Adaptive residual unscented particle filter in target tracking - Journal of ...

Journal of Engineering Technology (ISSN: 0747-9964) Volume 6, Issue 2, July, 2017, PP.784-791

Adaptive residual unscented particle filter in target tracking P. Sudhakar, D. Elizabeth Rani ECE Department, Vignan’s Institute of engineering for women, Visakhapatnam, Andhra Pradesh, India Department of Electronics and Instrumentation Engineering, GITAM University, Visakhapatnam, Andhra Pradesh, India Abstract: In the process of target tracking in radar systems, the information is extracted using a high end processor for data processing. As the target moves randomly, the state variables are constrained to nonlinear model. In general, we monitor non-Gaussian noise in target tracking application. So, an unscented particle filter (UPF) is proposed earlier which provides more accuracy for estimation compare to the other techniques. However, the computational complexity is more in UPF. In this paper, we propose a new algorithm called adaptive residual unscented particle filter (ARUPF) where adaptive residual resample and relative entropy are simultaneously used to improve the performance of unscented particle filter (UPF). The proposed algorithm is compared with the existing UPF and adaptive MCMC particle filter in terms of MSE, variance, standard error of mean (SEM), computational time and Average Euclidean error (AEE). The simulation results display that proposed method outperforms the other techniques. Keywords: Target tracking, UPF, ARUPF, MSE, AEE, SEM.

1. Introduction In the present scenario, the non-linearity is a basic problem in many applications of filters like statistical signal processing, radar tracking, engineering [1][2][4][5] etc. In target tracking, as the target performs random movements, the state variables are restricted to nonlinear model. In general, we observe non-Gaussian noise in target tracking application. So, particle filtering algorithm is applied to this system, but has many drawbacks. The particle filter uses sampling importance resampling which leads to less diversity and because of more number of particles used for estimation, computational complexity is more. Several algorithms are proposed earlier that includes Unscented Particle Filter (UPF)[7], GM-UPF with adaptive residual algorithm[11] and Markov Chain Monte Carlo Particle Filter (MCMCPF)[13] to resolve the less diversity and degeneracy problems. But these methods fail to resolve the computational complexity problem. An adaptive approach is needed to update the sample set which reduces the number of samples to estimate through relative entropy. Estimation through relative entropy was proposed earlier and is proved to be the improved approach than the other existing methods. In this paper, we propose a new algorithm which overcomes the above-mentioned drawbacks. In this new algorithm adaptive residual resample and relative entropy are simultaneously used to improve the performance of unscented particle filter (UPF). The adaptive residual algorithm is replaced by a sample importance re-sampling to resolve the less diversity problem which avoids uncensored replacing lower weight particles with higher weighted particles and has the ability to maintain sufficient diversity of particles without increasing the particles size but it has a drawback of computational time. During the estimation process the size of particles are adapted through relative entropy but it cannot resolve the less diversity problem. By combining both the algorithms in UPF, not only the above mentioned problems but also the accuracy can be improved.


The simulations are done to compare Unscented Particle Filter (UPF), proposed algorithm and adapted MCMC PF in terms of mean square error (MSE)[13]. From the results we can say that proposed algorithm is accurate and consumes less time compared to other algorithms. The new algorithm is suitable for target tracking. 2. State Space Model In target tracking the state of the target is to be estimated. We assume that the target path is nonlinear with non Gaussian noise. So, we need a model which suits the above conditions. In general, such a model can be described by dynamic state space model [11] with discrete time equations is as follows

………………………………..2.1 ………………………………………2.2 The above equation 2.1 and 2.2 represents the state and measurement equations. Where process noise and

represents measurement noise. The

represents

is drawn from a normal distribution.

are assumed to be independent and non Gaussian.

3. Unscented Particle Filter Designing the proposal distribution which approximates the true posterior distribution is hard in particle filter. By sampling the state transitions, new observations cannot be considered, so PF cannot produce ideal proposal distribution. As we know UKF [8] is a minimum mean square error estimator for nonlinear system. It utilizes the scaled unscented transformation to calculate the statistics of a random variable. UKF has higher accuracy than EKF especially when the models are highly nonlinear. In UPF, before sampling of the particles UKF is utilized to generate the proposal distribution which can consider the new observation. The proposal distribution generated by UKF has a bigger overlap with the true posterior distribution than PF. So UPF has relatively high accuracy, while in UPF at each time step each particle will utilize UKF to generate the proposal distribution, so the computation cost of UPF is huge. The Steps for UPF are as follows //unscented transform// 1. Generate 2L+1 sigma points Si={Xi,Wi} X0=Xm(mean of X) , i = 1,2,…..L , i = L+1,L+2,…..2L Where α……….spread of the sigma points around X (1≤α≤1e-4) K……….secondary scaling parameter (0 or 3-L) β………incorporate prior knowledge of distribution X=2(optimal) 785


Now weights are

i = 1, …….. 2L 2. Pass the sigma points through nonlinear transformation Yi = f(Xi) i=0, ….., 2L 3. Mean and covariance of Y

4. 5. 6. 7.

