4) 1199104minus 1199101015840
4
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119909119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
(
1199093+ 1199091015840
3
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 1199101015840
3
2) lowast (119910
3minus 1199101015840
3) 1199103minus 1199101015840
3
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119909119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
(
1199091+ 11990910158401
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 11991010158401
2) lowast (119910
1minus 1199101015840
1) 1199101minus 1199101015840
1
(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2) lowast (119910
2minus 1199101015840
2) 1199102minus 1199101015840
2
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
119910119861=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 9
119910119862=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199094minus 1199091015840
4(
1199094+ 1199091015840
4
2)lowast (119909
4minus 1199091015840
4) + (
1199104+ 1199101015840
4
2)lowast (119910
4minus 1199101015840
4)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199094minus 1199091015840
41199104minus 1199101015840
4
10038161003816100381610038161003816100381610038161003816
119910119863=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1199093minus 1199091015840
3(
1199093+ 11990910158403
2)lowast (119909
3minus 1199091015840
3) + (
1199103+ 11991010158403
2)lowast (119910
3minus 1199101015840
3)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199092minus 1199091015840
21199102minus 1199101015840
2
1199093minus 1199091015840
31199103minus 1199101015840
3
10038161003816100381610038161003816100381610038161003816
119910119864=
10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
1(
1199091+ 1199091015840
1
2)lowast (119909
1minus 1199091015840
1) + (
1199101+ 1199101015840
1
2)lowast (119910
1minus 1199101015840
1)
1199092minus 1199091015840
2(
1199092+ 1199091015840
2
2)lowast (119909
2minus 1199091015840
2) + (
1199102+ 1199101015840
2
2)lowast (119910
2minus 1199101015840
2)
1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816
1199091minus 1199091015840
11199101minus 1199101015840
1
1199092minus 1199091015840
21199102minus 1199101015840
2
10038161003816100381610038161003816100381610038161003816
dArr
1199090=119909119861+ 119909119888+ 119909119863+ 119909119864
4
1199100=119910119861+ 119910119888+ 119910119863+ 119910119864
4
(14)
The approach can also be applied to the localizationof mobile node in three-dimensional space The simulationresults show that ILSARSSI performs high feasibility andpracticality
5 Simulation Results
To evaluate the performance of our proposed approaches weuseMATLAB70 to conduct the simulations In the followingthe simulation parameters are listed in Table 2 We assumethat the trajectory of the mobile locating node is random(Figure 6 is a trajectory of the locating node) the packettransmission period among anchor andmobile locating nodeis in a certain time interval (1 s 2 s 3 s 4 s and 5 s) theaverage moving speed of the locating node is 2ms and thesize of sensor field is in an obstacle-free area of 100 lowast 100m2200 lowast 200m2 300 lowast 300m2 400 lowast 400m2 and 500 lowast 500m2Figure 7 plots the RSSI values received by locating node alongthe trajectory shown in Figure 6
In the first section we mainly validate the feasibility ofLSARSSI and LSARSSI algorithm and in the second sectionwe discuss the localization error of LSARSSI and ILSARSSIalgorithms
Table 2 Simulation parameters
Parameters Value(s)Packet transmission period (s) 1 2 3 4 5Moving speed (ms) 2
Size of sensor field (m2) 100 lowast 100 200 lowast 200 300 lowast 300400 lowast 400 500 lowast 500
51 Number of Locations Simulations Figure 8 compares thenumber of locations of LSARSSI algorithm and ILSARSSIalgorithm The average number of locations of ILSARSSI ismuch fewer than LSARSSI algorithm which demonstratesthat the ILSARSSI algorithm performs high feasibility
(1) Number of Locations versus Packet Transmission PeriodThe packet transmission period is the time interval oftransmitting message among the anchor and locating nodeFigure 8(a) indicates that the number of locations ofILSARSSI algorithm decreases with increasing the packettransmission period The average numbers of locations ofILSARSSI algorithm and ILSARSSI algorithm are approxi-mately 240 and 55 at different transmission period respec-tively
