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 Gajeon-ri Byeongcheon-myeon

Cheonan-City Chungnam Province, 330-708 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

: i-th estimated location of the node

j

x

: j-th 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 sub-blink 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 sub-blinks 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 sub-blinks. 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 sub-blinks when

we compare the performances each other. It is confirmed

that the more the number of sub-blinks 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 sub-blinks 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

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[4] J. Borras, P. Hatrack, and N.B. Mandayam, "Decision Theoretic

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[5] C. Ma, R. Klukas, and G. Lachapelle, "An enhanced two-step least

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[6]

P. Maybeck, Stochastic Models, Estimation and Control. New

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