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Path Planning Based Localization for Wireless
Sensor Network
Shivangi Kanungo1
Department of Computer Science & Engineering,, National Institute of Technology,, Hamirpur, Himachal Pradesh
location of the sensor is node is very necessary because
by this we know that the data is from which node. By the
use of GPS or manual methods the location was
distributed.Location information of these nodes are identified previously.It is very difficult for installation of of
not even with them .There comes many
eacha Nd every network.The use of GPS for this tast is
very expensive in terms of money and energy. GPS don't
situations when we need to have node's location
work well with indoor systems and underwater systems.
information to make effective use of the
Sensor nodes are of very low battery powers and using
data received.With unknown locations anchor nodes GPS ACN reduce the efficiency and life duration of nodes
are used to localise the unknown paths
drastically. To overcome the above two mentioned
drawbacks we introduce localisation algorithm.
by moving on a path in network. Localisation
accuracy and network cost is also improved
Sensor nodes in wireless sensor networks
(WSN) are randomly
when anchor nodes are used. To broadcast and
move it's location information. Paths that
are fixed are called as trajectories.The prime aim is
to create a trajectory with minimal errors
and to identify efficiently the nodes that are
Using Trilateration and mobile anchor nodes in this
paper we have proposed a localisation
Keywords: Wireless Sensor Network (WSN),
Localization, Sensor Node, Mobile Anchor Node,
Path Planning, Trilateration, Trajectory;
Localisation algorithm is basically classified into many
types. Anchor nodes are sometimes used to do
localisation,these are nodes which have location
information. Localisation is classified into range based
and range free Algorithms. In range free Algorithm
connectivity and hop counts are used to calculate
distance between network nodes.some examples of
Distance Vector-Hop (DV-Hop), Centroid, Amorphous etc.
range-based localization algorithm, preinstalled extra
devicesare used to calculate the unknown distance
between the nodesby getting the signal strength, angle of
arrival etc. information.
Some example of range-based algorithms are Time of
Arrival (ToA), Angle of Arrival (AoA), Received Signal
Strength Indicator (RSSI) etc.
A. Background and motivation
A. Background and motivation
Collection of large number of sensor nodes are
called as wireless sensor networks, which are used
to collect data from a targeted area,this is of low cost
and low power.Data such as humidity and
temperature are sensed from surrounding by sensor
Fig. 1: Classification based on range
nodes and sent via wireless problem with wireless
Further classification of algorithm is based on anchor
sensor network is of localisation.Knowing the
node,classified as anchor-based algorithm and
anchor free algorithm. In anchor-based algorithm,
localization is done by the help of anchor node,
nodes can be static or mobile.Anchor node
broadcast their location information and other nodes
make use of that information to localize
themselves.In anchor-free algorithm, no anchor node
is used, unknownnodes localize themselves by using
some transmission range,neighbouring nodes etc.
Fig. 2: Classification based on Anchor Node
Trajectory based and trajectory free Algorithms are
another forms of classification of localisation
algorithm.In trajectory based algorithm anchor nodes
follows a trajectory to traverse the network or a fixed
path to localise the unknown network,also called as
planned Dynamic and static are the further
classification of trajectory based algorithm.If path is
fixed prior to runtime it is called as static and if path is
decided during runtime then it is called as
dynamic.Some examples are SCAN,DOUBLE-SCAN,
HILBERT etc.There exit no Fixed path in trajectory
free According to the Algorithm used path is followed
by anchor nodes,also called as random algorithm.
Some examples are Random
Way Point, Gauss Markov.
Fig. 3: Classification based on Trajectory
In this paper, anchor path planning is done and a
static trajectory-based localization algorithm is
proposed. The an- chor node follows the sine wave
shaped trajectory. The anchor node moves along
the trajectory and broadcast the packet containing
its location, periodically. The unknown nodes
receive this signals and as any node gets three
signal from different location, it calculate its location
by applying trilateration. The unknown node also
calculate the distance between anchor node and
itself by using RSSI measures for the process of
trilateration. This trajectory is compared with the
algorithms and performance improvement is shown
by simulation results.
B. Contribution
In this paper, our main aim is to get efficient
result from the given trajectory. The proposed
trajectory can help in reducing the average
localization error as compared to other trajectories.
