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Due to the success of rapidly evolving wireless sensor networks (WSN), innovating localization
techniques have been proposed by researchers all over the world. Since wireless sensor nodes are small
devices with limited processing power and the channel conditions are difficult to predict, therefore, there
is a desperate need of a low complexity algorithm that can efficiently identify channel condition and
select an appropriate method of localization. Related to this, I present in this article a novel localization
scheme that is very efficient in detecting the location in real world environment which is usually a mixed
case of line of sight and nonline of sight. Simulation results show that this scheme reduces the delays in
localization and increases the lifetime of nodes while maintain a fairly low mean estimation error. The
results also demonstrate that this scheme performs fairly well even when there are limited numbers of
anchor nodes.
I. INTRODUCTION
Estimating the location of a roaming sensor node is one the most essential tasks of a wireless sensor
network application. For example, if sensor nodes are deployed to provide protection against fire and each
sensor node sends alarm message to other sensor nodes when it experiences sudden rise in temperature. In
such a crucial situation we want to know the exact location of those sensor nodes in very short period of
time, so that proper actions can be taken accordingly. Another useful example can be vehicular sensor
networks. Since communicating cars and roadside infrastructure collectively form a sensor network.
Therefore it is very important to know the exact location of car for collision avoidance, traffic light status
information and traffic congestion information etc. Moreover, some of the promising and famous routing
protocols, such as geographical routing [1, 2], make routing decisions on the basis of the location of
sensor nodes. Keeping in view these facts and many more a sophisticated localization scheme is necessary
i.e. a scheme which is fairly efficient even in case of very small number of anchor nodes.
The proposed scheme is a selective scheme based on the information gained through received
signal strength (RSS). This scheme is divided into following major tasks:
· The unsettled node whose location is to be calculated receives broadcast messages from the
anchor nodes.
· Based on the received power from these anchor nodes, the unsettled node calculates the variance
of the RSS and estimates whether a particular node has line of sight with the unsettled node or
not.
· After calculating the variance of all the anchor nodes it then sends this information to the sink
node.
· The unsettled node selects among the two localization scheme (i.e. trilateration or multilateration)
to estimate its position with sufficient accuracy.
The remainder of the paper is organized as follows. Section II discusses the lateration techniques used in
this article. Next in Section III, the proposed scheme is discussed in detail with two of its subparts. In
Section IV, I analytically evaluate the performance of the proposed scheme. Finally, Section V provides
some concluding comments.
II. LATERATION TECHNIQUES
The optimal localization scheme that is proposed in this research paper uses two of the most well
renowned RSSIbased localization techniques i.e. trilateration and multilateration
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Trilateration: Trilateration is a method to obtain relative position of the point in space by measuring
distance, using geometrical shapes like triangle, circles and sphere.
Since I am only considering two dimensional space therefore, only circles are considered. we
need atleast three circles to estimate the position of a point in 2D space. The interersection of these three
circles will give the estimated position of a point. This phenomenon is shown in following diagram:
Fig. 1. Trilateration technique using three circles
The general equation of a circle is given by:
=
+
(1)
For a circle centered at (X
A
, Y
A
) the above equation can be written as:
= ( 
) + ( 
)
(2)
Similarly for circles B and C
= ( 
) + ( 
)
(3)
= ( 
) + ( 
)
(4)
Equations (2.0), (3.0) and (4.0) can be expanded by opening the square:
=
+
 2
+
+
 2
(5)
=
+
 2
+
+
 2
(6)
=
+
 2
+
+
 2
(7)
In order to find the point of intersection equations (5), (6) and (7) are solved as:
(
+
)  2
 2
=


(8)
(
+
)  2
 2
=


(9)
(
+
)  2
 2
=


(10)
Rewriting equations (8), (9) and (10) into matrix representation, we get;
1
2
2
1
2
2
1
2
2
2
+
2
=
2

