Localization Of Source In Wireless Sensor Networks

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Nov 21, 2013 (3 years and 4 months ago)

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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

[1]

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

[2]

Panwar, Anita; Kumar, Sh. Ashok; , "Localization Schemes in Wireless
Sensor Networks,"

Advanced Computing & Communication
Technologies (ACCT), 2012 Second International Conference
on

, vol.,
no., pp.443
-
449, 7
-
8 Jan. 2012

doi:10.1109/ACCT.2012.6.

[3]

Zhetao Li, Renfa Li, Yehua Wei and Tingrui Pei, “Survey of
Localization Techniques in Wireless Sensor Networks,” Information
Technology Journal 9(8): 1754
-
1757, 2010

[4]

Tan Kok Sin Stephen
, “
S
OURCE LOCALIZATION USING
WIRELESS SENSOR

NETWORKS
,”

june, 2006
.

[5]

J. O. Smith and J. S. Abel, “Closed
-
Form Least
-
Squares Source
Location Estimation from Range
-
Difference Measurements,” IEEE
Transaction on Acoustics, Speech, and Signal Processing, Vol.
ASSP
-
35, No. 12, pp. 1661
-
1669, December 1987.

[6]


C. H. Knapp and G. C. Carter, “The generalized correlation method for
estimation of time delay,” IEEE Transaction on Acoustics, Speech, and
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24, No. 4, pp. 320
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327, August 1976.

[7]

K
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-
Based Bearing
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Vol. 42, No. 2, pp. 525
-
536, April 2005.

[8]

A. A. Ahmed, H. Shi, and Y. Shang, “Sharp: A new approach to relative
localizatio
n in wireless sensor networks,” in
Proceedings of IEEE
ICDCS
, 2005.


10
20
30
40
50
60
70
80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
no of nodes-->
R M S E in x-cordinate(m)-->


rms-x-LS
rms-x-WLS
10
15
20
25
30
35
40
45
50
55
60
0
0.5
1
1.5
2
2.5
3
3.5
4
no of nodes-->
R M S E in y-coordinate(m)-->


rms-y-LS
rms-y-WLS
10
20
30
40
50
60
70
80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
no of nodes-->
R M S E in range(m)-->


rms-r-LS
rms-r-WLS