//UKF// Particles are initialized to find mean Xm and covariance Do for each time interval Obtain sigma points Xi from above equation Time update Xi = g(Xi-1)

Yi = h(Xi.Xi-1)

8. Measurement update

9. Sample the particles Xi, i=1, …N from the proposal distribution N(

) 786


10. Compute the weights (wi) of each particle (Xi). 11. Normalize the weights as Wi = wi /sum (wi) (i=1,2….N) 12. Resample the particles Develop / remove particles 13. The output

i

i according

to weighted particles Wi.

is the state estimation of at the time step.

4. Adaptive Residual Unscented Particle Filter Basically UPF provides more accuracy for estimation when compared to the other techniques. So we choose UPF to estimate the state estimation problem. But to improve the performance of UPF we replaced the importance re-sampling with an adaptive residual re-sampling. However, UPF has computational complexity because it uses UKF for each particle at each time step. To reduce the computational cost, we use Relative entropy [12] which adaptively changes the number of particles for every iteration. To reduce the computational complexity by maintaining the accuracy, we propose an algorithm called adaptive residual unscented particle filter. Steps are as follows: 1. 2. 3. 4.

Particles are initialized to find mean Xm and covariance Do for each time interval Obtain sigma points Xi Time update Xi = g(Xi-1)

Yi = h(Xi.Xi-1)

5. Measurement update

6. Sample the particles Xi, i=1, …N from the proposal distribution N( 7. Compute the weights (wi) of each particle (Xi). 8. Normalize the weights as

)

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Wi = wi /sum (wi) (i=1,2….N) 9. Resample the particles using adaptive residual //adaptive residual resampling// 10. For samples

all Weights are multiplied by number of particles N to give copy particles

Whole number of copy particles is

.

So we obtain new particles 11. Find residual particles m=N-N’ If m>0 Calculate new weights for all the particles ( New particles are generated

. We choose max m weighted particles as copy particles

= max else 12. Draw residual particles } i= { 13. If ( falls into an zero resample bin) then 14. K=k+1; 15. While 16. Normalize the importance weights 17. Return 5. Simulation Results Here we elucidate the capability of ARUPF by comparing with UPF and adaptive MCMC PF. For this a great number of simulations are carried out. The utilization and performance of ARUPF in target tracking is explained in detail. To elucidate the effectiveness of ARUPF, a non linear system is considered which are shown in state space model section. The true path and the estimation by simulating ARUPF, UPF and adaptive MCMC PF is shown in fig.1. We can see that in a random model the estimated states of ARUPF are almost coincided with the true path where as UPF is bit closer to ARUPF. However adaptive MCMC PF have some deviations here and there compared to ARUPF.

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Figure. 1. True path and estimates of ARUPF, UPF and adaptive MCMCPF

. Figure. 2. MSE of ARUPF, UPF and adaptive MCMCPF To compare the estimation accuracy and elucidate the consistency and convergence of these three algorithms MSE [13] of ARUPF, UPF and adaptive MCMC PF are shown in fig.2. It is noticeable that MSE of ARUPF is lower than the other two techniques. The average Euclidean error (AEE) is nothing but the average of error of all the points. It reflects the estimation accuracy and it can be calculated by

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MSE Variance

Standard deviation

SEM

Run time(s)

Average Euclidean error(AED)

UPF

0.2995

0.5473

0.0500

0.089 s

0.2541

Adaptive MCMCPF

0.1704

0.4128

0.0377

0.093 s

0.2978

0.0232

0.1523

0.0139

0.047 s

0.1362

ARUPF

Table.1. MSE, AEE and run time for all three algorithms The MSE of all the three algorithms and AEE, execution time are shown in table.1. The computational time of ARUPF is lower than UPF and adaptive MCMCPF. Even though both ARUPF and adaptive MCMC PF are adaptively changing the number of particles in the process, ARUPF dominates. So, ARUPF is optimized. From standard error of mean (SEM), variance, standard deviation and AEE, it proves that the proposed ARUPF is more accurate for nonlinear tracking. 6. Conclusion The proposed algorithm reduces the computational time and improves the accuracy in estimating the path for target tracking in radar systems. ARUPF is best suited for nonlinear and non-Gaussian tracking applications compared to the UPF and adaptive MCMC PF. The proposed technique overcomes the limitation of UPF where the computational cost is relatively large that influences the real time capability. The ARUPF suits better for several real time applications in terms of both accuracy and computational time compared to several existing methods. The future work of our proposed method analyzes the technique to improve the influence of accuracy and computational time.

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