AWCL:Adaptive Weighted Centroid Target Localization Algorithm Based on RSSI in WSN Yanjun Chen, Quan Pan, Yan Liang and Zhentao Hu Institute of Control & Information College of Automation Northwestern Polytechnical University Xi'an Shaanxi 710072 Email:
[email protected]@
[email protected]
Abstract-Target localization and tracking is the canonical application of Wireless Sensor Networks. Unlike a centralized system, a sensor network is subject to a unique set of resource constraints such as limited on-board battery power and limited network communication bandwidth. So the traditional tracking algorithm can be directly nsed in WSN. Therefore efficient localization algorithms that consume less energy for computation and less bandwidth for communication are needed. The weighted centroid localization algorithm (WCL) based on RSSI is applied in most of actual systems. Only one uniform path loss exponent obtained through experiments is used to calculate the weights of nodes in general WCL. It is well known that the path loss exponent is the essential reflection of sensing surroundings. The actual sensing scenario can't be revealed in the traditional WCL algorithm, and therefore it is not appropriate that only one exponent is accepted all through the area covered by the sensor nodes. A new algorithm, adaptively weighted centroid localization (AWCL), is proposed in this paper. Firstly a more reasonable path loss exponent is adaptively estimated according to the surroundings where the target nodes situates. Secondly the target position will be calculated by using the weighted centroid method in which exponents estimated in the first stage are adopted. Theoretical analysis are presented to demonstrate the performance of the proposed localization method, the simulation results show that that the proposed algorithm outperforms the general WCL algorithm. Keywords-Wireless Sensor Networks, Weighted Centroid Lo calization, path loss exponent.
I. INTRODUCTION The wireless sensor networks is composed of distributed networked sensors perceiving the surroundings[l]. A sensor network is designed to perform a set of high-level information processing tasks such as detection, tracking, or classification. However, unlike a centralized system, a sensor network is subject to a unique set of resource constraints such as limited on-board battery power and limited network communication bandwidth. Each sensor node communicates wirelessly with a small number of local nodes within the radio communication range. So the traditional tracking algorithm can be directly used in WSN. Therefore efficient collaborative signal process ing algorithms that consume less energy for computation and
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less bandwidth for communication are needed[2], [3]. Target localization has found in numerous applications. In sonar signal processing, the focus is on locating underwater target using an array of hydrophones[4]. In forest fireproofing application, its destination is to locate the firing location. The important task is to find the mineworker station being buried in coal mine safe system. Some localization methods make use of three types of physical measurements: time delay of arrival (TDOA)[6], direction of arrival (DOA)[5], and received signal strength Indicator (RSSI)[7]. It is known that the intensity of signal attenuates as a function of distance from the source. Using this property, a RSSI-based indoor localization system named RADAR has been reported recently for locating target node[8].In this paper, we focus on the task of target location estimation based on RSSI in a wireless ad hoc sensor network. The localization techniques range from the coarse grained one to the fine grained one. Bulusu et al. proposed a coarse grained localization algorithm, which needs only a minimum of computation, called Centroid Localization (CL)[9]. In CL , suppose all the nodes know their location, target nodes position should be calculated as the centroid of the nodes' position within their communication range. This algorithm can be outperformed by the Weighted Centroid Localiza tion ( WCL) which uses the RSSI respectively to quantify the nodes in range and emphasizes the nearest one[IO]. In the traditional WCL method, the weight is calculated with the uniform attenuation exponent[7], [10], [11]. But this is not reasonable because the exponent has relations with the concrete surroundings. so a novel algorithm named adaptive WCL (AWCL) is proposed in this paper. First a more rational attenuation exponent is adaptively identified according to the surroundings where the target stay. Then the target position will be calculated by the use of the weighted centroid method. The remainder of the paper is organized as follows. In Section n, First of all three basic propagation mechanisms is introduced, then complying with the surroundings the most appropriate exponent is identified by the least squares error (LSE) or maximum likelihood (ML), finally the description of the main idea of the proposed AWCL algorithm is pro posed. After that the simulation environment and the result are discussed in Section Ill. Finally Section IV closes with conclusion and future work.
