Localization in 3D Sensor Networks Using Stochastic ... - Springer Link

2012, Vol.17 No.6, 544-548 Article ID 1007-1202(2012)06-0544-05 DOI 10.1007/s11859-012-0884-6

Localization in 3D Sensor Networks Using Stochastic Particle Swarm Optimization □ ZHANG Zhangxue1,2, CUI Huanqing3,4†

0

Introduction

1. Fujian Institute of Scientific and Technology Information, Fuzhou 350003, Fujian, China; 2. Fujian Strait Information Technology Co. Ltd. Fuzhou 350003, Fujian, China; 3. Shandong Computer Science Center, Shandong Provincial Key Laboratory of Computer Network, Jinan 250014, Shandong, China; 4. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, Shandong, China © Wuhan University and Springer-Verlag Berlin Heidelberg 2012

Abstract: Localization is one of the key technologies in wireless sensor networks, and the existing PSO-based localization methods are based on standard PSO, which cannot guarantee the global convergence. For the sensor network deployed in a three-dimensional region, this paper proposes a localization method using stochastic particle swarm optimization. After measuring the distances between sensor nodes, the sensor nodes estimate their locations using stochastic particle swarm optimization, which guarantees the global convergence of the results. The simulation results show that the localization error of the proposed method is almost 40% of that of multilateration, and it uses about 120 iterations to reach the optimizing value, which is 80 less than the standard particle swarm optimization. Key words: wireless sensor network; localization; stochastic particle swarm optimization CLC number: TP 393 Received date: 2012-06-11 Foundation item: Supported by the Fujian Province University-Industry Cooperation of Major Science and Technology Project (2011H6008) and the Natural Science Foundation of Shandong Province of China (ZR2009GQ002, ZR2010FQ014) Biography: ZHANG Zhangxue, male, Master, research direction: wireless sensor networks and information security. E-mail: [email protected] † To whom correspondence should be addressed. E-mail: [email protected]

The rapid development of wireless communications and electronics has triggered the large-scale applications of wireless sensor networks, and the location information is critically essential and indispensable in many of these applications; therefore, it is a key technology to obtain the location information. To localize a sensor network in the global coordinate system, most algorithms share a common feature that they need some special sensor nodes being aware of their positions as a prior, which are called anchors, and the other sensor nodes, which are called unknown nodes, measure the distances or angles to anchors to estimate their positions. The problem of localization can be formulated as a multi-dimensional optimization problem, which is solved by bio-inspired optimization methods such as genetic algorithm (GA) and particle swarm optimization (PSO) [1]. GA-Loc [2] is a GA based algorithm, which assumes that each unknown node can measure its distance from all its one-hop neighbors, and then GA estimates its location. A two-phase centralized localization scheme that uses simulated annealing and GA was presented in Ref. [3]. Another similar algorithm proposed in Ref. [4] addressed the flip ambiguity problem. These methods are all centralized, but distributed algorithms are more appropriate for the complexity and scalability issues in wireless sensor networks. The easy implementation and low memory requirement features of PSO make it suitable for highly resource constrained sensor network environments. A PSO-based localization scheme was proposed in Ref. [5].

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ZHANG Zhangxue et al : Localization in 3D Sensor Networks Using …

As an extension of this work, Ref. [6] used PSO for iterative node localization. A beaconless PSO-based localization method[7] employed both the deployment agent’s measurement and the neighboring nodes distance to construct the unknown node’s likelihood function of its exact position. The above methods are based on two-dimensional (2D) plane. However, wireless sensor networks are usually deployed over three-dimensional (3D) terrains in reality, and the localization methods in 3D are usually the extensions of those methods in 2D, whose localization errors are large. Moreover, the existing PSO-based localization methods are based on standard PSO, which cannot guarantee the global convergence. On the other hand, stochastic PSO (SPSO) can guarantee the global convergence, which is proved by many numerical experiments [8]. SPSO is widely used in many fields, such as mechanical design, bio-engineering, chemical engineering, and image processing and so on[9, 10]. Therefore, this paper presents an SPSO based localization method for 3D sensor networks, which can guarantee the global convergence.

