On Improvement of Cardinalized Probability Hypothesis Density Filter         Implementation by using Auxiliary Particle Filter

Raeis Danaei, Meysam

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	On Improvement of Cardinalized Probability Hypothesis Density Filter Implementation by using Auxiliary Particle Filter
پدافند الکترونیکی و سایبری
Article 3, Volume 3, Issue 4, April 2020, Pages 23-41 PDF (1.97 M)
Author
Meysam Raeis Danaei^*
Assistant Professor, Imam Hossein University (AS), