Localization Of Source In Wireless Sensor Networks
A
nita Panwar
Electronics & Communication Dept.
National Institute Of Technology
Hamirpur, India
anitapanwar15@yahoo.co.in
Sh.
A
shok Kumar
Electronics & Communication Dept.
National Institute
Of Technology
Hamirpur, India
ashok@nitham.ac.in
Abstract
—
The deployment of
accurate and low

cost
wireless
sensor networks is a critical requirement for signal emitting
source localization
as the design of sensor l
ocalization systems
will influence by various application requirements (such as
scalability, en
ergy efficiency, and accuracy)
. In this paper, we
describe measurement

based statistical models useful to describe
time

difference

of

arrival (TDOA) and range

difference

of

arrival (RDOA) measurements in wireless sensor networks.
S
ource which emits a calibration signal is detected by the sensor
nodes in the network measures the time

difference

of

arrival and
range

difference

of

arrival with respect to the sensor
node’s local
orientation coordinates of the signal emitted from that source.
The time difference of arrival (TDOA)
and range

difference

of

arrival (RDOA)
for the source received by the sensors is first
estimated using the generalized cross correlation (GC
C) method.
The estimated TDOA and RDOA values are
then used
by the
Least Square and
New
Weighted Least Square estimation
method to estimate the source location.
We also calculate
a
Cramer

Rao bound (CRB) on the location estimation precision
possible for a given set of measurements
using the above models
.
This paper also briefly presented the survey of large and growing
body of sensor localization algorithms.
Keywords

source;time
difference of arrival(TDOA)
;
range
difference of arrival(RDOA
)
;Cramer rao lower
bound(CRLB);Wireless Sensor Networks
;
Least Square (LS)
estimator;
New
Weighted Least Square (WLS);
generalized cross
correlation (GCC)
;
I.
I
NTRODUCTION
T
remendous growth in both
interests and applications of
wireless sensor networks
have witnessed
recent years.
The
deployment of accurate and low

cost
in
wireless sensor
networks is a critical requirement for signal emitting source
localization as the design of sensor localization
systems will
influence by various application requirements (such as
scalability, energy efficiency, and accuracy).
Wireless Sensor Networks
is a network of
number of sensor
nodes deplo
yed in the sensor fields
[2,3]
. The
sensor nodes
in
the field
have the capabilities of sensing, computing and
wireless communicating through multihop
or single hop
infrastructure.
A
dvancement in wireless communication and
various
scientific
technologies have enabled the development of low
cost, low

power, multifunc
tional sensor nodes
. Such sensor
nodes
are small in size and
can
communicate in short
distances.
Figure 1.
Wireless Sensor Network Architecture
“Fig. 1”,
shows architecture of wireless sensor network
[2]
and
it consists of field of sensor nodes,
sink nodes, remote users,
internet or satellites. Here
Sink
nodes acting as gateway are
capable to
communicate with remote user through internet,
satellites, etc.
S
ensor node are
consist of
a
sensing unit
, a
processing unit
, a
transceiver unit
, a
power un
it
, l
ocation
finding system
,
power generator
, and
mobilize
.
Source
localization in wireless sensor networks has assumed
increasing significance. A source
here refers to the place or
point from where
the information or message
s are generated in
the form o
f waves
, if something happens in their locality.
Hence
, localization of source
makes the collected information
valuable
.
Glo
bal Positioning Systems (GPS) [3
] has been widely
used
traditionally for locating source. B
ut
they are not supported by
all the ch
eap sensor nodes in wireless sensor networks
due to
their
drawbacks like heavy

weight and expensiveness
.
Hence,
cost effective, rapidly deployable and can operate in diverse
environments
alternate solution o
f GPS is required. Therefore,
source
localization
has become the hot research area
of
interest in
wireless sensor network.
L
o
calization approaches are
time

of

arrival (TOA), received
signal strength (RSS), time

diffe
rence

of

arrival (TDOA) or
Direction/angle

of

arrival (AOA).
RSSI is the
ranging
technique
,
which
estimate the distance
between two nodes
using
strength of the signal received by another
node [
1
, 2, 3
].
In TOA, the distance
between nodes
is calculated based on the
propagation time
of the signal (RF, Sound etc)
and the speed
of
the received signal
. In TDOA
the distance is estimated
similar to TOA only
difference
is that it uses two signals and
difference
between the receive ti
me of two separate signal is
used to estimate the distance between two nodes
[1, 2, 3
]
.
In
AOA d
irection
from where the
signal
is received can be used
for localization.
They basically r
ely on directional antenna or
special multiple
antennas which is the drawback of this
method
as system cost increases.
In this paper, we used the
time

difference

of

arrival
approach for localization.
The rest of the paper is or
ganized as follows. In Section II
, the
system model is described which is based on the Time