1 Localization in 3D WSN with SPSO 1.1

Stochastic Particle Swarm Optimization PSO is a population based search algorithm based on the simulation of the social behavior of birds, bees or a school of fishes[11]. In this algorithm, a candidate solution is presented as a particle, which explores the search place to find the global solution. The ith particle consists of three D-dimensional vectors: the current position Xi, the previous best position Pi, and the velocity Vi. In addition, a vector Pg is the position of the best particle. Initially, a swarm of particles with random positions and velocities are generated in the search space, and then repeat the following loop until a certain criterion is met. In each iteration k, Xi and Vi of ith particle are updated using Eqs. (1) and (2). Vi (k + 1) = wVi (k ) + c1r1 ( Pi − X i (k ) )

+ c2 r2 ( Pg − X i (k ) )

X i (k + 1) = X i (k ) + Vi (k + 1)

(1)

(2)

where c1 and c2 are constants, and r1 and r2 are random numbers uniformly distributed in [0, 1], and w is the inertia weight to control the scope of the search. Because the standard PSO algorithm may obtain a local optimization solution, Zeng et al[8] proposed SPSO

that can guarantee the convergence to the global optimization with probability 1. In SPSO, w is set to 0 in Eq. (1), so the jth particle will stop evolution when Xj(k) = Pj = Pg. In this case, particle j randomly re-selects a position in the search space as Xj(k+1), while the other particles still evolves following Eqs. (1) and (2). 1.2 Problem Statement A wireless sensor network in 3D space consists of N sensor nodes, each having a communication range of R. The sensor nodes are composed of M anchors, which know their positions as a priori and N-M unknown nodes, which are the nodes to be localized. The objective of this study is to provide locations of unknown nodes as accurate as possible. Let ( xˆui , yˆui , zˆui ) and ( xui , yui , zui ) be the estimated and real coordinates of unknown node U i (i = M + 1, M + 2, , N ), and ( xai , yai , zai ) be the coordinate of anchor Ai (i = 1, 2,, M ). Suppose the distances between pairs of sensor nodes (including unknown nodes and anchor) can be measured by some technologies, such as time of arrival (TOA), time difference of arrival (TDOA) and received signal strength (RSS), an unknown node can estimate its location if it has at least 4 non-coplanar neighbors being aware of their locations. The localization error is defined as the distance between the real and estimated locations of an unknown node: eui =

( xˆui − xui )

2

+ ( yˆui − yui ) + ( zˆui − zui ) 2

2

(3)

As mentioned above, the position estimation of a given unknown node can be formulated as an optimization problem, involving the minimization of an objective function representing the localization precision. Let dˆ ij

be the noisy measured distance between U i and Aj, the objective function for localization problem is:

f ( xˆui , yˆui , zˆui ) = where dij =

( xˆ

ui

(

1 K  dij − dˆij K l =1

)

2

(4)

− xaj ) + ( yˆui − yaj ) + ( zˆui − zaj ) , and 2

2

2

K ＞ 4 is the number of neighboring nodes knowing their positions. 1.3 SPSO-Based Localization Method In this section, we propose 3D-SPSOIter, the localization algorithm based on SPSO for 3D wireless sensor networks. To use the particle swarm optimization, we need to determine the search space of each particle. Suppose the transmission range of the sensor node vi is a sphere of radius R, which is represented by its circumscribed cubic of side length R. Therefore, it can be

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Wuhan University Journal of Natural Sciences 2012, Vol.17 No.6

formulated as: svi = [ xvi − R, xvi + R ] × [ yvi − R, yvi + R ] × [ zvi − R, zvi + R ]

Algorithm 2 Localize(S, Ui)//Localize Ui in S using SPSO

(5) For an unknown node U i , the particle’s search space is defined as:

Generate particles pi, i=1,2,…,q inside S randomly

2.

for all pi do Compute f (pi) using Eq. (4);

3.

Pi pi;

4.

K

Sui =  svj

1.

(6)

j =1

where K is the number of neighboring nodes knowing their positions, and vi knows its position. Therefore, the localization is an iterative procedure. The unknown nodes having 4 neighboring anchor nodes at least are localized first, and the localized unknown nodes are referred to anchors to assist the localization of the other unknown nodes. This step is repeated until there are no unknown nodes to be localized. Now, we can give the localized algorithm using SPSO as Algorithm 1. This algorithm needs to call Algorithm 2 to localize an unknown node.

5.

end for

6.

Pgargmin{f(pi |0＜i＜q+1};

7.

prePgPg;

8.

Loop0;

9.

PgNum0;

10.

repeat

11. 12. 13. 14. 15. 16.

Algorithm 1 3D-SPSOIter

Compute f(pi) for 0＜i＜q+1

19.

Compute Pi;

20.

end for Compute Pg; if Pg=prePg then

2.

for all Ui, i=M+1, …, N do

22.

Get search space S using Eq. (6);

5.

