An Ellipse-Centroid Localization Algorithm in Wireless Sensor Networks

Abstract—In recent years, there has been a growing interest in wireless sensor networks(WSNs) applications. Localization in wireless sensor networks gets more and more important. Weighted centroid localization provides a fast and easy algorithm to locate devices in WSNs.The algorithm is derived from a centroid determination which calculates the position of devices by averaging the coordinates of neighbour anchors. After analyzing the radio propagation route loss model, the most appropriate Log-distance distribution model is selected to simulate the propagation of RSSI signals. Based on the centroid algorithm and the weighted centroid algorithm, an ellipse-centroid localization algorithm is proposed in this paper. The algorithm using the features of the ellipse to estimate the unknown node’s coordinate. The main idea of the ellipse-centroid algorithm is the defining of the precision control factor(PCF), which can control the algorithm’s localization precision. In the ellipse-centroid algorithm, the located nodes are promoted to be anchors in order to enhance the anchor density dynamicly. The simulation results demonstrate that the ellipse-centroid algorithm is more efficient in precision than the centroid algorithm and weighted centroid algorithm.

Keywords- WSN; centroid localization; weighted centroid localization; ellipse-centroid localizaiton; PCF

I. INTRODUCTION Advances in micro-electro-mechanical systems have

triggered an enormous interest in wireless sensor networks (WSNs)[1].WSNs are formed by large numbers of densely deployed nodes enabled with sensing and actuating capabilities , limited energy resources and it is envisioned that they will be mass produced. Recently, such network has been applied in various applications such as military, agriculture, and transportation for many purposes, including object detection, eventtracking, environmental monitoring, transportation management,[1-4] etc. These applications primarily rely on the geographic information of sensor nodes to identify the position of the tracking object, to assist in delivering packets to the fields of interest, and to provide sensor deployment for mitigating coverage overlap.[5]

Recently, many localization algorithms for wireless sensor networks have been proposed to provide per-node location information[6].With regard to the mechanisms used for estimating location, we divide these localization protocols into two categories: range-based localization[7] and range-free localization[7].The former is defined by protocols that use absolute point-to-point distance estimates(range) or angle estimates for calculating location,it is include: TOA[8], TDOA[9],AOA[10] and RSSI[11].The latter makes no assumption

about the availability or validity of such information, it is include: Centroid[12], MDS[13], APIT[14], AHLos[15] and Euclidean[16] Dv-Hop[17]. Besides, the features of adhoc, robust, high-efficiency and distributed computing is required in the WSNs’ localization algorithm.

In this paper, we proposed an ellipse-centroid localization algorithm which is based on the weighted centroid localization algorithm. In the ellipse-centroid localization algorithm, a precision control factor PCF is firstly setted, then, some of the unknown nodes are located by the ellipse localization algorithm, then, the remained unknown nodes are located by the weighted centroid localization which is based on RSSI measurement. To validate the new proposed algorithm’s efficiency, several simulation experiments are implemented, and the simulation results demonstrated that the ellipse-centroid algorithm is more efficient in precise than the classical centroid localization algorithm and the weighted centroid algorithm.

II. ALGORITHM DESCRIPTION[18]

A. Radio propagation route loss model analysis Radio propagation route loss has a big influnce on the

accuracy of RSSI measurement. There are some common propagation route loss models which are include: Free space propagation model, Log-distance path loss model, Hata model, and Log-distance distribution model, ect. The wireless sensor nodes are always scattered in the open air, so the Free space propagation model or the Log-distance distribution model is selected to simulate the process of the radio propagation. The free space propagation route loss model is below:

10 1032.44 10 log ( ) 10 log ( )Loss k d k f= + × × + × × ( 1)

In the formula (1), ‘d’ is the distance between the target and the source, ‘f’ is the frequency of the RSSI signal, ‘k’ is the route loss factor.