Difference

Of

A
rrival (T
D
OA)
or Range

Difference

Of
Arrival (RDOA)
measurements approach.
In section III
trad
itionally used
Least Square (LS)
approach is described
.
After that in next section we described a
n improved approach
of Least square by weighing
the Least Square (LS) function
and
based on above approaches simulation results are shown.
Also for performance
measures of location accuracy
Cramer

Rao Lower Bound (CRLB) [1
] is reviewed. Finally, Future
Research work and conclusions are drawn in Section 4 and
Section 5 respectively.
II.
S
YSTEM
M
ODEL
Source
localization can be estimated
by using observed
difference
s in the signals received at different observation
points, such as angle of arrival (AOA),
time of arrival (TOA),
time difference of arrival (TDOA),
Range

Difference

Of
Arrival (RDOA),
received signal strength (RSS)
.
Several
m
ethods, usually based on
TDOA
and
Range

Difference

Of
Arrival (RDOA)
, have been developed
.
Here, the problem of source localization
[4,7]
can be
implemented using the time difference of arrival (TDOA) and
Range

Difference

Of Arrival (RDOA).
First time difference of
arrival (TDOA) or
Range

Difference

Of Arrival (RDOA)
is
determined by performing general cross

correlation
(
GCC)[4,6] on the received signals [2,3]
. The TDOA/RDOA
values are then used to estimate the location.
Figure
2
Time

difference

of

arrival (TDOA
) and Range

differ
ence

of

arrival(RDOA) at two sensors.
For the counter

sniper
or seismic
application
s studied in this
paper
, we propose the use of the
localization process
keeping
in mind the
speed
and the limited computational capabilities
o
f
the sensors.
Source
localization is the process of determining the spatial
location of a source
based on mult
iple observations of the
signal
emitting from the source
.
Let us consider the
source location S be [X
s
, Y
s
] and the
coordinate of i
th
fixed sensor node be [X
i
, Y
i
] a
lso one sensor
node is taken as reference node at coordinate [0, 0]
[5]
.
If t
otal
no of
sensor
node deployed is N then distance [5
]
between i
th
node and source node is denoted by d
i
, given as
d
i
=
√
i= 1, 2,….N
(2)
The generalized cross correlation (GCC)
[4,6]
technique is
used to estimate the time difference of arrival
(TDOA)
tˆ12 for
a pair of received signals
Y
1
(t) and
Y
2
(t)
.
̂
∫
(3)
The tˆ
12
values are then converted into range difference of
arrival
(RDOA)
d
12
values using
the relationship
.
d
12
̂
(4)
The measured RDOA values
̂
are modelled as
̂
= d
ij
+ n
(5)
where
n
is a white Gaussian noise with zero mean and
variance
i
2
III.
L
EAST SQUARE
Least square
algorithm traditionally used
minimizes
the
overall
solution
of
the sum of the errors made in solving every
single equation.
It is
a standard approach to the approximate
solu
tion of over determined systems in
which
sets
of equation
having
more
equations th
an unknowns [1,4,5
].
In this paper
the closed

