anchor node path planning for localization in wireless...
TRANSCRIPT
Anchor node path planning for localization in wireless sensornetworks
Ketan Sabale1 • S. Mini1
Published online: 10 June 2017
� Springer Science+Business Media, LLC 2017
Abstract Localization is one of the most important chal-
lenges of wireless sensor networks because the location
information is typically used in other domains such as
coverage, deployment, routing, and target tracking. There
exist some localization algorithms that facilitate the sensor
nodes to locate itself using the mobile anchor node posi-
tion. Some crucial attempts have been made in the past for
optimizing the mobile anchor node trajectory with good
accuracy. This paper presents a novel path planning
scheme, D-connect, which ensures the localization of all
the sensor nodes with minimum trajectory length. The
performance of the proposed scheme is evaluated through a
series of simulations. Experimental results reveal that the
shortest path for traversing the whole area can be traced
with the minimum localization error using this method. It
also shows that D-connect outperforms the existing meth-
ods in terms of the anchor node trajectory length as well as
the localization error.
Keywords Sensor network � Localization � Anchor node �Path planning mechanisms
1 Introduction
Wireless sensor networks (WSNs) are composed of large
collection of sensors that may be randomly deployed in a
certain geographical region. The sensor nodes collect
environmental data and forward that data to a remote
device where the data is analyzed and processed. If the
sensors cannot pass the information to the remote device
directly, some intermediate nodes have to forward the data
[8]. Sensor networks have a wide range of application areas
such as home, environment monitoring, military surveil-
lance, animal tracking, etc. WSNs can be used in the dis-
aster relief services where human operations are difficult.
Increased accuracy and minimizing time for location esti-
mation are the important factors to be considered in
emergency services. Sensor nodes have limited power
resources, computational power, and memory availability
[1]. Coverage, deployment, tracking and localization are
some challenges in WSNs. Since the location information
is used in other domains, it is necessary to determine the
origin of the information, prior to any information pro-
cessing. Localization can be defined as estimating the exact
physical location of the sensor node in a certain geo-
graphical area. Sensors can be located with the help of the
Global Positioning System (GPS). Due to the high cost and
poor performance of GPS indoors, it becomes inefficient to
equip all sensor nodes with GPS [3]. There have been some
localization algorithms that were proposed in the past, and
are still being used to locate unknown sensors. The clas-
sification of localization algorithms along several axes is
presented in Fig. 1.
In centralized algorithms, the sensor nodes send their
data to the central processing unit where the data is ana-
lyzed and processed to extract the positional information.
The approach in which each sensor node can locate itself is
& S. Mini
Ketan Sabale
1 Department of Computer Science and Engineering, National
Institute of Technology Goa, Farmagudi, Goa, India
123
Wireless Netw (2019) 25:49–61
https://doi.org/10.1007/s11276-017-1538-6
known as distributed localization. The main advantages of
the centralized approach is accuracy, precision and the
ability to process greater amounts of data. The disadvan-
tages of these algorithms are poor scalability and a single
point of failure. The distributed algorithms do not require a
central base station. In the distributed localization
approach, localization is done through node-to-node com-
munication. Localization which is carried out with the help
of signal properties is known as Range-based localization
[13]. The common techniques used in range-based local-
ization are Angle of Arrival (AOA), Time of Arrival
(TOA), Time Difference of Arrival (TDOA) and Received
Signal Strength Indicator (RSSI). These localization algo-
rithms are based on time and distance dependent mea-
surements. In the Angle of Arrival (AOA) method, the
location is estimated with the help of the angle at which a
signal arrives at a sensor. Distance information is obtained
in the Time of Arrival (TOA) and Time Difference of
Arrival (TDOA) methods by computing the transmission
time of the wireless signal. These approaches give better
location accuracy but use extra hardware. Received Signal
Strength Indicator (RSSI) is a measurement of the power
present in a received signal. There is no requirement of
extra hardware for estimating the distance using RSSI
technique. Estimated distance travelled by the signal up to
the receiver point is calculated with effective path loss.
Range-free techniques do not need extra hardware but
localization depends on the connectivity of the network.
Localization based on range-free techniques in which the
anchor node moves along a hexagonal pattern is discussed
in [18]. Cost-effective ways of localization with less
accuracy are provided by range-free techniques. The
methods in which a sensor node can locate itself by using
the location information of some specific nodes is known
as Anchor-based approach. The position of Anchor nodes
is predefined or can be located with the help of GPS. An
anchor node is also referred to as a Beacon or a Reference
node. Anchor-free localization does not depend on the
anchor nodes. In this approach, each node computes the
relative coordinates by measuring the distance to its
neighboring nodes by using either range-free or range-
based techniques.