II. A DAPTIVE WEIGHTED CENTROID LOCALIZATION ALGORITHM BASED ON RSSI
reference distance which is determined from measurements close to the transmitter. and is the T-R separation distance. is a zero-mean Gaussian distributed random variable with standard deviation 8. The value of a depends on the specific propagation environment. For example, in free space, a is equal to 2, and when obstructions are present, a will have a large value. The reference distance for practical systems is typically chosen to be 1m in indoor environments and 100m or 1km in outdoor environments. The reference signal strength is calculated using the free space formula given by Equation (1) or through field measurements at distance In this paper, the reference distance is set to be 1m, so the theory value 2 of D 0 IS (411yrL . . equal t0 PtGtGr>.
d
v
A. The Radio Propagation Model
Radio Propagation Model places fundamental limitations on the performance of localization systems. Propagation models have traditionally focused on predicting the average received signal strength at a given distance from the transmitter, as well as the variability of the signal strength in close spatial proximity to a particular location[12]. This part presents a number of common models used to characterize the radio propagation property. The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line of sight path between them. This free space power received by a receiver antenna which is separated from a transmitter antenna by a distance is given by the free space equation P. = (1)
do
rr(d)
Pr(do)
B. The Path Loss Exponent Identification
The value of path loss exponent a depends on the spe cific propagation environment. When the target situated in the different situation, the value of a is always different. Furthermore the value of a will impact on the localization result. So the attenuation coefficient should be identified when the circumstance surrounding the target varies. In this part, two identification methods for radio signal path loss exponent are given out, one is based on Least Square Error (LSE), the other is based on Maximum likelihood (ML)[13]. The vale of reference distance is set to be 1m, so at k time instant the received RSSI by sensor node i with a distance from the transmitter can be expressed as
do
di
pr(�, t)(d(tk)) = Pr(dao) + v\tk) (d�k))
(2)
Gt,Gr
ht
where has the same meaning of free space model, is the height of the transmitter and is the height of the receiver. The received power falls off with distance raised to the fourth power. This is a much more rapid path loss than is experienced in free space. All the above propagation models don' t take into account the specific surrounded environment. So practical propagation model is now presented. The third model is path loss normal shadowing model. The average signal strength for an arbitrary T-R separation is expressed as a function of distance by using a path loss exponent, a, affected by the surrounding environmental clutter
hr
(do) r(d) = Pr + v
P.
(3)
(tot
do,
The close-in reference distance the path loss exponent n, and the standard deviation 8 statistically describe the path loss normal shadowing model for arbitrary location having a specific T-R separations. and this model may be used in com puter simulation to provide received power level for random locations in communication system design and analysis. In this paper, we use path loss normal shadowing model for analysis and simulation of the complex application environments, the path loss exponent a and reference signal strength should be fixed on according to the specific surrounding.
d, tGtGr>. 2 r(d) P (4'llldL2 where Pt is the transmitted power, Pr(d ) is the received power which is a function of the T-R separation,Gt is the transmitter antenna gain, Gr is the receiver antenna gain, dis the T-R separation distance in meters, L is the system loss factor not related to propagation (L 2: 1), and>. is the wavelength in
meters. In a radio channel, a single direct path between the trans mitter and receiver is seldom the only physical means for propagation, and hence the free space propagation model of Equation (1) is in most cases inaccurate when used alone. The two-ray ground bounce model is a useful propagation model that is based on geometric optics, and considers both the direct path and a ground reflected propagation path between transmitter and receiver. This model has been found to be reasonably accurate for predicting the signal strength, it can be expressed as
do.
do
(4)
p;�)(d�k)) is the signal strength received by sensor node i with a distance d �k) from the transmitter at k time instant, Pr(do), v�k) has the same meaning of the Path Loss Normal where
a,
Shadowing Model. The time index k is omitted in the interests of brevity, so Equation (4) can be rewrite as (5)
Zi, di, S (d o) Pr .
where
has the same meaning of
p;,�)(d�k)), d�k),
I) Least Square Error Identification: This method fits the scenario that the target nodes will be localized passively, that is to say, the target nodes receive signal from the nearby nodes. Let n denote the average neighbor node number of sensors
where a is the path-loss exponent which indicated the rate at which the path loss increases with distance, is the
do
332
Rewrite Equation (7) using the matrix form
•
Ig Zl,m Igz ,m 2
1 1
- lgd m" - lgd,m 2
19z,m n
1
- lgd,m n
[ 1[
•
d
set
•
Z
D
C
H
(a) LSE Identification
X V
d!l
[
j
- logdl,m 2 - logd,m
n - logd,m d!l log8m a f d!l [ log V I logv2
Fig. I.
ML Identification
logz,m n ]T
1
logv3f (8)
(HT H) - Iis
a full
Algorithm Sketch
•
each node knows itself location, and furthermore sensors node surrounding the target are in the same environment. n 2: 3, that means one sensor node can be detected by at least three nodes at any instant.