form least squares
(LS) source
location estimation based on
the
Sp
herical Interpolation
method [5
] for
the measured range difference of arrival
(RDOA)
values
[1]
.
Assuming that sensor 1
is selected as the reference node (i.e.,
(
x
1
, y
1
)
=
(0,
0 ),
than
the source location estimate is given as
̂
(6)
where P
r
is the projection matrix
,
S is the sensor location
matrix
, a
nd d
is the range difference of arr
ival vector.
IV.
W
EIGHTED
L
EAST
S
QUARE
In weighted least square we define the weights using different
approach compare to the traditionally used method weighted
least square method
[1,8]
.
Now weighting matrix W is added to have
better performance
which leads to optimization of constrained
.
T
he source location
with weights can be estimate
given as
̂
(7)
A.
New algorithm for calculating
weighting matrix
W
First we define
the range of the source node
based on the distance between estimated
position and reference node at (0
, 0
).
Second the sensor nodes deployed in the field
with known diameter range.
Third we calculate the range difference between
estimated source position
and the deployed
nodes.
If calculated range is inside the range of the
estimated source diameter range than the weight
of those sensor nodes are taken as 1, if the range
is outside then the weight is taken as 0.
Finaly, the diagonal elements of the weight
ing
matrix are taken as weight W.
V.
CRAMER

RAO
LOWER
BOUND
(CRLB)
The Cramer

Rao Lower Bound (CRLB) gives a lower bound
on variance achievable by any unbiased estimat
or
[1,4]
.
An estimator that is:
unbiased and
attains the CRLB
is
said to be an “Efficient Estimator”.
CRLB for the position
estimation problem is derived by
deriving t
he Fischer information matrix (F(s)) for
integrat
ing
the sensor position errors
trace (F

1
(s))=min E[(
̂
̂
)
T
]
(8)
then
From (8)
, it can be shown that the minimum variance of
the
estimates of the source position is equal to the trace of the
inverse of the
Fischer information matrix which is nothing but
CRLB.
CRLB=
trace (
F

1
(s))
(9)
T
h
u
s
the
analysis is done
for the
proposed estimator [18
]
to
see the effect of position error of node on the performance
limit of source localization
.
VI.
S
IMULATION
R
ESULT
In this section, the
simulation results
are presented
to show the
performance of the
source localization
algorithm. In
a
ll
simulations presented in this section, Simulation has
been
done in Matlab and following parameters have been
considered for simulation purpose
.
The simulation model is
based on the known p
ositions of the
sensors and
time

delayed copies of a source
signal are
generated for each sensor
sensor 1 is chosen as reference
sensor at origin
.
For simulation
u = 345m/s is the speed of
sound
and
an a
dditive white Gaussian model is used
.
The
number of Monte Carlo runs is 100.
Figure 3:
Simulation output of the location estimation
using LS and proposed
WLS
methods
.
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
Sensor and Source Location
x coordinates
y coordinates
sensor location
actual source location
calculated source location (LS)
calculated source location (WLS)
Figure
4
.
RMSE in X

Coordinates V/S number of sensor nodes
Figure
5
.
RMSE
in Y

Coordinates V/S number of sensor nodes
F
IGURE
6
.
RMSE
IN RANGE
V/S
NUMBER OF SENSOR N
ODES
CONCLUSION
AND
FUTURE
WORK
In this paper, we estimated the location
sources in wireless
sensor networks. Two TDOA/RDOA

based location
algorithms are
developed.
The first Least Square (LS)
algorithm and the second method is
a new
proposed
weighted
Least Square (
N
WLS) which is an improved version of the
first algorithm
and traditionally used WLS estimator
.
The
second algorithm decre
ases the computational complexity
compare to the previous algorithm. Both this algorithms
shows
decrement
in the RMSE (
Root mean square error) with the
increase in no. of nodes and the results of NWLS
are more
accurate compare to LS and
attends the Cramer

Rao Lower
bound (CRLB).
As a future work
the work
can be extended
to multiple sources
and
for mobile source localization.
Also since the environment
is
line

of

sight (LOS) based schemes therefore investigating
the effect of non

line of sight on the joint estimation in future.
Also the work can be extended to other source types
, such as
RF and s
eismic signals, can also be included in the simulation.
A
CKNOWLEDGMENT
This research is supported by Ministry of Human Resource
and Development (MHRD) Government of India through
teaching assistantship.
.
R
EFERENCES
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Anita Panwar, Anish Kumar and Sh. Ashok
Kumar. Article: Least
Squares Algorithms for Time of Arrival Based Mobile Source
Localization and Time Synchronization in Wireless Sensor
Networks.
IJCA Proceedings on International Conference on Computer
Communication and Networks CSI

COMNET

2011
comnet(
1):97

101,
2011. Published by Foundation of Computer Science, New York, USA
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449, 7

8 Jan. 2012
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OURCE LOCALIZATION USING
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