Usually WSN is used in remote geographical areas
where human operations are impossible. It is infeasible to
deploy beacons at known positions. So beacon nodes must
be equipped with GPS receivers. Cost effective WSN is
dependent on the minimum number of anchor nodes used.
So the motivation behind designing the D-connect trajec-
tory is to locate all the sensor nodes with the help of a
single beacon node. The beacon node broadcasts its loca-
tion information while travelling in the region of interest.
Beacons do not broadcast constantly. Advertising Interval
describes the time between each broadcast. Stability of the
signal depends on the Advertising Interval. The signal is
more stable for shorter intervals. It is very beneficial to use
such anchor nodes for localization. The fundamental issue
is to find an optimum path for a mobile beacon trajectory in
the region of interest. Before defining any path planning
mechanism, certain properties of optimum path planning
mechanisms should be investigated. Due to the poorly
designed trajectory, some sensor nodes may not be
localized.
The existing anchor node trajectories are different from
one another in the pattern they follow. The Mobile Anchor
Centroid Localization [8] traverses the region along a spiral
path. Due to the spiral nature of the path taken by the
anchor node, sensor nodes present in the corner of the
network do not get sufficient number of beacon positions,
which leads to an increase in the localization error. [9]
presents the Hilbert curve approach that solves the local-
ization and coverage problems. In this approach the
unknown sensor estimates its position by using h keys.
Scan and Double Scan [11] minimizes the anchor node
trajectory length but increases the localization time as the
Fig. 1 Classification of
localization algorithms
50 Wireless Netw (2019) 25:49–61
123
sensor has to wait for non collinear positions for location
estimation. The Z-curve [10] follows the path in a Z pattern
while LMAT [12] follows an equilateral triangle pattern.
All these trajectories differ in terms of construction and
work, but all try to achieve the same goal. To the best of
our knowledge, no literature provides a sufficient and
optimal trajectory to solve the problems of localization and
coverage.
In this paper, we propose a path planning scheme,
D-connect, for anchor-based localization using a range-
based technique. It guarantees the localization of all
unknown sensor nodes from a certain geographical region
with minimized localization error. It uses two signals with
two different transmitted signal powers which are required
to increase the accuracy while taking care of the
collinearity issue. For maximum accuracy, the anchor node
has to travel near the boundary of the region. In D-connect,
the increased power of the signal resolves this problem. For
locating any unknown sensor accurately, at least three non-
collinear beacon signals are required. If the sensor node
receives more than three beacon node positions, at least
one non-collinear position is required to eliminate any
collinear beacon.
The rest of the paper is organized as follows: Sect. 2
summarizes the related work on different existing local-
ization algorithms and path planning mechanisms with
more clarity. Section 3 defines the problem and describes
the D-connect method. The experimental results are
reported and discussed in Sect. 4. Sect. 5 concludes the
paper.
2 Related work
There have been several research efforts on tackling
problems related to localization in WSN. The various
hierarchical architectures of WSN are presented in [2].
Most existing localization schemes for WSNs are mainly
classified into two groups, computation based and range
based. A detailed classification is provided in [3]. Dis-
tributed computation based methods are discussed in [4, 5]
and [6]. The Monte-Carlo Localization algorithm is pre-
sented in [4]. The Monte-Carlo algorithm estimates the
position of an unknown sensor by considering the near and
the farther anchor node constraints. At first, the sensor node
constructs a possible location set which denotes the pos-
sible location of the sensor. In the filtering phase the
locations which are not satisfying the anchor node con-
straints are removed and the average of the remaining
location set gives the final estimated location of the
unknown node. The efforts for increasing the efficiency of
the Monte-Carlo algorithm are done in [5]. Drawing sam-
ples is a time consuming process, so Monte-Carlo
Localization Boxed algorithm constrains the area from
which the sensor draws samples. This method is known as
Monte-Carlo Localization Boxed (MCB) algorithm. The
increased accuracy and reduced localization time can be
obtained by using relay nodes. Self Localization
Scheme using relay nodes and anchor nodes is presented in
[6]. Relay nodes are also sensor nodes which get their
positional information from the anchor node. Sensor nodes
calculate their position by the received information about
the relay node position. The various conditions for relay
node selection are discussed in [6].
The efficiency of anchor based localization algorithms is
dependent on the trajectory of the anchor node. For
defining any new beacon node trajectory certain conditions
must be satisfied by the trajectory. First of all, trajectory
should pass closely to the unknown sensor for best position
estimation. Also each sensor node should have at least
three non-collinear anchor node positions to locate itself.