2

2
2

2

2
2

2

2
(11)
The above equation can also be written in following form:
Circle C
Circle B
(X
C
, Y
C
)
(X
B
, Y
B
)
(X
A
, Y
A
)
d
A
d
B
d
C
Circle A
4
. =
(12)
The solution of can be found using least square method. Hence the above equation becomes:
= ( . )
.
(13)
It is to be noted that value of matrix A and b can easily be found using only reference points and within a
small fraction of time. Since it is only matrix multiplication, therefore, no extensive computation is
needed.
Multilateration: It a proven localization scheme that has been used for military purposes for decades.
There are many flavors of multilatertion but in this article I am only considering Nonlinear Least Square
Multilateration. It is a variation of Newton method for finding a smallest of a function. It uses Gauss
Newton method to find the minimum value of a function. Initially, the position of a node is randomly
selected, let this random position be (X
r
,Y
r
). Moreover, equation (11) can be written in general form as:
1
2
2
1
2
2
:
1
:
2
:
2
2
+
2
=
2

2

2
2

2

2
:
2

2

2
Where N represents the total number of nodes which is greater than three. The equation (13) can be
rewritten as delta:
= (
.
)
.
( , ) = ( ,
) 
Where
represents the delta value of i
th
node whose location is represented by
( , ). Iterative method
is used to accurately locate the position of a node. As the number of iterations increase the estimated
location of
( , ) becomes more precise as shown in figure below. As the area increases the number of
iterations to correctly estimate the location of node must also be increased. Furthermore, with the increase
in number of anchor nodes the value of delta reduces for same area. This shows that as the no. of anchor
nodes increases the value of delta also reduces. Hence, less number of iterations is required for estimating
the position of sensor node correctly.
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Fig. 2. Delta value vs iterations for area of 50 sq. meters
Fig. 3. Increase in Delta value with the increase in area for specific number of anchor nodes
Dependence on RSSI:
The above mentioned techniques will give accurate position of x and y i.e. the position of the required
node. Since these techniques depend heavily on measured distance and due to the complexity of modeling
the environmental effects the RSSbased distances are not always correct. Therefore, many physical
phenomenons like scattering, diffraction and reflection cause diverse path losses for same distances.
Measurements have confirmed that at any given distance the path loss is random and follows a normal
distribution. Hence the probability distribution of estimated distance is given by:
10
 10
=
[
]
(14)
The above equation can also be written as:
= + (10
 1)
(15)
Where
is Gaussian random variable with zero mean and standard deviation , n is the path loss
coefficient, d is the actual distance and is the measured distance.
This standard deviation increases in case of NonLine of Sight (i.e. the variation of channel increases)
which will effect on the overall measure distance. This will resultantly increase the error in estimation of
position of unsettled node.
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III. PROBLEM SETUP
Fig. 4. Problem setup containing a sink node, four anchor nodes and an unsettled sensor node
As shown in Fig. 1, I consider wireless sensor network consisting of a sink node and five sensor nodes.
Out of these sensor nodes four are anchor nodes A1 , A2 , A3 and A4 whereas, there is one unlocalized
nodes U1. I have assumed that all the anchor nodes know their position through GPS receiver. The
coordinates of anchor nodes are (Xk ,Yk), where k=1,2,3,4. The anchor nodes transmit the information
about their location with a signal of normalized intensity to an unlocalized node U1. Sink node has the
connectivity to the entire network. It is also considered that channel is quasistatic between sink node and
anchor node (i.e. it does not vary for a given transmission time). In this problem only the energy
dissipated by unsettled node is considered, since in most of the real world scenarios unsettled node is the
one with limited amount of energy. Sink node is able to transmit and receive data to every single node in
the network. However, it has only information about the location of the anchor nodes and it does not
know the location of U
1
in the network.
Proposed Scheme:
1.
Channel Prediction:
Whenever the sink node wants to find the location of an unsettled node, it first asks all the anchor nodes
to be in transmission mode and unsettled node to be in reception mode. The mobile node receives the
