THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS Vdume 14, Issue 1, March 2007

GUO Li, GUO Yan, LIN Jia-ru, LI Ning

Ad-hoc network DOA tracking via sequential Monte Carlo filtering CLC number TN911.23 Document A Article ID 1005-8885 (2007) 01-0012-04

Abstract A novel sequential Monte Carlo (SMC) algorithm is provided for the multiple maneuvering Ad-hoc network terminals direction of arrival (DOA) tracking. A nonlinear mobility and observation model is adopted, which can describe the motion features of the Ad-hoc network terminal more practically. The algorithm does not need any additional measurement equipment. Simulation result shows its significant tracking accuracy.

Keywords Baymian infmnce, Ad-hoc network, DOA tracking, SMC

the sequential Monte Carlo filter. But they use the steering vector in the observation model, which leads to complicated computation and additional measurement equipment. Besides, the DOA mobility models in those algorithms are usually linearized [7,8], and are not really suitable in applications.

In this article, a novel SMC algorithm is presented that does not use the complicated steering vector, and a nonlinear mobility model is also presented in the algorithm, which can meet the observed natural phenomena. Simulation results show its high accuracy and fast tracking speed.

2 SMC method and resample

2.1 Sequential Monte Carlo filter The Ad-hoc network has been amacting more and more attention from the academic and industry fields because of its quick and automatic organization of temporary networks [l, 21. Some scholars have proposed to use smart antennas instead of the omni-directional antennas in the Ad-hoc network, which means a huge increase in capacity, a decrease in signal interference, and finally a huge increase in communication quality [3,4]. The prerequisite, however, is the exact kbowledge of the DOAs of the mobile users. The computing capacity of the CPU in the Ad-hoc network is usually limited, whereas, the estimation of the DOA as MUSIC [S] or ESPRITE [6] is very complex, thus more system time is spent in computing the DOA. So it is not realistic to assume that the target DOA is perfectly known during the entire movement. DOA tracking and prediction are significant in many applications. If accuracy DOA tracking and prediction are realized, the system time cost will reduce sharply.

The problem is solved under a Bayesian framework, where online posterior distribution of the DOA will be estimated. Many DOA tracking algorithms have been proposed based on

Received date: 2006-10-17 GUO Li (a), LIN Jia-ru Key Laboratory of Infomation Processing and Intelligent Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China GUO Yan, LI Ning Institute of Science, PLA University of Science and Techology, Nanjing 21ooo7, China E-mail: Guo-li@bupt.du.cn

SMC methods approximate the sequence of probability and distributions of interest using a set of random samples, named particles [9]. Sequential importance sampling (SIS) and resampling [lo] mechanisms are used to get these particles. Convergence results guarantee that the particles can approximate any statistics of the distribution with arbitrarily fine accuracy by increasing the number of particles. However, for practical scenerios, a finite and sometimes quite restricted number of particles have to be considered in terms of the tradeoff between the system accuracy and computation costs.

Consider the following dynamic system models: z, = J(Z,-,,W,) (1) Yt = gr(zr*vr) (2) where z, , w, , y, , v, are the state variable, the state noise, the observation, and the observation noise at time t respectively.

It is intended to carry out a timely estimation of a function of state variable z, say h(z,) , based on observation y, .

From the Bayesian theorem, it can be concluded that the optimal solution to this problem is:

(3) M

E{h(z,)l y,}= jWZt)P(Z, 1 Y,)& =Ch(z ," ' ) j=l

where P stands for probability density function and. z.,? are the samples according to P(z, I y, 1 .

Generally speaking, it is difficult to get samples from the

No. 1 GUO Li, et al.: Ad-hoc network DOA tracking via sequential Monte Car10 filtering 13

posterior distribution P(z, I y , ) . Let also R( zt I y, )be a valid

probability density function, known as the importance function, whose support contains the support of P(z, I y , ) .

Suppose the states and the observations are sampled at each discrete time rk =to +kAr , where k is a nonnegative

integer. The basic SIS particle filter algorithm consists of a set of

NP particles Z, =Lz,“, zp), ..., z?)] according to the

importance function R ( z , I ~ , - ~ , y , ) and assigning to those

particles proper (normalized) weights as w, =[w:I), wp), ..., w y q

(4)

Then the weighted average x?, w ~ ) z ~ ) converges in some

statistical sense to the optimal minmum mean square error (MMSE) estimate E[h(z , ) I y , ] at each instant, t, .

That is:

N.

where W, = w:)

(5 )

Besides, there would be correlated random acceleration r, in each direction. Then the motion equations in each direction are modeled as follows:

(6)

(7)

(8)

(9)

(10)

(11) where zk,+, zk,y represent the terminal‘s x and y coordinates

separately. v ~ , ~ or v,,~ is terminal velocity in x or y

directions. w, is the independent Gaussian variable with zero mean and variance /3 . The subscript k , k -1 indicate the sample instances. a is a auto regression (AR) coefficient.

Finally, this observation model is defined as:

2k .x = Zk-l .x + Afvk- l .x

‘k.x = ‘k-1.x + Ar%-19x + &k,x +

5 . x = a%l.x + wk,.r

4 . y = 6 - 1 . y + Afvk-l ,y

‘k,y = ‘k-1.y + “%-l ,y +buk,y +&k,y

- 5 . y - a%-l,y + wk,y

y , =arctan - ‘ a , (12) r::: 1 where ak indicates the Gaussian white noise.

Then the DOA and also the position of the Ad-hoc network terminal can be tracked through SMC. The DOA and position prediction can be obtained if needed.

j = l

3.2 Optimal importance function approxlmatlon

2.2 Resample

Resample technique is used in SMC to avoid particle degeneracy. The main idea is to generate multiple copies of high-weight particles, even as low-weight samples are discarded. The most well-known selection strategy is to resample according to the particle weights [lo].