[7] illustrates the conditions that are to be satisfied by the
anchor node trajectory. The various schemes to reduce the
trajectory length of the anchor node are discussed in [8–11]
and [12]. [8] presents the trajectory in a spiral form. The
position estimation of sensor nodes is done with the help of
the range-free localization technique called Centroid
algorithm. The position of each sensor is calculated by
taking the average of the total received beacon messages in
the time interval t. The length of the Spiral trajectory is
more than all other trajectories. The localization algorithm
that uses the Spiral trajectory is known as the Mobile
Anchor Centroid Localization (MACL). The trajectory
based on the Hilbert space filling curve is presented in [9].
The Hilbert space filling curve is a one-dimensional curve,
which visits every point exactly once without crossing
itself within a two or three-dimensional space. The Hilbert
curve is generated recursively. A superior path planning
mechanism called Z-curve is explained in [10]. Z-curve
handles the collinearity issue occurring in the anchor node
trajectory by using the determinant of the matrix that
contains consecutive beacon positions received by the
sensor node. The received beacon positions are said to be
non-collinear if the determinant of the matrix is non-zero.
The Z-curve trajectory is tested for an obstacle presence
scenario. Scan and Double Scan methods are explained in
[11]. The Scan method has the disadvantage of collinearity.
In the Scan method, the mobile beacon node travels along
one dimension and when it reaches the end of the network
it travels along the second dimension where the length of
the path along the second dimension is equal to the reso-
lution. The procedure is repeated till the entire network is
traversed. The Double Scan method traverses the network
along both directions. The collinearity problem of the Scan
method is resolved by the Double Scan strategy up to some
extent. But the length of the Double Scan trajectory is
Wireless Netw (2019) 25:49–61 51
123
double, compared to the Scan mehod for the same reso-
lution. The Hilbert curve method overcomes the disad-
vantages of the Scan and Double Scan methods. Since the
Hilbert curve trajectory takes more turns, it gives better
position estimation compared to the Scan and Double Scan
trajectories. As Hilbert curve connects the centers of two
successive cells in the network, it will never move along
the border of the deployment area. This is a drawback of
the Hilbert curve method. Localization with a Mobile
Anchor node based on Trilateration (LMAT) is presented
in [12]. In LMAT trajectory, an anchor node moves along
the boundaries of the region based on an equilateral tri-
angle pattern.
After designing the optimum trajectory for an anchor
node, the next main task is to estimate the physical position
of the unknown sensor nodes using anchor node positions.
For estimating the position of an unknown node various
range-free and range-based methods can be used. The
range-free and range-based techniques are discussed in
[13]. The cost effective method in range-based localization
algorithm called RSSI is presented in detail in [14] and
[15]. Distance estimation using RSSI is dependent on path
loss. Various propagation models for mobile communica-
tion are discussed in [16]. Path loss and fading are the main
characteristics of the radio channel. The RSSI calculations
are basically influenced by path loss and fading. Free space
model, Two ray ground model and Log-normal shadowing
model are the RSSI propagation models used in wireless
sensor networks. When the transmitter and receiver have a
clear unobstructed line of sight between them, the free
space propagation model is used [16]. The Two ray ground
model is considered only when there exists a single direct
path between the transmitter and the receiver for the
propagation of the radio signal. The directed path and a
ground reflected propagation between the transmitter and
the receiver is considered in two ray propagation model.
The Log-normal shadowing model is the most suitable ra-
dio propagation model as it provides a number of param-
eters for configuration for different environments (indoor
and outdoor). This study mainly focuses on the develop-
ment of optimal anchor node trajectory for localization of
unknown sensors using the Log normal shadowing model.
3 Proposed work
3.1 Problem statement
Given a geographic region R, and a single anchor node A to
locate m sensor nodes S ¼ fS1; S2; S3; :::; Smg, the objectiveis to identify the minimum length trajectory for anchor
node A, such that all unknown sensor nodes are located
with minimum localization error.
If the mobile anchor node A, is at position ðx1; y1Þ andthe sensor node Si, ð1� i�mÞ is at location ðx2; y2Þ then A
can locate sensor Si iff sensor node Si lies within the
communication range r of A. That is,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðx1 � x2Þ2 þ ðy1 � y2Þ2q
� r ð1Þ
where r is the communication range of anchor node A.
Let (X, Y) and ðxi; yiÞ represent the estimated and orig-
inal coordinates of sensor Si, respectively. Then the
localization error is calculated by,
ErrorSi ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðX � xiÞ2 þ ðY � yiÞ2q
ð2Þ
The average localization error for all unknown sensors is
calculated by,
Erroraverage ¼X
n
i¼1
ErrorSim
ð3Þ
where m denotes the total number of unknown sensors
deployed throughout the region.