(2) Number of Locations versus Size of Sensor Field The sizeof sensor field is the moving range of the locating nodeFigure 8(b) shows that the number of locations of ILSARSSIalgorithm increases with expanding the size of sensor field
52 Average Localization Error Simulations
(1) Average Localization Error versus Packet TransmissionPeriod Figure 9 compares average localization error for Ssursquos[28] BT [29] and our algorithm Figure 9(a) shows that thelocalization accuracy for both Ssursquos and BT algorithms canbe improved by reducing the packet transmission periodHowever our LSARSSI algorithm performs higher accuracywith increasing packet transmission periodwhich can reducethe communication cost and energy consumption If packettransmission period is 5 s the average localization error ofSsursquos and BT is approximately 15m but our algorithm is lessthan 3m
(2) Average Localization Error versus Size of Sensor FieldFigure 9(b) shows the impact of moving range on the local-ization error as the size of sensor field expands from 100 lowast
100m2 to 500 lowast 500m2 The increased size of sensor fieldmakes the Ssursquos and BT algorithms less accurate but ourlocalization error remains within 5m
(3) Average Localization Error of LSARSSI and ILSARSSIFigure 10 demonstrates the localization error of ILSARSSIalgorithm depends on the locating time With increasingthe locating time the locating accuracy becomes more andmore precise That is because the possible location falls intoa smaller enclosed region However the estimated errorof LSARSSI algorithm varies slightly with the increase oflocating time
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 International Journal of Distributed Sensor Networks
60
50
40
30
20
10
0200 300 400 500 600 700 800 900 1000
Aver
age l
ocal
izat
ion
erro
r (m
)
LSARSSI algorithmILSARSSI algorithm
Time (s)
Figure 10 Average localization error of LSARSSI and ILSARSSI
6 Conclusions
In this paper we propose a localization algorithm namedLSARSSI for mobile node with single anchor by aid ofinertia module The simulation results demonstrate that ourLSARSSI algorithm outperforms than other range-free local-ization mechanisms for example Ssursquos and BT algorithmsAs the number of locations needed is approximately 200 wefurther proposed an improved algorithm named ILSARSSIILSARSSI utilize the signal attenuation model to narrow theregion of the anchor and finally we regard the centroid of theenclosed region as its physical position The average numberof locations of ILSARSSI algorithm is much fewer whichperforms high feasibility Our scheme uses only one location-known anchor which is useful in low density environmentwithout using additional hardware Because our algorithmsare adapted to the obstacle-free outdoor scenario our futurework will focus on indoor environment
Acknowledgment
This work was supported by the National Natural Sci-ence Funds (Grant no 60970129) the Public Science andTechnology Research Funds Project of Ocean (Grant no201105033) and the Localization Algorithms of UnderwaterSensor Networks Research Funds (Grant no 61170258)
References
[1] I F Akyildiz W Su Y Sankarasubramaniam and E Cayirci ldquoAsurvey on sensor networksrdquo IEEE Communications Magazinevol 40 no 8 pp 102ndash114 2002
[2] A Youssef A Agrawala and M Younis ldquoAccurate anchor-freenode localization in wireless sensor networksrdquo in 24th IEEEInternational Performance Computing and CommunicationsConference (IPCCC rsquo05) pp 465ndash470 April 2005
[3] F Dellaert D Fox W Burgard and S Thrun ldquoMonte Carlolocalization for mobile robotsrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo99) pp 1322ndash1328 Detroit Mich USA May 1999
[4] N Bulusu D Estrin L Girod and J Heidemann ldquoScalablecoordination for wireless sensor networks self-configuringlocalization systemsrdquo in International Symposium on Commu-nication Theory and Applications (ISCTA rsquo01) Ambleside UKJuly 2001
[5] N Bulusu J Heidemann D Estrin and T Tran ldquoSelf-configuring localization systems design and experimental eva-lutionrdquo ACM Transactions on Embedded Computing Systems(TECS) vol 3 pp 24ndash60 2004
[6] A Iqbal Increasing Localization Precision in Sensor Networkswith Mobile BeaconsmdashA Genetic path planning ApproachResearch Commons Library 2009
[7] T V Srinath A K Katti and V S Ananthanarayna ldquoAnalysisof mobile beacon aided in-range localization scheme in ad hocwireless sensor networksrdquo in International Wireless Communi-cations and Mobile Computing Conference (IWCMC rsquo06) pp1159ndash1164 July 2006
