Multiple Sensor Multiple Object Tracking With GMPHD Filter - ISIF

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At the second sensor, the number of Gaussian components is Jk 2 = Jk(1 1 + jZkj) 2 = (J k 1 + J ;k )(1 + jZkj)(1 1 + jZkj) 2 (21) So, the number of Gaussian components in v k (x) is J k = J Q k = (J k 1 + J ;k )(1 + jZkj) 1 (1 + jZ Q k j) (22) The number of Gaussian components in GMPHD with multisensor increases so much with the time that leading to high computation. So, at each time, methods to reduce the number of Gaussian components are required. There are some rules to reduce the number of Gaussians, such as Gaussian components that have small weights will be cut, Gaussian components that are close together will be merged into one Gaussian, and if the number of Gaussian components is over a threshold L, rst L Gaussian components with high weights will be chosen for propagating in the next iteration [12]. V. EXPERIMENTAL RESULTS A. Gaussian mixture probability hypothesis density lter with multi-sensor for bearing and range tracking First, we consider a bearing and range tracking application to demonstrate the effectiveness of GMPHD lter with multisensor. There are objects that appeared and disappeared at different times. Each object has the survival probability p S;k = 0:99 and follows a nonlinear nearly constant turn model [12] in which the target state takes the form x k = y T k ; ! k T , where y k = [p x;k ; p y;k ; _p x;k ; _p y;k ] T is the coordinate (x; y) and velocity in each dimension of object, and ! k is the turn rate. The state dynamic equations are given by y k = F (! k 1 )y k 1 + G! k 1 ; (23) ! k = ! k 1 + u k 1 ; where = 1s, ! k N (; 0; 2 wI 2 ), w = 15 m/s 2 , u k N (; 0; 2 u), and u = =180 rad/s. 3 sin! 1 cos! 1 0 ! ! 1 cos! sin! F (!) = 6 0 1 ! ! 7 4 0 0 cos! sin! 5 , 0 0 sin! cos! 2 3 G = 6 4 2 2 0 0 2 2 0 0 7 5 We assume no spawning and that the spontaneous birth RFS is Poisson with intensity where k (x) = 0:1N (x; m ; P ) m = [0; 0; 2000; 0; 0] T ; P = diag([2500; 2500; 2500; 2500; (6=180) 2 ] T ): Fig. 1. Position (x; y) of targets with measurements from sensor 1 Each object has a probability of detection p D;k = 0:98. Observations consist of bearing and range measurements from 2 sensors. The position of the sensors are p 1 s = [0; 0] (24) p 2 s = [1000; 1000] (25) The observation model at sensor i is given by 2 3 px;k p arctan i s;x zk i = 4 p y;k p q i s;y 5 + k ; (26) (p x;k p i s;x) 2 + (p y;k p i s;y) 2 where k N(:; 0; R k ) with R k = diag([ 2 ; 2 r] T ), = =30 rad/s and r = 10 m. The clutter RFS follows the uniform Poisson model over the surveillance region [ =2; =2] rad [0; 3000] m, with c = 1:1 10 3 radm 1 (i.e., an average of 10 clutter returns on the surveillance region). The pruning parameters for the GMPHD lters are T = 10 5 , merging threshold U = 4, and maximum number of Gaussian components J max = 100. (More details on these parameters are in [12]). Figure 1 and 2 show the position estimations with measurements from sensor 1 and 2 respectively. Because of the high clutter and high noise, there are some errors in the lter outputs. Figure 3 shows the position estimations with GMPHD method. The performance outperformed with using one sensor. This is because the results from sensor 1 is the good prediction for sensor 2. Thus, the information from both sensors is collaborated to give the state estimates. B. Gaussian mixture probability hypothesis density lter for multiple speaker tracking Second, we tested the GMPHD lter in multiple speaker tracking. We simulated an acoustic room to test the performance of GMPHD in tracking multiple speakers. The dimensions of the room are 3m 3m 2.5m. There are four
delay of arrival measurement (TDOA) z q k is measured from the q-th microphone pair at time k. The measurement equation is z q k = T q (x k ) + v q k ; q = 1; :::; Q (28) T q (x k ) = kx k p 2;q k kx k p 1;q k (29) c where p i;q is the position of microphone i of pair q, c is the speed of sound, and v q k N(0; 4 10 9 ) is uncorrelated noise. Because the measurement equation (28) is not linear Gaussian, we need to approximate the linear system by using unscented transform in GMPHD lter [12]. Each speaker has a probability of survival at time k is p S;k = 0:95, the probability of detection is p D;k = 0:7. To extract the TDOA for multiple speakers, we applied the method from [13]. Figure 4 shows an example to collect TDOA measurements at a microphone pair (for example microphone pair 2). Fig. 2. Position (x; y) of targets with measurements from sensor 2 Fig. 4. GCC TDOA measurements Fig. 3. Position (x; y) of targets with fusion method microphone pairs, each of them has an inter-sensor spacing of 0.5m. The speaker sources are all female. The acoustic image method [16] was used to simulate the room impulse responses. The reverberation time of the room impulse responses is about T 60 = 0:15s. The speech signal to noise ratio is about 20dB. There are 60 frames. The time frame length for measuring TDOA is 256ms, and they are non-overlapping. There are two speakers. They appeared and disappeared at different times. Let x k be the state of a speaker at time k. Here, the state is the position (x; y) of speaker. We assume that the dynamic moving equation can be given x k = Ax k 1 + w k (27) where A = [I] and w k N([0; 0]; diag([0:01; 0:01])). This means the average distance from the previous time k 1 to k of a speaker is about 10 cm. Given a speaker x k , the time Figures 5 and 6 show the multi-speaker tracking performance of particle PHD lter [14]. Because of the unreliable in clustering technique, the state estimaties are affected. Figures 7 and 8 show the multi-speaker tracking performance of our method. This performance is better than particle PHD lter. In most of the time that two persons speak simultaneously, our method can give reliable estimations. This is because GMPHD lter does not depend on clustering techniques. The state estimates are extracted from means of Gaussian components that have high weights. The above result is the performance for one trial. To measure the average performance, we used the performance measurement from [13]. It includes the probability of correct speaker number, expected absolute error on the number of speaker and conditional mean distance error by Wasserstein distance. The probability of correct speaker number is dened by P (j ^X k j = jX k j) (30) where ^X k is the estimation of multi-speaker state and X k is ground-truth. The expected absolute error on the number of speaker is E(j ^X k j jX k j) (31)
Page 1 and 2: Multiple Sensor Multiple Object Tra
Page 3: 1 (x) with measurement set Z1 k by
Page 7: Fig. 9. Probability of correct spea

Multiple Sensor Multiple Object Tracking With GMPHD Filter - ISIF

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