signal strength from all the anchor nodes. The unsettled node receives the pulse input through an
unknown channel. It then analyses the variance of RSS. Based on the experimentally determined value of
threshold it decides whether the channel is line of sight or nonline of sight. For both line of sight and
nonline of sight channel the variance is shown in the following diagrams:
Sink node
Anchor node A
1
Anchor node A
2
Anchor node A
4
Anchor node A
3
Unlocalized node U
1
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Fig. 5. Variance value for line of sight environment
Fig. 6. Variance value for nonline of sight environment
The value of threshold that determines whether channel is LOS or NLOS with around 80% accuracy can
easily be determined from following graph:
Fig. 7. Determination of threshold value to differentiate between line of sight and nonline of sight environment
Hence the condition of the channel can be found from given relationship:
:LOS channel
:NLOS channel
Where
is the calculated value of variance for a given set of pulses,
is the experimentally
determined value of threshold of variance i.e. 0.3. This process is done for RSS value of all the anchor
nodes. Since this process does not involve any sort of complex computation, therefore, the delay caused
by this process is negligible and does not significantly affect the overall delay.
2.
Localization
a.
Case 1: when 3 or more nodes have LOS
When unsettled node has line of sight with three or more nodes it shows that the distance calculation that
will be done for localization would not be affected much. Furthermore, the variance of the noise added in
case of line of sight will not be great enough to cause any serious problems in localization. This condition
favors the use of trilateration technique. Hence the unsettled node uses trilateration method for
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localization to estimate its position and informs the sink node regarding its coordinates. Since
trilateration method involves only multiplication of matrix in a linear fashion, therefore, this localization
technique is suitable for unsettled node and will not increase the complexity of hardware of sensor node.
b.
Case 2: when less than 3 nodes have LOS
When unsettled node has line of sight with less than three anchor nodes it shows that channel conditions
are not suitable to use trilateration technique. Since the distance calculation from nonline of sight anchor
nodes will inculcate high variation of added noise. Using trilateration with further worsen the location
estimation as trilateration itself uses linear method to calculate position of node. It leads us to
multilateration. However, multilateration due to its nonlinear computation method is not a good choice
for sensor node, as it will increase the complexity of hardware and will require more computation power.
Therefore, the sensor node will inform about the situation to sink node. The sink node will then send a
command to unsettled node to change to transmission mode and will also inform anchor nodes to change
to reception mode. The unsettled node will then send 1000 bit pulse to all the anchor nodes at least 5
times (since at least 5 iterations are required to make the value of delta zero for area of 100 sq. meter and
correctly estimate position). The anchor nodes will receives these pulses and calculate the distance
individually and will send these distances to sink node. The sink node will then use the multilateration
technique to calculate the coordinates of unsettled node.
IV. PERFORMANCE EVALUATION
1.
Delay Reduction:
It is vividly clear from the following diagrams that the localization delay has been significantly reduced.
Even when the number of sensor nodes increase significantly. These graphs have been drawn for 4 anchor
nodes which show that the proposed scheme performs fairly well even with limited number of anchor
nodes.
Fig. 7. Estimated path of mobile sensor node using the proposed scheme
There is up to 1 meter mean estimation error which is insignificant as compare to the area (100m
2
).
Moreover, the proposed scheme successfully detects the mobility pattern of the sensor node which is
extremely helpful in navigation. In case of multilateration the delay curve increases very rapidly, whereas,
for the proposed scheme delay curve increases at a slow pace; even for large number of sensor node. The
results show that the proposed scheme's mean estimation error is at par with multilateration used in LOS
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environment, even when the proposed scheme experiences mixed (LOS and NLOS) environment.