•
each node knows itself location, and furthermore sensors node surrounding the target are in the same environment. n 2: p 2, that means if the dimension of sensing area is two, target node can be detected by at least four nodes at any instant.
+
As shown in Figure 1(b), the target node is detected by the nearby seven sensor nodes named A, B," ', G, Because target node are position-unknown, so the distance are unknown also. Let M be the number of target nodes in the sensing field being covered by the n sensor nodes, be an unknown p x 1 vector denoting the position vector of the mth target node; and be a given p x 1 vector denoting the position vector of the ith stationary sensor, so Equation (5) can be rewrite as
d,1d,2 . . .,d7
As shown in Figure l(a), the target is detected by the nearby seven sensor nodes, and each node can communicate with not less than three sensor nodes, for example, node named A can talk with sensor nodes named B, C, D. Because nodes are position-known, so the distance are also known.
Pm
dl, d2, d3
r i
According Equation (5), we can get
8 i fori = 1· ..n Zi,m = (d� ,mm )a + V
X is the estimated value of the path
2) Maximum Likelihood Identification: This method adapts to the scenario that the target nodes will be localized actively, that is to say, the target nodes transmit signal to the nearby nodes. Let n denote the node number of sensors node with themselves in the target node communication range, and p denote the dimension of the location coordinates .. Suppose
node with the target node in their communication range, M denote the number of target nodes in the sensing field being covered by the n sensor nodes. Suppose
(6)
Zi,m
Zi,m
where is RSSI received by the ith sensor node, be ing influenced by the mth target node at k time instant, are zero mean independent Gaussian random variables. so rv
[ 1
(9)
(b)
V i N(0 ,82)
[
Z = HX + V
The second element of loss exponent.
•
]
It is obvious that Rank(H) 2: 2, so rank matrix. The result X of LSE can be get
B
•
IgVl Ig8m + Ig V2 a : Igv3
d!l [ log Z I ,m 2 ,m logz
so
A
1
8m i (d� ,m )a + V 8m i for' = 1···n lil a +V P II m - r 2
z i '%
(10)
where is RSSI received by the ith sensor node, be in% influ�nced by the mth target node at k time instant, ) are zero mean independent Gaussian random variables.
v i
333
rv
N(O ,82)
Let us now define the following matrix notations.
d!! [ Zl,m/a Z,2m!.a 1 2 G d!! diag [ ';1 .1. (12 Z
D d!!
1
8 d!! 8m H d!! GD e d!! [6
] ]T
..1... (1n
1
""k
d�,k
[ d�'k
�
Zn'm!.an
These conditions lead to the following set of relations:
]T
6
.
..
en f
where
(11) The joint probability density function of expressed as
f (Z 10)
n
=
{1
( 211T"2 exp -2(Z
Z then can be
- H8)
T (Z - H8) }
a
(12)
p� f Pm
l (0)
=
li Z - GD8112
(13)
Thus, the maximum likelihood parameter estimation of be obtained by minimizing (0).
l
0 can
Equation (13) is a nonlinear least square cost function because the matrix D that contains n elements is a nonlinear function of the mth unknown target node coordinates P is the dimension of the location coordinates. The vector S also contains one unknown parameter 8 , that is the mth target node RSSI 8 received at reference distance. The path loss exponent a is a unknown variable that we want to identify . Since there are p + 2 unknown parameters, there must be at least or more p + 2 sensors reporting RSSI readings to yield a unique solution
Pm ,
m
m
To minimize where
l (0), the solution must lie on a stationary point 8l (0) 8pm 8l (0) 88m 8l (0) 8 a
1
(1",
(15)
)
(16)
)
Equations (14) , (15) and (16) can be used together to yield an iterative solution similar to the E-M algorithm. With this solution, we assume the source intensity is the missed data rather than unknown parameter. We initiate the mth unknown target node location and the path los exponent a at the beginning. During the iteration, we estimate the missed data according to (14), and then, we maximize the log-likelihood function using (15) and (16) to get the updated estimation of and a. The iteration keeps on going until convergence. This ML algorithm has much more computation complexity compared to the LSE solution.
