Cooperative Localization Algorithm
for Sensor Node in Wireless Sensor Networks
Chulgyu Kang, Hyunjae Lee and Changheon Oh
School of Information Technology, Korea University of Technology and Education
308 Gajeonri Byeongcheonmyeon
CheonanCity Chungnam Province, 330708 Korea
Abstract The wireless localization in sensor network is a
work deciding a location of a sensor node. It is necessary to
perform the important role such as the geometrical routing,
tracking and the detecting based on localization. In this paper,
we propose a cooperative localization algorithm to estimate a
location of the sensor node in wireless sensor network over
LOS signals and NLOS signals environment and analyze the
error performance of the estimated location. The proposed
algorithm gets each location coordinate using all received
signals because it is difficult to identify NLOS signals due to
the all received signals. After eliminating the estimated
locations from the NLOS signals iteratively, we decide a
location of the sensor node with LOS signals. We apply TDOA
method which uses arrival times to estimate the location and
make a group with three readers to get the location
information as much as possible. From the results, we confirm
that the elimination of the reasonable number of the estimated
NLOS location improve the estimation error performance.
I. I
NTRODUCTION
According to develop the technology of the wireless
sensor network, in the near future, the localization service
will be used in the almost everywhere. The first step for
supplying this service is the finding a correct location of the
sensor node. If we use a GPS (global positioning system)
system, it is very easy work finding a precise location.
However, it is supposed to give a lot of load economically
setting up a GPS receiver to each sensor node and difficult
to use GPS system in a heavy rain forest or an inside
building where the GPS signal cannot be received.
Therefore, we use TDOA (time difference of arrival), TOA
(time of arrival), and TSOA (time sum of arrival) methods
to estimate a node location in a wireless sensor network. It
starts from this assumption fundamentally that those
methods use the received signal propagated through LOS
(line of sight) path[1],[2].
In real wireless sensor network, the precise location
estimation is effected by many factors such as Gaussian
noise and delayed signals propagated through NLOS (non
line of sight) path. The estimation error of Gaussian noise is
an error occurred by the thermal noise at location estimation,
but it can be overcome as a high SNR (signal to noise ratio).
The estimation error of NLOS signal is happened by using
the delayed signal which is blocked by many obstacles such
as buildings and guideboards during the propagation.
Between the both factors, the signal propagated through
NLOS path brings the depth estimation errors.
The research identifying NLOS signals has reported to
reduce the estimation error. The idea is to find some distinct
properties of NLOS signal distribution and develops
hypothesis tests to segregate NLOS signals from LOS
signals. Especially, Wylie and Holtzman observes that
NLOS signals have greater variance than the variance of
LOS signal distribution, and develops a hypothesis test to
identify NLOS signals based on a consecutive sequence of
range measurements[3][4]. However, the statistical
information is needed in this method.
In this paper, we don’t need any primitive knowledge
about NLOS signal, and, in this presupposition, we propose
a cooperation location estimation algorithm to reduce the
estimation error. The paper is organized as follows. Section
Ⅱ is devoted to introduce the system architecture. Section
Ⅲ explains the NLOS error model, and simulation results
and conclusions are presented in Section Ⅳ and
Ⅴrespectively.
II. S
YSTEM
M
ODEL
The estimated location of the sensor node is affected lots
of factors. In those factors, NLOS signals give a depth effect
to estimate a precise location. Therefore, the elimination is
necessary to estimate a precise location. In this section, we
estimate a node location with the all signals, LOS and
NLOS signal, and then explain the decision mechanism of
the final location of a node with LOS signals eliminating
NLOS signal iteratively. If there is no information with
respect to a NLOS sensor node, we can eliminate the
estimated NLOS signals depicted in Figure 1, and Figure 2
shows the deciding process of the proposed algorithm.
Figure 1. Location decision algorithm.
Figure 2.
Deciding process of the proposed algorithm.