Because of the around surroundings, there are some errors exist in radio propagation route loss model, the errors are influnced by environment factors, such as, height, plant, transmitting power, packaging, ect. So the Log-distance distribution model is more efficient than the free space propagation model. The Log-distance distribution model is listed below:

0 00

( )[ ] ( ) 10 log( )dPL d dB PL d k Xd

= + × × + ( 2)

LI Jie1,LI Zhi2*, WANG Qing2, ZHAO Hu2,SONG Jun-de1 1.School of Electronics Engineering Beijing University of Post and Telecommunications ,Beijing,China 2.School of Electronics and Information Engineering, Si Chuan University,Cheng Du,China

dr.elitelee@gmail.com

*correspond author

978-1-4244-3693-4/09/$25.00 ©2009 IEEE

In the formula (2), PL(d)[dB] is the propagation loss after passed ‘d’ meters, X0 is a gauss random variable which average value is 0.Based on the above formula, the signal intensity that is received by the unknown node is:

( )SEND ANTRSSI P G PL d= + − ( 3)

In the formula (3), PSEND is the transmitting power, GANT is the gain of the antenna, PL(d) is the route loss.

B. Centroid Localization The classical centroid localization algorithm is proposed

by N.Bulusu and J.Heidemann, the unknown nodes are located by their neighbour anchors which are sending signals that contained their own coordinate（Xi,Yi）,the centroid calculation formula is below :

( ) 1 2 1 2, ,N Nest est

x x x y y yX YN N

+ + + + + +⎛ ⎞= ⎜ ⎟⎝ ⎠

… … ( 4)

to improve the algorithm, an advanced algorithm is proposed to increase the localization precision, it is called weighted centroid localization.

C. Weighted centroid localization The RSSI measure errors will be increased when the

distance of the two nodes increase. To diminish the localization errors, a new concept ‘weighted’ is introduced here. The weighted centroid localization algorithm is described below.

Figure 1 weighted centroid localization

In the figure 1, A,B,C are three anchors, D is an unknown node, and the RSSI signals that are sended by node A,B,C can be received by node D, the distance d1,d2,d3, between node D and the three anchors A,B,C can be calculated. Supposing D’ is the centroid of the triangle ABC, the D’ ’s coordinate can be calculated, and the distance d1’,d2’,d3’ between node D’ and the three anchors A,B,C can also be calculated. Finally, the weighted centroid localization algorithm deduced the unknown node D’s coordinate as :

( ) 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 1 2 2 3 3 1 1 2 2 3 3

' / ' / ' / ' / ' / ' /, ,'/ '/ '/ '/ '/ '/

d X d d X d d X d d Y d d Y d d Y dX Yd d d d d d d d d d d d

+ + + +⎛ ⎞= ⎜ ⎟+ + + +⎝ ⎠ ( 5)

d1’/d1，d2’/d2，d3’/d3 are the ‘weighted’ of the three anchors: A,B,C.

D. Ellipse Localization Algorithm In the figure 2, P1,P2 are two anchors in wireless sensor

networks, node P is an unknown node, the length of PP1 and PP2 are measured as a and b. Thus, node P is located at the ellipse which focus are P1,P2 ,and the fixed length is a+b. We

make a plumb line from the point P to the line P1P2 , and intersect P1P2 in P’. The ellipse localization algorithm take the P’’s coordinate as the unknown node P’s coordinate. The position error is PP’.

From the figure 2, we can see that, the more close of the P1PP2 to 180°, the higher localization precision will be

gained by the ellipse localization algorithm. To enhance the precision of the ellipse localization, a maximum error should be setted. In the figure 3, the maximum error can not be exceeded the length of the minor semi-axis.

Figure 2 ellipse localization principle

In the figure 3, the maximum error of the ellipse localization is the length of OA.

Figure 3 maximum error

The ellipse’s minor semi-axis is the maximum error of the ellipse localization algorithm, different precisions will be get by different ellipses. So a precision control factor PCF should be proposed to control the precision of the ellipse localization algorithm, and we defined it as:

1 2

a bPCFP P

+= ( 6)

From the formula (6), the PCF is sure to equal 1 or exceed 1,and the more close of the PCF to 1, the higher localization precision will be gained by the algorithm.

Assume the largest effective measure length of RSSI is L, so the biggest P1P2 in wireless sensor networks is 2L.If the maximum error is E, we can know the length of OA is E. In the figure 4, the PCF can be calculated.