3.2 Mobile beacon node trajectory
The proposed strategy, D-connect, assumes that the anchor
node can transmit different signals with different power
from predefined points to overcome the collinear beacon
problem and creates an optimum path for traversing the
region in order to reduce the localization time. As D-con-
nect trajectory is deterministic and the anchor node posi-
tions for message transmission are already known, the
anchor node can send the signal with more power from
some fixed positions.
The basic curve of the trajectory is shown in Fig. 2. The
region is divided into sub-squares based on the level. The
concept of level is used in such a way that for level n, the
region is divided into 4n sub-squares. The mobile anchor
connects the centres of the sub-squares such that it will
form D-connect trajectory. The centres of the sub-squares
are c1; c2; c3. The sub-squares are named as Sq1, Sq2 and
Sq3 respectively. The level 3 and 4 are illustrated in Figs. 3
and 4 respectively. The resolution of a trajectory is equal to
the length of the side of each sub-square. The resolution is
given by l=2n, where l is the length of the geographical
region. The D-connect anchor node trajectory construction
is divided into 3 phases:
– Phase 1: Localizability relation
– Phase 2: Communication range definition
– Phase 3: Non-collinearity checking
Localizability Relation phase mainly focuses on deriv-
ing the relation for locating unknown sensors with the help
of anchor node positions. Communication Range phase
52 Wireless Netw (2019) 25:49–61
123
defines the communication ranges for different anchor
node positions. For estimating the sensor node position, at
least three non-collinear anchor node positions are
required. The obtained positions are checked for
collinearity in Non-Collinearity Checking phase.
– Localizability relation All unknown sensors are
localizable only if:
8siði¼1;::::;nÞ9fajðj ¼ 1; 2; 3Þjðdistðaj; siÞ� r1ÞVðdistðaj; siÞ� r2g
where si denotes unknown sensors and aj denotes the
anchor node messages which have been transmitted
from three different positions. r1 and r2 are communi-
cation ranges from two different positions. distðaj; siÞ
Fig. 2 D-connect travelling
mechanism
Fig. 3 D-connect travelling
mechanism
Fig. 4 D-connect travelling
mechanism
Wireless Netw (2019) 25:49–61 53
123
indicates the distance between the unknown sensor and
the anchor node position.
– Communication range definition To locate any
unknown sensor, the first requirement is that the
unknown sensor should receive an anchor node posi-
tion. The unknown sensor can receive a beacon position
only if it is within the communication range of the
beacon node. The communication range of the beacon
node should be adjusted in such a way that all unknown
sensors are covered. Each sub-square has resolution
d. To obtain three beacon node positions, it is required
that the unknown sensor should receive the beacon
node position from the same square or from adjacent
sub-squares whichever is nearer.
The sub-squares with centres at distance d from the con-
sidered sub-square are called adjacent sub-squares. For
example, c7 and c8 in Fig. 5 are the centres of adjacent sub-
squares.
This phase defines the communication range for differ-
ent anchor positions. In Fig. 5, let s1 denote the most dis-
tant sensor from c3 which is the centroid of the neighbor
sub-square. If s1 receives beacon message from c3 then s1can receive beacon messages from all adjacent sub-squares.
According to the Pythagoras theorem, in Fig. 5,
r21 ¼ ðd2Þ2 þ ð3d
2Þ2
r1 ¼ffiffiffi
5
2
r
d:
ð4Þ
c14
c2
c4 c
6
c5
c7
c8
c9
c10
c11
c12
c1
c3
d/2s1
3d/2
r1
r2
d
2d
s2
c13
Fig. 5 Communication range definition for an anchor node
r1 is the distance between c3 and s1. From this we can say
that the unknown sensor can receive the beacon position
from an adjacent sub-square centroid only if r1 �ffiffi
52
q
d.
Sometimes the beacon positions from adjacent sub-
squares are not sufficient. To receive three beacon mes-
sages and also to complete D-connect trajectory, we need
the third beacon position from another sub-square, other
than the same sub-square and the neighboring one. Let s2be the most distant sensor from c4 which is not in the
neighboring sub-square. If s2 receives beacon message
from c4 then s2 can receive beacon messages from sub-
squares other than adjacent sub-squares. Applying
Pythagoras theorem as shown in Fig. 5,
r22 ¼ðdÞ2 þ ð2dÞ2
r2 ¼ffiffiffi
5p
d:ð5Þ
r2 is the distance between c4 and s2. From this we can say
that an unknown sensor can receive a beacon position from
a sub-square other than the adjacent sub-squares only if
r2 �ffiffiffi
5p
d. The anchor node positions with communication
range r2 are fixed as the movement and beacon positions
for message transmission are already known and the
D-connect trajectory is deterministic.