The contribution of this paper are as follows:
1) For this localization process, an efficient
trajectory of anchor node is to be selected to
insure that all the unknown nodes get location
information to locate them- selves. So, to
maximize the location accuracy of the unknown
node, an efficient trajectory is studied. That is,
the anchor node travel the network along the
sine wave curve. Compared with other
trajectories this trajectory gives less localization
and is able to locate all unknown nodes.
2) The
performance by adjusting the number of sine
waves according to deploy- ment area in a
WSN. Thus, if unknown node situated
obstacle avoidance mechanism which provide noncollinear points around obstacles. The main drawback of
MMAPP-NDC is it has longest path length among four
algorithms, since it use a group of mobile anchor nodes
to traverse the ROI to reduce localization time and
improve localization ratio. An effective path planning
algorithm can significantly improve the localization
performance.In [3],both dynamic and static path planning
Algorithms have been proposed for mobile based
localization.This algorithm makes mobile anchor to stop
Wireless Sensor Network (WSN) is used in a lot of
at minimum number of nodes to cover the monitoring
application now a days. It has become a very
area with shortest path length.In proposed static
interesting area of research. WSN consist of a lot of
approach trilateration with shorter path and loss anchor
research issues. The main issue of WSN is
are used to determine path.The both static and dynamic
localization, as every node in the network need to be
algorithms use a two-phase procedure to search the
localized by some localization algorithm as it reduces
surveillance region and decide the mobile anchor
the cost of GPS and also helps in getting the required
trajectory. In the search-phase, they divide the region
information about the data. Different localization
into circular grids and detect the sensors inside. In the
algorithms are proposed which achieve high accuracy.
decision-phase, they revisit the grids with sensors for
The location of unknown node can be determined
localization. This algorithms performs better compared to
either by using another device i.e. a mobile anchor
other algorithms.
node or without using any device. There are many
advantages of using anchor node base localization.
In [4], author proposed a Hilbert space filling trajectory to
First, it reduce the energy consumption of the nodes
reduce the collinearity problem. A n-level HILBERT
in the network.Second, the localization accuracy can
curve divides the space into 4 n squares, which
be improved by choosing a correct algorithm or a path
increases the path length as “n” increases. In this
for anchor node to traverse the network or to transmit
algorithm, sensors located near the border of the
the messages. We can control the anchor node easily,
surveillance area are not localized effectively.In [5],
because they are less in number as compared to the
author proposed a localization algorithm which is
other nodes.
Efficient Localization Algorithm based Path Planning for
Mobile Anchor (ELPMA). This algorithm is based on a
In [1], the author proposed a Localization algorithm
one mobile anchor which is moving in adjustable circular
with a Mobile Anchor node based on Trilateration
trajectory to scan the network. It uses received signal
(LMAT) in WSN.The mobile anchor node used in this
strength indicator as ranging function to determine the
Algorithm uses a fixed trajectory in the network where
distance between mobile anchor and sensor nodes. In
periodically locations are shared to nearby nodes with
this algorithm, mobile anchor starts the motion from the
the help of sensors embedded in it.High accuracy and
centre of the target area. The traveling path is planned in
better coverage are provided by equilateral
advance based on the distance measurement between
triangles,and that is used in this paper.Trilateration is
the mobile anchor and sensor node.
applied to calculate coordinates of unknown nodes
from the received message packets.This lead to high
accuracy and reduced error.In [2], author propose
three Mobile anchor nodes Path Planning (MAPP)
algorithms namely,IMAPPP-NDC, SMAPP-NDC and
MMAPP-NDC. The proposed algorithm combine
network-density-based clustering, Inter-clustering path
planning and intra-cluster path planning together to
improve localization and utilize rate of virtual beacons.
This algorithm used hexagon shaped trajectory.
SMAPP-NDC and MMAPP-NDC algorithms employ
at the corner of the area will also get
localized. Thus, localization coverage and
accuracy of unknown node also increases.
3) Compared to existing algorithms such as
this algorithm pro- vides better solution to
solve the problem of collinearity for the
process of localization.
In [6], author proposed a novel idea of localizing the
target node with moving single anchor node, using
application of Particle Swarm Optimization (PSO)
and H-Best Particle Swarm Optimization
(HPSO).The anchor node localize other nodes and
moves in HILBERT trajectory. Localization algorithm
have been implemented for distributed WSN and
using RSSI based (range based) technique by this
algorithm. HILBERT trajectory is followed by anchor
node in the proposes algorithm,any deployed target
node falls under the range of moving anchor node,
the Euclidian distance between anchor and unknown
node is calculated. After calculating the distance, six
virtual anchor nodes at a distance same as Euclidian
distance are projected with an angle difference of 60
degree around the anchor node. After projecting the
virtual anchor node, two anchor node are used to
find 2D coordinates of the target node. The anchor
node is moving with a constant speed and algorithm
runs after a fix time interval.
B. Trajectory
Fixed path to move in a network by anchor node is called
as trajectory. All other nodes can be localized with only
one anchor node in the network if we use trajectory. As
Location signals are transmitted periodically when anchor
nodes are moved along the trajectory.The challenging
part is to select the most optimal trajectory which provides
the best result. Main goals for choosing the correct
trajectory for Localization are:1.High network coverage should be provided by
2.Less Localization error should be provided by trajectory.
A. Network Model
In proposed approach, the WSN consist of a number of
randomly deployed unknown sensor node and a moving anchor
node. The size of network is L*B, which can be changed
according to the size. All the sensors including the mobile
anchor node consist of same communication radius i.e. r,
which can be changed according to need. The anchor node
sends the message containing its location
information after particulate interval of time. When
at least three packet received by unknown node, it
calculated its own location by applying trilateration.
Fig. 4: Traveling Trajectory of anchor node in sine wave shape
C. Trilateration Process
When location containing signal information is
received by any unknown node from three different
locations,trilateration method
is used to determine the relative location of itself.
Absolute relative location is of any node is determined
by calculating the distance. For calculation of the
distances geometrical figures are used such as circle,
spheres, triangles.The condition required for applying
trilateration is that ,we need to have three coordinates
known prior to method implementation .Since
mathematically to identify location in 2D space we need
to have three coordinates atleast.
Here, three points with known location A, B, C
and (x1, y1), (x2, y2), (x3, y3) respectively are
there coordinates. The intersection point of three
sphere is the unknown node is at which distance of
d1, d2, d3 from A,B,C respectively. The equations
for finding (x, y) coordinates areThe distance between
the anchor node and1
un- known node is
calculated by RSSI2
er that the packet can be sent and received in the
circular region within the radius.
(x1 − x)2 + (y1 − y)2 = d2
(x2 − x)2 + (y2 − y)2 = d2
(x3 − x)2 + (y3 − y)2 = d2
Fig. 5: Trilateration Process
By solving (1),(2),(3) equations we can calculate
the value of (x, y) We can expand out the squares
in each one:
x2 − 2x1x + x21+ y2 − 2y1y + y21= d21
The algorithm proposed in this paper can be
summarized by the following steps:
1) The anchor node move along the trajectory in
the network.
2) When the anchor node broadcastthe location
3) If a unknown node is within the range of
4) Then unknown node stores the location
packet and calculate the estimated distance to
5) Else do nothing.
6) If the unknown node receives packets from at
least three different anchor locations.
7) Then unknown node perform Trilateration.
8) Else do nothing.
9) If the trilateration is applied correctly, we get
the coor- dinates of unknown node.
10) Then repeat 3.
11) End.
The steps shows the step by step method by which
x2 − 2x2x + x22+ y2 − 2y2y + y22= d22
proposed algorithm can be implemented.
x3 − 2x3x + x23 + y2 − 2y3y + y23 = d23
A. Simulation parameter
On subtracting eq. (5) from eq. (4), we get
(−2x1 + 2x2)x + (−2y1 + 2y2)y
= d2 − d2 − x2 + x2 − y2 + y2
HILBERT, SPIRAL. The deployment area is set to 100m X
On subtracting eq. (6) from eq. (5), we get
(−2x2 + 2x3)x + (−2y2 + 2y3)y
= d22 − d23 − x22 + x23− y22+ y23
100m, other parameters are mentioned in table
given bellow.