Fig. 8. Delay comparison of multilateration technique and proposed scheme using 4 anchor nodes
2.
Energy Consumption:
The energy models for a wireless sensor node use an elementary assumption that a sensor node consumes
it power in three functions: communication (energy transmission and energy reception), processing the
data and acquisition.
Fig. 9. Energy consumption model
The first function i.e. communication consumes a large amount of power due to the fact that it constitutes
of two suboperations. The energy model used in this article is called the firstorder radio model.
According this model, the node consumes
( , ) amount of energy in transmitting p bits of
information over a distance given by d [4].
( , ) = .
+ .
.
(16)
When k bits of information is transmitted by N nodes the total energy is given by:
= .
(
+
.
) (17)
Whereas,
( ) is amount of energy that is consumed when p bits of information are received, given by:
( ) = .
(18)
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Parameter
Definition
Units
Energy dissipation rate to run
the radio
50nJ/bit
Path loss coefficient
2.5
One path model for the
transmitter amplifier
10pJ/bitm
2
Data length
1000 bits
Table 1. Definition of parameters used in energy consumption model [4]
Fig. 10. Energy consumption comparison of multilateration technique and proposed scheme using 4 anchor nodes
The simulation result show that the proposed scheme performs better than the multilateration scheme. It is
to be noted that the difference between energy consumption, as compare to the multilatertion, increases
when the number of sensor nodes increase. This difference is due to the fact that as the numbers of sensor
nodes increase the probability of finding line of sight with anchor nodes increase. This results into
utilization of trilateration technique, which operates in reception mode, hence utilizing less power.
V. CONCLUSION AND FUTURE RESEARCH
In this article I have proposed a scheme that focuses on reduction of delay during localization at the same
time utilizing minimum amount of energy. It is done while maintain a fairly low position estimation error.
It shows that the proposed scheme is extremely useful for detecting the position of highly mobile (i.e.
delay intolerant) wireless sensor nodes. This article also introduces a simple yet effective mechanism to
detect the channel condition in case of both LOS and NLOS.
In this paper, I only examined the delays and energy consumption for single antenna, where each anchor
and sensor node is equipped with only one antenna for transmission and reception. However, it is of high
interest to extend the results of delay and energy consumption for a MIMO system utilizing multiple
antennas. Keeping in view that for channel condition multiple or single antenna can be used which can
lead to fascinating possibilities. I leave this thoughtprovoking and interesting problem for future work.
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VI. REFERENCES
[1] Karp, B., Kung, H.T.: GPSR: Greedy perimeter stateless routing for wireless networks. In: Proc. Of the Int.
Conf. on Mobile Computing and Networking (MOBICOM), pp. 243254 (2000)
[2] Yu, Y., Govindan, R., Estrin, D.: Geographical and energy aware routing: A recursive data dissemination
protocol for wireless sensor networks. Technical Report UCLA/CSDTR010023, UCLA Computer Science
Department (2001)
[3] Dixon, John C., (2009), "Suspension Analysis and computational Geometry: John Wiley and sons limited
[4] J. Wang and Y. K. Lee, "Determination of the optimal Hop number for wireless sensor networks," in
Proceedings of the International Conference on Computational Science and Its Applications: Part
II,Seoul,Korea,2009.
[5] A. PagesZamora, J. Vidal, and D.H. Brooks, Closedform solution for positioning based on angle of
arrival measurements, The 13th IEEE Int. Symposium Personal, Indoor and Mobile Radio Communications, vol. 4,
Sep 2002.
[6] S. Capkum, M. Hamdi and J.P Hubaux, (2004), "GPS free positioning in mobile adhoc networks". In
Hawaii international conference in system sciences (Hicss 34), pages 34813490, maul, Hawaii
[7] B. Han, D. Z. Zhang and T. Yang, "Energy Consumption Analysis and Energy Management Strategy for Sensor
Node," International Conference on Information and Automation, Proceedings of the 2008 IEEE, Vol. 6, 2008, pp.
211214.
11 of 11 pages
 Quote paper
 Furqan Jameel (Author), 2016, Minimizing Localization Delays (MILD) for Wireless Sensor Networks, Munich, GRIN Verlag, https://www.grin.com/document/337114
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