For estimating a location of the node, we need at least 3
readers (
3≥N
) receiving a signal from a node and sending
the time information to the server, so the number of the total
estimated locations is decided according to the number of
the total readers, N, and the number of readers participating
in a location calculation. For instance, if the number of the
total readers is 5,
5=N
, there are 16 eligible candidates.
One could choose all 5 possible readers, or select 4 out of 5,
or select 3 out of 5. That is,
1. Select 5 out of 5 :
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
5
5
1 estimated location
2. Select 4 out of 5 :
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
4
5
5 estimated locations
3. Select 3 out of 5 :
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
3
5
10 estimated locations
In this paper, there are eight readers to estimate locations,
and three readers participate in a location calculation at one
time. Therefore, there are 56 estimated locations then, in
among them, we identify the estimated locations which are
the signal propagated through NLOS path. We need the
central location to separate NLOS signals, so the central
location is decided by equation (1).
( )
∑∑
∈ ∈
−=
all
Si
all
Sj
2
.min arg
~
ji
xxx
(1)
⋅
: the norm operation over a vector
ji
xx
−
: Euclidean distance between
i
x
and
j
x
S
: the nodes index set
i
x
: ith estimated location of the node
j
x
: jth estimated location of the node
x
~
: accumulated Euclidean distance
After deciding the central location, we calculate the range
from the decided central location to an estimated location,
which uses only LOS signals when it is estimated, to
identify NLOS signals as equation (2). If the estimated
locations pass over the range of equation (2), they are
presumed that the estimated locations are used NLOS
signals and eliminated from the next calculation, this range
calculation is iteratively performed to an optimum threshold.
( )
.
minarg
~
~
2
SSize of
x x
x R
all
Si
all
Sj
ji
∑∑
∈ ∈
−
+=
(2)
III. NLOS
D
EGRADATION
NLOS error depends on the propagation environment and
changes from time to time, but at each time instance, NLOS
can be considered as a constant. We can estimate the value
of NLOS error when there are enough readers available to
determine the sensor node.
We write the TDOA hyperbolic equations as
.
1 iiii
e nR R Ct
+
+
−
=
(3)
Where C is the speed of light,
i
t
is the measured TDOA
between reader
i
and
1
,
i
R
is the distance between the
sensor node and reader i,
1
R
is the distance between the
sensor node and reader 1,
i
n
and
i
e
are the TDOA
measurement noise and NLOS error, respectively. We
assume that
i
n
is a Gaussian random variable with zero
mean and variance
i
σ
. For NLOS readers,
i
e
is a positive
random variable with mean
nlos
μ
and variance
nlos
σ
. We
further assume that
inlos
σ
σ
>
, which is consistent with
field test results[5].
To derive the ML (maximum likelihood) estimator for the
NLOS contaminated TDOA, we first derive the probability
density function of the sum of the Gaussian noise
i
n
and the
exponentially distributed NLOS error
i
e
with mean
λ
1
=
杩癥渠批=
=
=
.
σ
λσx
erf e
λ
f
i
i
λσ
xλ
en
i
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
+
2
1
2
2
2
2
(4)
Where
(
)
⋅
erf
denotes the error function. Rewrite
equation (4) and (5) in a matrix from
V. H L
+
=
(5)
where
(
)
T
N
R,R, R, R RRRH
11312
−−−=
L
,
,tCL
2
(
=
†
T
N
, t, t
)
3
L
,
( )
t
NN
enenenV +++=, , ,
3322
L
.
Maximizing the conditional joint PDF
(
)
(
)
.xHLfLf
v
x −=
(6)
( )
( )
.
2
exp
2
1
2
1
2
2
21
1
2
2
2
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
−
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+=−
∏
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−
i
i
N
i
i
i
i
λσ
xλ
V
RRCt
σ
λσx
erf e
λ
xHLf
i
σ
σπ
(7)
Under the assumption that
i
n
and
i
e
are independent
random variables, we derive equation (7).