From the above equations we can get two
equations with two unknowns
Ax + By = C
DX + Ey = F
The simulation of this algorithm is done in
MATLAB sim- ulator. In this we compare the
performance analysis and local- ization error of
different algorithms mainly SCAN, DSCAN,
TABLE I: Simulation Parameters
Network Size(in m)
Unknown Nodes(n)
Radius (in m)
Node Density
100 x 100
B. Node Density
On solving
Node density of the deployed node affects the
efficiency of localization algorithm, as the density
of unknown nodes
is larger, it increases the
energy consumption of network and also
communication overloads of sensor node. In the
(6) shown the comparison between different
algorithms by comparing the localization error with
For determining the value of d1, d2, d3 RSSI
(Received Signal Strength Indicator) Measures are
used. Distance can be calculated by using RSSI
Measure using following formulad = 10(A−RSSSImax)/10n
Where, RSSI max is maximum RSSI value A is
received signal power in the distance d0 between
two points n is path loss exponent.
ode density.
C. Traveling Speed of anchor node
The traveling speed of anchor node varies from
o.5 to 2m/s. It is observed that the speed of anchor
node does not affect the localization error of the
algorithm. The proposed trajec- tory performs well
as compared to other. Figure (7) shows
localization error of different algorithms with
respect to traveling speed of anchor.
Fig. 6: Localization error vs. Node Density
Fig. 8: Number of Reference node of different algorithms
E. Localization Error
Localization error is main issue of any
localization al- gorithm. Inefficient algorithm and
mobility of sensor is the main reason of increase in
localization error. Localization error is summation
of the difference between the estimated and real
coordinates of localized sensor node divided by the
total number of nodes. Localization error is used to
calculate the localization accuracy of the algorithm.
Mathematically, Average localization error (L) can
be calculated as followL=
E(i) =
Fig. 7: Average Localization Error vs. Traveling Speed of
anchor node
(Est xi − xi) 2 + (Est yi − yi) 2
Where, E(i) is the error of single node, n is total
number of node, (xi,yi) is actual coordinates of
the sensor and (Estxi,Estyi) is estimated coordinates
of the sensor which is calculated by applying the
D. Number of reference node
Localization error reduces with the increase in
number of reference node(Rn) as it increase the
accuracy of unknown
Mathematically, number of reference node can be
calculated as1Σ
C(R i)
n 1
Rn =
Where, n is the total number of localized node
and Ri is the total number of reference node used
to localize the unknown node i. C(Ri) is the
cardinality of set Ri. Figure (8) shows the number
of reference node used by each algorithms. Though, the
number of reference node of HILBERT is higher that
proposed trajectory, despite of that proposed trajectory
has less localization error.
Fig. 9: Localization Error of different
As seen in the figure localization error of SCAN
and proposed algorithm(SINE) is somewhat equal
but proposed algorithm reduces the problem of
collinearity which is main problem in SCAN
algorithm. Due to the collinearity problem (i.e.
getting the anchor node locations in same line),
there is error in calculating the estimated position
of any unknown node. Thus, it is observed that
SINE outperform well among other algorithms. In
comparison, the radius is 40m and there are 100
number of unknown nodes.
F. Results
Figure (10) shows the localization error occurred
when the number of unknown nodes changes in
the network by keeping the network size same i.e.
100 X 100m.
Fig. 10: Localization Error vs. Number of
nodes Figure (11) shows the comparison
between the real and
estimated position of the unknown nodes. It can be
observed that most of the estimated position is
same as real position and some are very close to
them. Rest of the differences come due to the
localization error which can be caused by many
reasons. Thus, Proposed algorithm has performed
In this paper we first propose the trajectory on
which our mobile anchor node moves and transmit
its location periodically and the trilateration is used
to determine the location of unknown nodes. By the
proposed algorithm, we conclude that path planning
for the mobile anchor node affects the localization
process in WSN. While choosing the correct path
or trajectory, two points we should keep in mind that it
should provide high location accuracy and energy
consumption by the sensor nodes are less. This
trajectory would definitely decrease the localization
error compared to other trajectories. The comparisons
is done between SCAN, DOUBLE SCAN, HILBERT,
SPIRAL trajectories. By simulation results, we conclude
that the proposed algorithm performs great with respect
to other algorithms. Proposed algorithm decrease the
localization error and also increase the localization
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Fig. 11: Comparison of real and estimated position of
sensor node
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