The transmitted signal power is varied as a function of
distance. The transmitted signal power for the points using
r2 communication range increases as the ratio r1 to r2increases. Thus, the transmitted signal power for the
communication range r2 is 1.41 times transmitted signal
54 Wireless Netw (2019) 25:49–61
123
power of the communication range r1. The communication
range depends on the resolution d.
– Non-Collinearity Checking As shown in Fig. 5, any
unknown sensor can use the beacon message from the
intersection of sub-squares eg. c2; c4; :::. After receiving
three beacon messages collinearity condition should be
checked to eliminate the third collinear point. The three
coordinates are collinear if they lie on the same line.
Let MAT represent a matrix formed by the coordinates of
the three received beacons ðxc1 ; yc1Þ,ðxc2 ; yc2Þ,ðxc3 ; yc3Þ frompositions c1; c2 and c3.
MAT ¼ xc2 � xc1 yc2 � yc1xc3 � xc1 yc3 � yc1
� �
ð6Þ
The three received beacons are non-collinear, when
jMAT j ¼ ðxc2 � xc1Þðyc3 � yc1Þ � ðyc2 � yc1Þðxc3 � xc1Þ 6¼ 0
ð7Þ
where jMAT j represents the determinant of matrix MAT.
The total length of the trajectory is determined by
adding the length of the segments connecting the non
adjacent sub-square centres (c1 and c2 in Fig. 5) and the
length of segments connecting the adjacent sub-square
centres (c7 and c8 in Fig. 5). The total number of segments
connecting the non-adjacent sub-squares in one-side
traversing from c1 to c7 is ð2n � 1Þ. The total number of
such one-sided traversals in the whole region is ð2n�1Þ. Thelength of an individual segment connecting two non-adja-
cent sub-squares is ðffiffiffi
2p
� dÞ. The total number of seg-
ments joining adjacent sub-squares having length equal to
resolution (d) is ð2n�1 � 1Þ.Therefore the total length of the D-connect trajectory is
given by,
DD�connect ¼ ð2n � 1Þð2n�1 �ffiffiffi
2p
� dÞ þ ðð2n�1 � 1Þ � dÞð8Þ
where DD�connect represents the total length travelled by the
D-connect strategy for level n and resolution d.
3.3 Location estimation
After receiving three non-collinear beacon positions, the
location estimation is to be done using the RSSI technique.
In a realistic channel model like log normal shadowing, the
RSSI value at a distance d from the transmitter is given by
[15],
RSSIðdÞ ¼ PTrans � PLðd0Þ � 10g log10d
d0þ Xr ð9Þ
where PTrans is the transmission power of the signal at the
source, PLðd0Þ is the path loss at a reference distance (i.e.
d0), and g is the path loss exponent. The value of the path
loss exponent increases with obstructions in the environ-
ment. The path loss exponent value lies between 2 and 6.
The random variation in RSSI is modeled as a Gaussian
random variable Xr ¼ Nð0; r2Þ. The values of g and r can
be set depending on the propagation environment.
Table 1 lists path loss exponents for various mobile
radio environments. The value for shadowing deviation rdBis different for different environment. It ranges from 4 to
12 for outdoors. For every unknown sensor, after getting
sufficient distances between unknown sensor and beacon
positions, the triangulation method is used to obtain the
possible location for the unknown sensor.
In Fig. 6, let s be the unknown sensor to be localized.
a1; a2 and a3 are the three non-collinear anchor node
positions. Let d1; d2; d3 denote the euclidean distances
between anchor node positions a1; a2 and a3 and the sensor
node. ðx1; y1Þ; ðx2; y2Þ; ðx3; y3Þ are the known anchor node
positions. The possible coordinates for sensor s can be
obtained by [6],
X ¼ ðy2 � y1Þc� ðy3 � y2Þe2ððx2 � x1Þðy3 � y2Þ � ðx3 � x2Þðy2 � y1ÞÞ
Y ¼ ðx2 � x1Þc� ðx3 � x2Þe2ððx3 � x2Þðy2 � y1Þ � ðx2 � x1Þðy3 � y2ÞÞ
Table 1 Path loss exponents for different environments [17]
Environment Path loss exponent(g)
Free space 2
Urban area cellular radio 2.7–3.5
Shadowed urban cellular radio 3–5
In building line-of-sight 1.6–1.8
Obstructed in building 4–6
Obstructed in factories 2–3
Fig. 6 Localization of a sensor node using triangulation
Wireless Netw (2019) 25:49–61 55
123
where c ¼ ðx22 � x23 þ y22 � y23 � d22 þ d23Þ and
e ¼ ðx21 � x22 þ y21 � y22 � d21 þ d22ÞLet (X, Y) and ðxi; yiÞ represent the estimated and orig-
inal coordinates of sensor Si, respectively. Based on the
calculated position, the localization error is calculated by
(2). The average localization error for all unknown sensors
is calculated by (3).