Call Localize(S, Ui);

6.

end for

8.

repeat

9. 11.

Get search space S using Eq. (6);

14. 15.

25. 26. 27.

2 if it has k＞4 localized neighbors then

13.

24.

Pg NumPg Num+1; else Pg Num0; end if until Loop＞Ther1 or Pg Num＞Ther2

Simulations and Analysis

if Ui is not localized then

10. 12.

23.

end if

7.

Update pi using Eqs. (1) and (2) with w=0;

18.

Measure the distances between neighboring nodes;

4.

Regenerate pi in S; else end if

1.

if Ui has k＞3 neighboring anchors then

for i=1 to q do if f(pi)= f(Pi)= f(Pg) then

17.

21

3.

IterNumIterNum+1;

Call Localize(S, Ui); end if end if until no unknown nodes can be localized

In Algorithm 1, the unknown nodes owning 4 neighboring anchors at least are localized through lines 2 to 7, and the other unknown nodes are localized through lines 9 to 15 through the repeat blocks. Algorithm 2 initializes q particles in search space S in lines 1 to 5, and the optimal solution to Eq. (4) is computed through the repeat block. The repeat block is terminated when Loop＞Ther1 or Pg Num＞Ther2, where Loop is the number of loop, Pg Num is the occurrence number of equal Pg continuously, and Ther1 and Ther2 are thresholds of Loop and Pg Num, respectively.

To evaluate the localization performance of 3DSPSOIter, we conducted a simulation study to compare the performances of localization methods using multilateration, standard PSO and SPSO algorithms. The localization algorithms are evaluated by localization error and loop number. The simulation is performed in Matlab 7.0. There are 200 unknown nodes and 30 anchors distributed in a square of side length 100 m at random, and the transmission range of anchors and unknown nodes is 60m. Because any ranging technique has error, we set the ranging error e=0.05t, t=0, 1,  , 10. PSO and SPSO algorithms use 50 particles, and the parameters are Ther1=500, Ther2=100, and c1=c2= 1.8. Figure 1 shows that the localization error of each localization algorithm increases with the ranging error, but the localization error of multilateration increases faster than PSO-based algorithms. When e ≤ 0.15, the localization errors of standard PSO and SPSO methods

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ZHANG Zhangxue et al : Localization in 3D Sensor Networks Using …

propagation media and the heterogeneous properties of devices [12]. In 3D space, the radio irregularity is represented by degree of irregularity (DOI): Kθ ,α = if α = 0 or θ = 0  1,   Kθ −1,α + Kθ ,α −1 ± r × DOI, ∧ 0 ∧ 0 ∧ θ 180,∧ α  2 

Fig. 1

Average localization error with ranging errors

are similar, but SPSO-based localization algorithm is more accurate than standard based method when e ＞ 0.15. If e=0.5, the localization error of standard PSO based localization method is 56.66% of that of multilateration, and that of SPSO based algorithm is 40.51% of that of multilateration. The number of iterations of PSO algorithm reflects the efficiency of the localization methods. The localization method of less iteration occupies less resource, which makes it more feasible for the sensor network. As shown in Fig. 2, both standard PSO and SPSO based localization methods need about 30 iterations if e=0, but if e ＞ 0, the standard PSO based method needs more iterations than SPSO based method. SPSO needs about 120 iterations if e ＞ 0 while standard PSO needs more than 200 iterations. Therefore, localization algorithm using SPSO is more effective than standard PSO.

360

(7) where θ and α are the inclination and azimuth of a point in a spherical coordinate system, respectively. In our simulations, DOI=0.05t, t=0,1,  ,10. Figures 3 and 4 show that the localization errors and average number of iterations under different DOI are almost similar, but they increase with the ranging error.

Fig. 3 Average localization error with ranging errors and DOI

Fig. 4 Average number of iteration with ranging errors and DOI

Fig. 2

Average number of iteration with ranging errors

Furthermore, we evaluate the localization performance in the case of radio irregularity. In general, the radio irregularity is caused by the anisotropic properties of the

3

Conclusion

Localization is one of the key techniques of wireless sensor networks, and the node localization in 3D space is more complicated than that in 2D space. Particle swarm

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optimization algorithm has the advantages of easy implementation and quick convergence. In this paper, the localization problem in 3D WSN is formulated as an optimization problem, and stochastic PSO algorithm is utilized to solve this problem. The simulation results show that our proposed method is more effective than those based on multilateration and standard PSO.

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[7]

Low K, Nguyen H, Guo H. A particle swarm optimization approach for the localization of a wireless sensor network [C]

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