8m
Pm
C. Adaptive Weighted Centroid Localization Algorithm
is the vector of unknown parameters. is the mth source location, and 8 is the mth source energy. The negative log likelihood function is proportional to a quadratic form
m
=
(14)
Pm
where
0= [ 8
(
8m 'Yi ad .t ,im+ cx 2 Zi,m - � 't,m
1)
'"
(
1
o
where N(O, are independent Gaussian random vari ables. Using these notations, Equation (10) can be represented as
ei
n ii E 'Y i=l T n i E 'Y i=l n 8m L ad .'t,mcx+1 Zi,m - a .'t,mC!' d 't t i=l
o o o
334
Suppose that the node has the circle communication area within which it can communicate with other nodes, The centroid localization algorithm which can be performed on each target node uses the location information of all nodes in its own range to calculate its position as the centroid. Let ( X, be the position of mth target given by its two dimensional coordinates, let be the known position of ith node, 8 be the number of sensor nodes with the target node in their communication range (LSE identification scenario) or with themselves in target node communication range (ML identification scenario), the formula shuld be represented as
Pm
y)
Bi(x,y)
Pm ( x,y)
=
s
1 LBi(x,y) S
i=l
(17)
The low accuracy in location estimation of CL has motivated the development of WCL. WCL introduced the quantification of the nodes depending on their distance to the target node. The aim is to give more influence to those nodes which are nearer to the target. As the RSSI as well as LQI (Link Quality Indicator) also increases with a decreasing distance it is selected as an appropriate quantifier.But RSSI is different when the environment is change, that means the same RSSI can't assure the same distance, so the weights is different too. So when we localize the target using only the RSSI, the error is large. Therefore we use the distance from the node to target node to valuate the weight of each node. The basic idea of WCL, published in [10], is to quantify each node position with a quantification function that uses the
distance from an target node to each node in communication range. The quantifier is described as shown in (18), where describes the quantification for ith node used by mth target node. The distance between ith node and mth target node is given by and 9 symbols a degree.
W ,im
d,im
W ,im where
d,im
=
1
TABLE I THE PATH LOSS EXPONENT
I
y(m)\x(m) o
20
rv
(18)
(d,m ot ) 9
20
rv
40
may calculate using Equation (6) or (10)
d,im
=
( m )1 �,mt Z
fa
40
(19)
8m
The value of a and in Equation (19) should be estimated using the LSE or ML identification algorithm expatiated in second part of Section II. At the time that the target nodes traverse through the boundary of two different environments, some boundary detection method should be invoked to an nounce that the target node will enter into a new scene, so the value of a and will be calculated again. So the weight calculated by Equation (18) will vary adaptively according the surroundings that the target node situates in, and target nodes will be localized using WCL method. This is the reason that this algorithm is named Adaptive Weight Centroid Localization (AWCL). Using this quantification the CL Equation (17) has been expanded for WCL as shown in Equation (20).
60
80
=
rv
80
100
=
The sensing area is 100m x 100m square area which is partitioned into 25 subareas. One hundred nodes whose communication range is 10m are randomly deployed in this region. Let 8, the RSSI received at the reference distance for each sensor node, be 5000J, and N(O, 10 2 . Two simulation scenarios are given to demonstrate the performance of AWCL. In the first scenario there are two targets each carrying a sensor node traveling through the area diagonally, while there are only one target node traversing across the area round about in the second scenario. The path loss exponents in these subareas are different each other. When the target nodes are situated in one subarea, the path loss exponent is estimated using LSE and ML methods. Then the target nodes should be localized using the WCL approach. From Table(I), the performance of these two estimation methods is comparative almost, so their localization errors are always identical. The localization result of target nodes using AWCL, as shown in Figure (2), is given to illustrate these sensing scenarios. A performance indicator should be proposed to show that AWCL
)
I
20
rv
40
2.293
I
40
rv
60
2.028
I
60
rv
80
1.591
I
80
rv
100
1.588
2.181
2.158
1.498
1.590
1.658c
2.056
1.986
1.551
1.540
2.216
2.399
2.060
1.785
1.992
2.158
2.245
2.268
1.651
1.853
2.096
2.058
2.185
1.689
1.874
2.051
1.691
2.347
2.065
1.697
2.154
1.584
2.256
2.025
1.856
2.251
1.542
2.248
2.256
1.842
2.133
2.166
1.758
1.966
2.151
2.059
2.158
1.709
1.856
2.056
2.156
2.147
1.689
1.810
2.098
1.821
1.947
1.955
1.848
1.770
0.758
1.845
1.845
1.842
1.759
1.795
1.843
1.922
1.843
1.789
bEstimation using LSE method cEstimation using ML method
p(X
III. SIMULATION AND RESULTS
rv
20
=
i� I Xt - Xt l 1 2 N
(21)
where Xt, Xt is the estimation and true position of target node at tth time instant, N is the simulation number. The cumulative probability of RMSE is defined as
An appropriate value for 9 was found in one. By the way, WCL with 9 0 is equal to CL. In this paper, the value of 9 is set to be equal one.