4 Results and discussion
The performance of the proposed trajectory was evalu-
ated by a series of simulations using MATLAB. The
parameters are listed in Table 2. We consider a 100 m�100
m grid for experimentation. The number of sensors to be
localized are 100 with the help of a single anchor node. The
communication range of the anchor node varies with
respect to resolution (d). The resolution depends on the
level (n). For experimental results for all trajectories except
D-connect the communication range is set to r ¼ffiffi
52
q
d.
This communication range varies with resolution. D-con-
nect uses two communication ranges r1 and r2 from
equation 4 and equation 5 respectively. The transmitted
signal power for r2 is 1.41 times r1 as the transmitted signal
power is a function of distance. Other trajectories have
transmission power equal to the transmitted signal power
for r1. Path loss exponent is taken as 3.3 for shadowed
urban cellular radio network. The standard deviation for
noise is taken from 2 to 8. Path loss PLðd0Þ at a reference
distance 1 meter is considered as 55 dB. Results are
reported as an average of 50 different instances.
The length of geographical region is considered as 100
m. The communication range depends on the resolution
and level. The resolution corresponding to specified level is
shown in Tables 3 and 4. The results for trajectory length
have been evaluated for each level. The trajectory length
for an anchor node in LMAT, SPIRAL algorithms are
calculated respectively as [12]
DLMAT ¼ 2ffiffiffi
3p � L� dL
re þ ðLþ
ffiffiffi
3p
rÞ ð10Þ
DSpiral ¼X
dLre
t¼1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r2 þ 4r2p2t2 þ 4r2t sin 4ptp
ð11Þ
where r is the communication range and L is the length of
the geographical region.
The Scan trajectory consists of ðLd� 1Þ segments of
length L parallel to the x axis and ðLd� 1Þ segments of
length d parallel to the y axis as shown in Fig. 7.
The trajectory length for the Scan algorithm is given by,
DScan ¼L
d� 1
� �
� Lþ L
d� 1
� �
� d ð12Þ
DScan ¼L
d� 1
� �
� ðLþ dÞ ð13Þ
Basically the Double Scan trajectory doubles the dis-
tance travelled by the Scan trajectory. The Double Scan
trajectory is presented in Fig. 8. The total length for
Double Scan trajectory is given by,
DDoubleScan ¼ 2L
d� 1
� �
� ðLþ dÞ� �
þ T ð14Þ
where T is the turn taken by the anchor node when it
completes one Scan trajectory. In this case T ¼ffiffiffi
2p
� d4.
A hybrid localization approach explained in [9] uses the
Hilbert curve mechanism for the anchor node trajectory as
shown in Fig. 9. In the Hilbert curve method, the region is
divided into 4n square cells. The anchor node connects the
Table 2 Simulations parameters
Parameter Value
Network size 100 m�100 m
Unknown sensors 100
Beacon nodes 1
Path loss exponent(g) 3.3
Standard deviation 2,4,6,8
PLðd0Þ 55 dB
d0 1 m
Transmission power -28–14.1 dBm
Simulation runs 50
Table 3 Trajectory length comparison for 100 m � 100 m region
Level (n) Res.(d) LMAT Spiral Scan D-connect
2 25 514.8 1495.9 375 237.1
3 12.5 827 2611.7 787.5 532.4
4 6.25 1387.3 4100.4 1593.8 1104.4
5 3.12 2533.4 7161.5 3196.9 2238.9
6 1.56 4838.5 13345 6398.4 4503.2
Table 4 Trajectory length comparison for 100 m � 100 m region
Level (n) Res. (d) Double scan Hilbert Z-curve D-connect
2 25 758.8 375 437.1 237.1
3 12.5 1579.4 787.5 911.7 532.4
4 6.25 3189.7 1593.8 1842.3 1104.4
5 3.12 6394.9 3196.9 3693.9 2238.9
6 1.56 12797 6398.4 7392.6 4503.2
56 Wireless Netw (2019) 25:49–61
123
centres of these cells by using ð4n � 1Þ lines of length
equal to the resolution d. The travelling length of the
Hilbert trajectory is given by,
DHilbert ¼ ð4n � 1Þ � d ð15Þ
The total distance travelled by the anchor node using Z-
curve trajectory is given by [10],
DZ�curve ¼ dð58� 4nÞ � 1ed þ bð3
8� 4nÞc
ffiffiffi
2p
d ð16Þ
Table 3 shows the path length comparison for LMAT,
Spiral, Scan and D-connect strategies. Table 4 compares
the path length for Double Scan, Hilbert, Z-curve and
D-connect strategies. From Tables 3 and 4, we deduce that
when the level is 2, resolution i.e. the length of the sub-
square will be 25 m. At this resolution, the path length
travelled by an anchor node using LMAT strategy is 514.8
m whereas the Spiral strategy takes 1495.9 m to complete
the trajectory. Although the Scan method gives better
results as compared to the Spiral and LMAT methods, it
still suffers from the collinearity problem for high resolu-
tion. It gives three collinear beacon points for localization.
