Unscented Auxiliary Particle Filter Implementation of the Cardinalized Probability Hypothesis Density Filters

Document Type : Research Article

Authors

1 Electrical Engineering Department, Imam Hossein Comprehensive University (IHCU), Tehran, Iran

2 Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

Abstract

The probability hypothesis density (PHD) filter suffers from lack of precise estimation of the expected number of targets. The Cardinalized PHD (CPHD) recursion, as a generalization of the PHD recursion, remedies this flaw and simultaneously propagates the intensity function and the posterior cardinality distribution. While there are a few new
approaches to enhance the Sequential Monte Carlo (SMC) implementation of the PHD filter, current SMC implementation for the CPHD filter is limited to choose only state transition density as a proposal distribution. In this paper, we propose an auxiliary particle implementation of the CPHD filter by estimating the linear functionals in the elementary symmetric functions based on the unscented transform (UT). Numerical simulation results indicate that our proposed algorithm out performs both the SMC-CPHD filter and the auxiliary particle implementation of the PHD filter in difficult situations with high clutter. We also compare our proposed algorithm with its counterparts in terms of other metrics, such as run times and sensitivity to new target appearance.

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References

[1] W. K. Ma, B. Vo, S. Singh, and A. Baddeley, “Tracking an unknown and time-varying number of speakers using TDOA measurements: A random finite set approach,” IEEE Transactions on Signal Processing, vol. 54, no. 9, pp. 3291–3304, 2007.
[2] B.-N. Vo, S. Singh, and A. Doucet, “Random finite sets and sequential Monte Carlo methods in multi-target tracking,” in Proceedings of the International Conference on Information Fusion, Cairns, pp. 792–799, 2003.
[3] H. Sidenbladh and S.-L. Wirkander, “Tracking random sets of vehicles in terrain,” in Computer Vision and Pattern Recognition Workshop, Madison, Wisconsin, USA , pp. 98–98, 2003.
[4] R. Mahler, “Multi-target bayes filtering via first-order multitarget moments,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1152–1178, 2003.
[5] R. Mahler, “PHD filters of higher order in target number,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 4, pp. 1523–1543, 2007.
[6] R. Mahler, “A theory of PHD filters of higher order in target number,” in Signal Processing, Sensor Fusion, and Target Recognition XV, SPIE Defense and Security Symposium, April 2006.
[7] E. Delande, M. Uney, J. Houssineau, D. Clark, “Regional Variance for Multi-Object Filtering,” IEEE Transactions on Signal Processing, vol. 62, no. 13, pp. 3415 – 3428, 2014.
[8] R. Georgescu and P. Willett,” The GM-CPHD Tracker Applied to Real and Realistic Multistatic Sonar Data Sets,” IEEE Journal of Oceanic Engineering, vol. 37, no. 2, pp. 220 – 235, 2012.
[9] C. Lundquist, K. Granstrom, and U. Orguner, “An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation,” IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 3, pp. 472 – 483, 2013.
[10] B. Li, “Multiple-model Rao-Blackwellized particle CPHD filter for multitarget tracking,” Nonlinear Dynamics, vol. 79, Issue 3, pp. 2133-2143, 2015.
[11] G. Battistelli, L. Chisci, C. Fantacci, A. Farina, and A. Graziano, “Consensus CPHD Filter for Distributed Multitarget Tracking,” IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 3, pp. 508 – 520, 2013.
[12] J. Y. Yu, M. Coates and M. Rabbat, “Distributed multi-sensor CPHD filter using pairwise gossiping,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016, pp. 3176-3180.
[13] J. Gan, M. Vasic, A. Martinoli, “Cooperative Multiple Dynamic Object Tracking on Moving Vehicles based on Sequential Monte Carlo Probability Hypothesis Density Filter,” Proceedings of the IEEE International Conference on Intelligent Transportation Systems, Rio de Janeiro, Brazil,, 2016.
[14] B.-N. Vo, S. Singh, and A. Doucet, “Sequential Monte Carlo methods for multi-target filtering with random finite sets,” IEEE Transactions on Aerospace and Electronic Systems, vol. 41, no. 4, pp. 1224–1245, 2005.
[15] B.-N. Vo, B-T. Vo, and A. Cantoni, “Analytic implementations of the cardinalized probability hypothesis density filter,” IEEE Transactions on Signal Processing, vol. 55, no. 7, pp. 3553–3567, 2007.
[16] B. Ristic, D. Clark, B.-N. Vo, and B.-T. Vo, “Adaptive target birth intensity for PHD and CPHD filters,” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no. 2, pp. 1656 –1668, 2012.
[17] N. P. Whiteley, S. S. Singh, and S. J. Godsill, “Auxiliary particle implementation of the probability hypothesis density filter,” Transactions on Aerospace and Electronic Systems, vol. 46, no. 3, pp. 1427–1454, 2010.
[18] E. Baser, M. Efe, “A novel auxiliary particle PHD filter,” in Proceedings of the International Conference on Information Fusion, Singapore, pp. 165-172, 2012.
[19] M.R. Danaee and F. Behnia, “Auxiliary unscented particle cardinalized probability hypothesis density,” in 21st Iranian Conference on Electrical Engineering (ICEE), pp. 1 – 6, 2013.
[20] R. Mahler, Statistical Multisource Multitarget Information Fusion, Norwood: Artech House, 2007.
[21] O. Erdinc, P. Willett, and Y. Bar-Shalom, “Probability hypothesis density filter for multitarget multisensor tracking,” in Proc. 8th Intl Conf. on Information Fusion, 2005.
[22] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, 1999.
[23] M. K. Pitt and N. Shephard, “Filtering via simulation: Auxiliary particle filters,” Journal of the American Statistical Association, vol. 94, no. 446, pp. 590–599, 1999.
[24] M. R. Danaee and F. Behnia, “Extension of particle filters for time-varying target presence through split and raw measurements,” IET Radar, Sonar & Navigation, vol. 7, no. 5, pp. 517 – 526, 2013.
[25] D. Schuhmacher, B.T. Vo, and B.-N. Vo, “A consistent metric for performance evaluation in multi-object filtering,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3447– 3457, 2008.S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, 1999.
AUT Journal of Electrical Engineering
Volume 49, Issue 1
June 2017
Pages 95-106

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