V i
rv
1.701" 1.652b
RM8Et
(20)
___
0
is better than the traditional WCL in terms of the localization accuracy. The RMSE of target nodes localization, which is represented as Equation (21), is given to illustrate the performance of AWCL
s
Pm ( X,y)
rv
60
'True Value
8m
,imBi(X,y) 2: W .:...i= -= l'--:S:-2: ,im i=lW
rv
I
::; x o)
=
ro f( x)dx
io
(22)
where is the density function of RM8E. The result for above two scenarios is illustrated as Figure (3). As shown in the Figure 3(a), the probability that RMSE is less than 3m is increased from 50 percent to nearly 80 percent for first target node, while from 60 percent to nearly 80 percent for second target node in the first. W hile in second scenario, from the Figure 3(b), the probability that RMSE is less than 3m is increased from almost 55 percent to nearly 85 percent. This means the localization result using AWCL have better accuracy than that using WCL.
f( x)
do
IV. CONCLUSION AND FUTURE Weighted centroid algorithm is a simple mathematical ap proach of target localization algorithm, but when the envi ronment is complex, its performance is greatly affected when using only a path loss exponent throughout all the sensing area. In this paper the adaptive weighted centroid localization algorithm is propose using the reasonable exponent estimated throught LSE and ML methods to achieve good localization
335
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Cumulative Probabilty of RMSE for Target Nodes Localization
Sensing Scenario of Wireless Sensor Networks
performance. But the complexity of this approach is high, so how to reduce the complexity of the algorithm and save the cost of localization algorithm is a common problem. Furthermore localization using RSSI is not practical in some applications, so we want to seek localization approach using the acoustic signal in future. REFERENCES [1] I. F. Akyildiz,W. Su,Y. Sankarasubramaniam,and E. Cayirci, "Wire.. less sensor networks: a survey," Computer Networks-the International Journal of Computer and Telecommunications Networking,vol. 38,pp. 393..422,1990..03-01 2002. [2] Z. Feng, S. Jaewon and 1. Reich, "Information.. driven dynamic sensor collaboration," Signal Processing Magazine, IEEE, vol. 19, pp. 61..72, 2002. [3] Z. Feng, L. Jie, L. Juan, L. Guibas, and 1. Reich, "Collaborative signal and information processing: an information-directed approach," Proceedings of the IEEE,vol. 91,pp. 1199 .. 1209,2003. [4) A. Tolstoy, Matched field processing for underwater acoustics: World Scientific Singapore,1993.
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[5) L. G. Taff, "Target localization from bearings..only observations;' Aerospace and Electronic Systems, IEEE Transactions on, vol. 33,pp. 2..10,1997..01..01 1997. [6) c.w. Reed,R. Hudson,and K.Yao,Direct joint source localization and propagation speed estimation,in Proc. ICASSP,Phoenix,AZ,1999,pp. 1169Cl172. [7) K. Benkic,M. Malajner,P. Planinsic,and Z. Cucej, "Using RSSI value for distance estimation in wireless sensor networks based on ZigBee," in Systems, Signals and Image Processing, 2008. IWSSIP 2008. 15th International Conference on,2008,pp. 303..306. [8] P. Bahl and V. N. Padmanabhan, "RADAR: an in ..building RF-based user location and tracking system," in INFOCOM 2000. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings.IEEE,2000,pp. 775-784 vol.2. [9) Nirupama Bulusu, John Heidemann, and Deborah Estrin. GPS..less low cost outdoor localization for very small devices. IEEE Personal Communications Magazine,7(5):28C34,October 2000. [10) Jan Blumenthal, Ralf Grossmann, Frank Golatowski, and Dirk Tim.. mermann. Weighted Centroid Localization in Zigbee..based Sensor Net .. works. In IEEE International Symposium on Intelligent Signal Process.. ing,WISP 2007,Madrid,October 2007. [11] R. Behnke and D. Timmermann, "AWCL: Adaptive Weighted Centroid Localization as an efficient improvement of coarse grained localization," in Positioning,Navigation and Communication,2008. WPNC 2008. 5th Workshop on,2008,pp. 243-250. [12) T. S. Rappaport,Wireless communications: principles and practice 2nd Edition: Prentice Hall PTR New Jersey,2002. [13] S. Xiaohong and H. Yu..Hen, "Maximum likelihood multiple.. source localization using acoustic energy measurements with wireless sensor networks," IEEE Transactions on Signal Processing, , vol. 53, pp. 44.. 53,2005.