The Double Scan strategy resolves the collinearity problem
faced by the Scan method but it also increases the path
length. The Hilbert and Z-curve methods take 375 and
437.13 m to complete their trajectories respectively.
However, they also take more path length as compared to
the D-connect trajectory.
As the level increases, the resolution decreases. At level
3, resolution will be 12.5 m. The path length taken by the
D-connect method is still less compared to all other
strategies. Small resolutions result in more path length
which is unacceptable for a 100 m� 100 m area. The Spiral
trajectory length is always more than any other trajectory.
The results over other methods show the efficiency of
D-connect in terms of the trajectory length.
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100Fig. 7 Scan travelling
mechanism
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100Fig. 8 Double scan travelling
mechanism
Wireless Netw (2019) 25:49–61 57
123
In a real time environment, the resolution for a grid is
considered by the power of a transmitted signal. For high
resolution, transmission power should be more.
Given a 100 m�100 m region, with small resolution, if
the trajectory length exceeds 2000 m then it will not be an
efficient trajectory. As we have power constraints, it is
always a good choice to keep resolution high with respect
to the power of the transmitted signal. While traversing the
region, the beacon node periodically transmits a position
message packet with its coordinates. In Scan, Double Scan
and Hilbert strategies, an unknown sensor node receives
three message packets that are transmitted from three dif-
ferent beacon positions and using those positions, the
unknown sensor node calculates the position using the
centroid method. We estimate the position of the unknown
sensor in the D-connect method using the RSSI technique.
Figure 10 represents the comparison of the localization
error for the Scan, Double Scan, Hilbert, Z-curve and
D-connect strategies. The localization error depends on the
environment and reliable wireless communication devices.
In a real time environment, various multipath fading fac-
tors cause large random signal variations. We have done
simulations to calculate the localization error for the
communication range 4.93–39.53 m for regular anchor
node positions. At the same time, the communication range
for special anchor node positions varies from 6.98 m to
55.90 m.
Figure 10 shows the localization error for different
strategies for standard deviation 2. The average localiza-
tion error produced by the D-connect trajectory after 50
simulation runs for level 2 is equal to 0.8315 m. The
localization error decreases as the level increases. Similarly
when the resolution of the grid is 12.5 m, the localization
error produced by the D-connect method is 0.3307 m. The
localization error produced by the D-connect strategy is
0.0698 m when the resolution is small (d\5 m). The
localization errors for Scan, Double Scan and Hilbert tra-
jectories are more than the D-connect trajectory error for
level 2. They are 9.16, 6.7157 and 9.15 m respectively. For
Z-curve, the error is less than D-connect and all other
trajectories but the length of the Z-curve trajectory is more
than the D-connect trajectory length. Z-curve gives 0.4256
m error for level 2 and gives 0.0430 m for level 5. The
difference between the errors produced by D-connect and
Z-curve decreases as the communication range increases.
Figure 11 presents the localization error comparison for
standard deviation 4. For r ¼ 4, the error produced by
D-connect is still less than Scan, Double Scan and Hilbert
trajectories. When standard deviation of noise is equal to 4,
the localization error for D-connect trajectory is 0.6738 m
and error for Scan, Double Scan and Hilbert trajectories are
3.6264, 2.9025 and 3.6377 m respectively. The error for
Scan, Double Scan and Hilbert strategies decreases as the
level increases. The Scan, Double Scan and Hilbert
strategies have collinearity problem. For large resolution an
unknown sensor may get collinear beacon node positions
for location estimation. The value of localization error
increases if the sensor gets collinear beacon positions. The
collinearity issue is handled by increasing the level and
decreasing the communication range. When the commu-
nication range is less, the sensor may get non-collinear
beacon positions as it may receive more number of beacon
node positions.
If any of the unknown sensors get the collinear beacon
positions for location estimation, it affects the average
localization error. The performance of the Scan, Double
Scan and Z-curve increases with reduction in communi-
cation range. D-connect and Z-curve methods resolve the
problem of collinearity before position estimation. Because
of the collinearity checking done by D-connect and
Z-curve trajectories, the performance of these trajectories
is always better than the others. The trajectories considered
for evaluation performs better for small resolution than for
large resolution.