IV.
S
IMULATION AND
R
ESULTS
In this chapter, we simulate the proposed algorithm with
total eight readers, three readers make one group for
estimating the location of the sensor node in 300m×300m
area to verify the error performance.
Figure 3. Estimation error performance according to the number of iteration.
Figure 4. Estimation error performance according to the number of blink.
We assume that the system uses TDOA method as a
localization method, and there are subblink signals of the
sensor node from one to eight. In addition, both LOS and
NLOS signals are existed between the sensor node and
readers. When we estimate a location, we change the
number of NLOS signals to inspect the estimation error
performance according to the number of NLOS signals.
Figure 3 shows the estimation error performance
according to the number of subblinks and the number of the
eliminations of the estimated locations owing to NLOS. The
estimation error performance is the worst because one of the
reader in a group of readers uses NLOS signals. When we
analyze the performance with NLOS NUM=4, the
estimation error is decreased according to increasing the
number of the iteration. However, the estimation error is
increased even though the number of the iteration is
increased at NLOS NUM=5 and NLOS NUM=6. It is
caused that the number of the estimated locations with LOS
signals is very few.
Figure 4 shows the error performance according to the
number of subblinks. The estimation error performance is
increased according to the number of iterations at NLOS
NUM=5, the same result as figure 2. However, under NLOS
NUM=4, the estimation error performance is increased until
3 iterations. It is also caused that the number of the
estimated locations with LOS signals is very few. In
addition, the estimation error performance is decreased
according to increasing the number of the subblinks when
we compare the performances each other. It is confirmed
that the more the number of subblinks is increased, the
more the number of the estimated location is increased, so
the number of the estimated location with LOS signals is
increased.
V.
C
ONCLUSION
In this paper, we propose an algorithm which decides the
sensor location with the signals propagated through LOS
path after eliminate the signals propagated through NLOS
path iteratively from the all estimated locations. We apply
TDOA method which uses arrival times to estimate the
location, and, to estimate a location coordinate, we make a
group with three readers to get the location information as
much as possible.
From the results, we confirm that the number of sub
blinks gives effects to the estimation error performance
because the more the number of subblinks is increased, the
more the number of the estimated location is increased, and
the elimination of the reasonable number of the estimated
NLOS location increase the estimation error performance.
Therefore, we need to investigate on the number of the
elimination of the estimated location as NLOS path to
enhance the error performance of the proposed algorithm
after this work.
R
EFERENCES
[1] PiChun Chen, “A nonlineofsight error mitigation algorithm in
location estimation,” IEEE Wireless. Communications and
Networking Conf., pp. 316320, Sep 1999.
[2] B. Ahmed, K.Tsuji, “Mobile location estimator with NLOS mitigation
using Kalman filtering,” IEEE Wireless Communications and
Networking, pp. 19691973, Mar 03.
[3] M.P. Wylie, and J. Holtzman, "The NonLine of Sight Problem in
Mobile Location Estimation," 5th IEEE Int. Conf. Universal Personal
Communications, vol. 2, pp. 827831, Sep 1996..
[4] J. Borras, P. Hatrack, and N.B. Mandayam, "Decision Theoretic
Framework for NLOS Identification," 48th IEEE. Vehicular
Technology Conf., vol. 2, pp. 15831587, May 1998..
[5] C. Ma, R. Klukas, and G. Lachapelle, "An enhanced twostep least
squared approach for TDOA/AOA wireless location," Proc. IEEE
ICC 2004, vol.2, pp.987–991, May 2003.
[6]
P. Maybeck, Stochastic Models, Estimation and Control. New
York: Academic, 1979, vol. 1.
.
[7] N. Thomas, D. Cruickshank, and D. Laurenson, “Performance of a
TDOAAOA hybrid mobile location system,” in Second
International Conference on 3G Mobile Communication Technologies,
pp. 216–220, March 2001..
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