In the figure 4, the length of P1P2 is 2L, the length of OA is E. Since the angle of AOP1 is 90°, so the length of AP1 is:

2 21AP E L= + ( 7)

∠

Figure 4 calculation of PCF

It is obvious that the length of AP1 is the half length of a+b, so the PCF can be calculated by the formula (8):

1APPCFL

= ( 8)

E. Ellipse-Centroid Localization Algorithm The ellipse-centroid localization algorithm is the

combination of the ellipse localization and the weighted centroid localization. In the ellipse-centroid localization algorithm, some of the unknown nodes are located by the ellipse localization algorithm, then, the located nodes are promoted to be anchors which can increase the density of anchors in the wireless sensor networks. Finally, the rest of unknown nodes are located by the weighted centroid localization algorithm.

III. SIMULATIONS To approve the efficiency of the ellipse-centroid

algorithm, a series of simulation experiments are practised. We also made several contrast experiments between the ellipse-centroid algorithm and the centroid algorithm, weighted centroid algorithm. The position error is defined as:

100%e aL L

PositionR−

= × er r or ( 9)

The notation Le is the node’s estimated distances, the notation La is the node’s real distances, and the notation R represent the node’s communication radius.

A. Comparison Simulations The three algorithms, centroid, weighted centroid, and

ellipse-centroid are abbreviated as C, WC, and EC. Assume that all the nodes scattered even in the wireless sensor networks, and the PCF is setted as 1.1.The figure 5 shows the comparison simulation results when the density of anchor is 5%.As the density of anchor rise to 10%,the similar simulation result is showed in the figure 6.

The figure 5 and 6 shows that the ellipse-centroid algorithm is more efficient in precision than the centroid algorithm and weighted centroid algorithm. The three algorithms’ localization precision are relevant to the density of anchor in the networks. With the density of anchor rising, the position error of the three algorithms are all decreasing, but the ellipse-centroid algorithm gained the least position errors. So it is obvious that the ellipse-centroid algorithm is the best algorithm in the three algorithms.

Figure 5 comparison simulation results when

the density of anchor is 5%

Figure 6 comparison simulation results when

the density of anchor is 10%

B. Different PCF Simulations In the previous chapter, we have narrated that the PCF

takes an important role in the ellipse-centroid algorithm. To validate the importance of the PCF, several simulations are put into practise, the simulation results are showed in figure 7 and figure 8.The figure 7 shows the comparison of different PCF simulations when the density of anchor is 5%.As the density of anchor rise to 10%,the similar simulation result is showed in figure 8.

Figure 7 different PCF comparison simulation

results when the density of anchor is 5%

Figure 8 different PCF comparison simulation

results when the density of anchor is 10% Compare the figure 7 and 8, we can see that the position

error is influnced by the density of anchor in the networks too. The ellipse-centroid algorithm will get higher accuracy with the density of anchor in the networks increase.

IV. CONCLUSIONS AND FUTURE WORK A new distributed localization algorithm ellipse-centroid,

based on the briefly describing the centroid and weighted centroid algorithm, is proposed in this paper. The model of Log-distance distribution model is selected to simulate the propagation of RSSI signals after analyzing the radio propagation route loss model. The ellipse-centroid algorithm set the precision control factor PCF, combine all the anchors with the rules of two anchors for one group, and locate the unknown nodes which accord with the precision control conditions. The located nodes are promoted to be anchors. Thus, all the anchors are used by the weighted centroid algorithm to locate the rest of the unknown nodes. Finally, all the unknown nodes in wireless sensor networks are located.

At the same time, some disadvantages are exist in the ellipse-centroid algorithm, it consumes more power than the centroid algorithm and weighted centroid algorithm. The ellipse-centroid algorithm is based on the ellipse localization algorithm, as the density of anchor in the networks few, huge position errors will be get by the ellipse-centroid algorithm. The main idea of the ellipse-centroid algorithm is PCF, so the PCF setting method needs to be improved in the future work. Furthermore, the implementation of ellipse-centroid algorithm in the uneven environment is also a future work waiting for us.

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