3 SMC In moblle M I A ttrrcklng

3.1 A M o c termlnal motion equations

The dynamics of the mobile terminal DOA are described by a nonlinear state-space model in two-dimensional Cartesian coordinates where the x axis denotes the horizontal position and the y axis denotes the vertical position.

In real application scenerios, the mobile user may have a sudden acceleration change in either of the x or y directions. Although, on the other hand, the acceleration may be highly correlated to its former value. Following Ref. [lll, the two situations are colligated to describe our terminal motion model as follows:

Suppose there is all together M acceleration speed, say , U =[.I, u2 ,..., uu] in each of the two directions, then the

transition probability between the states is expressed as qj .

The main drawback associated with conventional filtering is that the variance of the importance weights increases with time, leading to particle degeneracy [12]. The strategy to mitigate particle degeneracy is to use the optimal importance function: R(zk Iz:?-l9ytk)=P(zk I zl<i,yk) (13)

From Bayesian’ law and the Markov assumption, it can be written as:

Then approximately the following can be obtained:

This filler is called bootstrap filler. Finally, the DOA tracking formula is shown as follows:

(16)

2057 14 The Journal of CHUPT

1.5

1.0

0.5 B 5 f 0 - - OD

4 -0.5

-1.0

This corresponds to having

-

-

-

-

-

4 sbrktksr,

Simulations are performed to test the algorithm performance using MATLAB. A uniform linear antenna array with four ports is used. The range of DOA is set between -n/2 and d 2 and the acceleration vectors in two directions are U = [O,+6,-6,+3,-3]. The signal noise ratio (SNR) of the terminal emitting signal is 20 dB. The measurement data can be obtained from the pilot signal or by using the DOA estimation method, such as, MUSIC.

Other parameters are set as the following in the simulations: 0.8 i = j 0.04 i # j

, a=0.8, At=Is , p=O, 0=0.6 8.. =

Figures 1 and 2 show the DOA tracking result with 300 and 600 particles, when there is only one terminal

. . 1.0. f

C : I

$ . i t 2 0 . 4 1 2 :

-1.0- i'

3 0 . 5 -

-0.5- f

-1 .5 . I

600 particles, when there is only one terminal 2.0-

1 . 5 . 1.0.

p.. .... .-... -1 : 1 ;

I;

6 1.

1.

f ; 1 \ j """"'Actual DOA trajectory I i - -WAtrackingtrajectory by SMC

5 3 0 . 5 - $ . i t 2 0 . 4 1 2 :

1 ;

Ii _.._.._..-.. -..-..-..-

-0.5- f g / . . /.. -1.0- i' i j -1 .5 . I

1 t - - W A tracking trajectory by SMC 1 """"'Actual DOA trajectory I i

t...... 0 5 10 15 20 25 30

Timels

-2.0

Fig. 1 DOA tracking with 300 particles

0 5 10 15 20 2 5 30 Time/s

-1.5 I

Fig. 2 DOA tracking with 600 particles

It is well known that the presence of multiple targets also increases the tracking complexity. But our algorithm also has high accuracy without any additional information. Figure 3 shows the situation when there are two terminals around the circumstance.

1 .o

0.5

cm 9 0 e

2 -0.5

- M

-1.0

- 1 . :

* DOAI tracking trajectory with SMC

p DON tracking trajectory with SMC 4 --. Actual DOAI trajectory

- -_ Actual DOA2 trajectory

5 10 15 20 25 30 Timels

Fig. 3 Two DOA tracking with 600 particles

From the simulations, it is clear that the SMC method has high accuracy in the nonlinear terminal motion. The DOA was tracked after 10 intervals in the f i s t situation and after four intervals in the second and third situations separately. The accuracy is higher when there are more particles. More simulations show that the measurement data of the algorithm is the source provider of the algorithm. If the transmitting environment is severe, for example, there is signal fading or multi-path, more methods should be used to avoid or reduce the influence, before the DOA measurement. For example, channel code technology and OFDM technology. For the information, refer to Ref. [13].

5 Condudon8

The article considers a novel DOA tracking method using an SMC filter, which can be further used to predict the mobile DOA. On the basis of the specific state model and observation model, the directions of arrival for multiple maneuvering terminals are to be sequentially estimated with high accuracy and fast speed. The measurement data is otained from the pilot signal or by using the DOA estimation algorithm, which can be influenced by t;he wireless environment. If the algorithm is used in a bad wireless environment, more technologies should be taken initially, to avoid or reduce the channel influence. After well tracking, this algorithm can be used to predict the future DOA with which the system cost will be reduced sharply. The future works will focus on the DOA prediction and better system accuracy in the algorithm.

Acknowledgements This work is suppor&ed by the National Natural Science Foundation of China (60402005,60372099).

No. 1 GUO Li, e t al.: Ad-hoc network DOA tracking via sequential Monte Car10 filtering 15

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Biographies: GUO Li, the School of Information Engineering, Beijing University of Posts and Telecommunications, Ph. D. Candidate, associate professor. She is engaged in multimedia communication and information processing, wireless communication, and embedded application system design.

GUO Yan, the Institute of Science, PLA University of Science and Technology, Ph. D., associate professor. Her research interest includes smart antenna and adaptive signal processing.

LIN Jia-ru, the School of Information Engineering, Beijing University of Posts and Telecommunications, Ph. D., professor and doctor supervisor. His research interest includes wireless communication. LI Ning, the Institute of Science, PLA University of Science and Technology, Ph. D. Candidate, associate professor. His research interest includes Ad-hoc network technology.