[8] K Kim and W Lee ldquoMBAL a mobile beacon-assisted local-ization scheme for wireless sensor networksrdquo in 16th Interna-tional Conference on Computer Communications and Networks(ICCCN rsquo07) pp 57ndash62 August 2007
[9] G Zhongwen G Ying H Feng et al ldquoPerpendicular inter-section locating wireless sensors with mobile beaconrdquo in Real-Time Systems Symposium (RTSS rsquo08) pp 93ndash102 December2008
[10] M L Sichitiu and V Ramadurai ldquoLocalization of wirelesssensor networks with a mobile beaconrdquo in IEEE InternationalConference on Mobile Ad-Hoc and Sensor Systems pp 174ndash183Fort Lauderdale Fla USA October 2004
[11] L Hu and D Evans ldquoLocalization for mobile sensor networksrdquoin Proceedings of the Tenth Annual International Conference onMobile Computing and Networking (MobiCom rsquo04) pp 45ndash57New York NY USA October 2004
[12] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in 19th IEEE AnnualJoint Conference of the IEEE Computer and CommunicationsSocieties (INFOCOM rsquo00) pp 775ndash784 Tel Aviv Israel March2000
[13] A Savvides C C Han and M B Strivastava ldquoDynamic fine-grained localization in ad-hoc networks of sensorsrdquo in 7thAnnual International Conference on Mobile Computing andNetworking pp 166ndash179 New York NY USA July 2001
[14] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in 22nd IEEE Annual Joint Conference on theComputer and Communications Societies(INFOCOM rsquo03) pp1734ndash1743 April 2003
[15] J Hightower R Want and G Borriello SpotON An Indoor3-D Location Sensing Technology Based on RF Signal StrengthUniversity of Washington Seattle Wash USA 2000
[16] T S RappaportWireless Communications Principles and Prac-tice Prentice-Hall Englewood Cliffs NJ USA 1999
[17] G Zhou T He S Krishnamurthy and J A Stankovic ldquoModelsand solutions for radio irregularity in wireless sensor networksrdquoACMTransactions on Sensor Networks vol 2 no 2 pp 221ndash2622006
[18] N Bulusu J Heidemann and D Estrin ldquoGPS-less low-costoutdoor localization for very small devicesrdquo IEEE PersonalCommunications vol 7 no 5 pp 28ndash34 2000
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 11
[19] T He C Huang B M Blum J A Stankovic and T Abdelza-her ldquoRange-free localization schemes for large scale sensornetworksrdquo in Proceedings of the Ninth Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo03) pp 81ndash95 New York NY USA September 2003
[20] C Liu K Wu and T He ldquoSensor localization with ringoverlapping based on comparison of received signal strengthindicatorrdquo in IEEE International Conference on Mobile Ad-Hocand Sensor Systems pp 516ndash518 October 2004
[21] N B Priyantha H Balakrishnan E D Demaine and S TellerldquoMobile-assisted localization in wireless sensor networksrdquo inIEEE Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo05) pp 172ndash183 March2005
[22] P Bergamo and G Mazzini ldquoLocalization in sensor networkswith fading andmobilityrdquo in 13th IEEE International Symposiumon Personal Indoor andMobile Radio Communications (PIMRCrsquo02) pp 750ndash754 September 2002
[23] LMihaylova D Angelova D Bull andN Canagarajah ldquoLocal-ization of mobile nodes in wireless networks with correlated intimemeasurement noiserdquoMobile Computing vol 10 pp 44ndash532011
[24] H Miura K Hirana N Matsuda H Taki N Abe and SHori ldquoIndoor localization for mobile node based on RSSIrdquoin Knowledge-Based Intelligent Information and EngineeringSystems vol 4694 of Lecture Notes in Computer Science pp1065ndash1072 Springer Berlin Germany 2007
[25] M Bertinato G Ortolan F Maran et al ldquoRF Localizationand tracking of mobile nodes in wireless sensorsnetworks architectures algorithms and experimentrdquoTech Rep University of Padova Padua Italy 2008httppaduaresearchcabunipdit1046
[26] D B Faria ldquoModeling signal attenuation in IEEE 820 11 wirelessLANS-Vol 1 Kiwi Projectrdquo Tech Rep TR-KP06-0118 StanfordUniversity Stanford Calif USA 2005
[27] H R Jacobs Geometry Freeman San Francisco Calif USA1987
[28] Y Ganggang Y Fengqi and F Lei ldquoA three dimensionallocalization algorithm using a mobile anchor node underwireless channelrdquo in International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 477ndash483 Neural Networks June2008
[29] P Chen Z Zhong andTHe ldquoBubble tracemobile target track-ing under insufficient anchor coveragerdquo in 31st InternationalConference on Distributed Computing Systems (ICDCS rsquo11) pp770ndash779 June 2011
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
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