Figure 12 gives the comparison for localization error
when r ¼ 8. The performance of Scan, Double Scan,
Hilbert strategies does not depend on the standard devia-
tion of noise. These trajectories estimate the position of an
unknown sensor by taking the average of the three received
beacon positions. Techniques which use RSSI calculations
for position estimation depend on the noise produced in the
environment. The accuracy of the position estimation
depends on the quality of the signal. The quality of the
signal degrades as noise in the environment increases. The
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
Fig. 9 Hilbert travelling mechanism
58 Wireless Netw (2019) 25:49–61
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performance of D-connect decreases for standard deviation
of noise equal to 8. For communication range 39.53 m, D-
connect produces 3.3336 m error which is greater than the
error produced for small values of r for the same com-
munication range. With the same conditions Z-curve pro-
duces 1.7272 m error while Scan, Double Scan and Hilbert
trajectories gives 9.3990, 6.7174, 9.3924 m respectively. If
we increase the level, the communication range decreases.
This increases the performance of all trajectories. For level
3 with communication range 19.76 m, the errors produced
by D-connect, Scan, Double Scan, Hilbert and Z-curve
methods are 1.2947, 3.6095, 2.8867, 3.6043 and 0.7779 m
respectively. The Z-curve gives better performance in
terms of minimum localization error as compared to
D-connect and all other trajectories, but the length it takes
for completing the trajectory is 911.7 m which is almost
380 m more than that taken by the D-connect method. The
error produced by the following D-connect trajectory is
about 0.50 m more than the Z-curve trajectory, but the
length of trajectory decreases by about 380 m.
Fig. 10 Level versus
localization error (r ¼ 2)
Fig. 11 Level versus
localization error (r ¼ 4)
Wireless Netw (2019) 25:49–61 59
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D-connect trajectory is susceptible to noise like other
methods. However it consistently gives better results in
terms of localization error. Figures 10, 11 and 12 show that
D-connect performs more efficiently than all other methods
in terms of length and localization error.
A relay node can be used to propagate beacon node
positions to sensors for minimizing the trajectory length.
But D-connect achieves the same goal by varying the
transmitted signal power. Simulations are done for regular
regions that can be divided in the grid. It is necessary to
partition the region in equal parts to fix the communication
range. For irregular regions, results may differ based on
how the regions can be divided. Thus, it is challenging to
adjust the power in irregular regions with multipath,
obstacles, etc.
5 Conclusion and future work
This paper presented D-connect, a strategy that gives three
non-collinear beacon node positions for the location esti-
mation of an unknown sensor while maintaining the
shortest trajectory. This paper also provides some existing
approaches for localization that are applied to WSN. The
proposed D-connect strategy is compared with other
existing strategies. The results show that D-connect out-
performs LMAT, Spiral, Scan, Double Scan, Hilbert and
Z-curve methods in terms of the length of its trajectory.
D-connect gives better results for localization error as
compared to the Scan, Double Scan and Hilbert trajecto-
ries. The results confirm that the D-connect trajectory is
efficient in terms of length of trajectory and localization
error. D-connect follows a different approach by varying
the power of the transmitted signal and ensures that the
sensor node will receive sufficient number of beacon
positions for location estimation. D-connect also solves the
coverage problem by providing beacon information to each
and every sensor which leads to the localization of all
sensors. We plan to test the D-connect strategy on networks
with sensors in the presence of obstacles and multipaths to
study real-time performance. We also plan to improve the
energy efficiency of the scheme by designing efficient
power transmission schemes in the future.
Acknowledgements The authors would like to thank Dr. Ankit
Dubey, Assistant Professor, Department of Electronics and Commu-
nication Engineering, National Institute of Technology Goa, India for
his valuable and constructive suggestions during the development of
this research work.
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Ketan Sabale received the B.E.
degree in Computer Engineer-
ing from University of Pune,
Maharashtra, India, in 2012 and
the M.Tech. Degree in Com-
puter Science and Engineering
from National Institute of
Technology, Goa, in 2016. He is
currently pursuing the Ph.D.
degree with the Department of
Computer Science and Engi-
neering, National Institute of
Technology, Goa. His research
interests include wireless sensor
networks, mobile ad hoc net-
works, and swarm intelligence.
S. Mini received the master’s
degree in Computer and Com-
munication from Anna Univer-
sity, Chennai, India, and the
Ph.D. degree in Computer Sci-
ence from University of Hyder-
abad. She is currently an
Assistant Professor in the
Department of Computer Sci-
ence and Engineering, National
Institute of Technology, Goa.
She is the principal investigator
of a project sanctioned under the
Early Career Research Award
Scheme of Science and Engi-
neering Research Board, Department of Science and Technology,
Government of India. Her research interests include wireless sensor
networks, internet of things, swarm intelligence, and combinatorial
optimization.
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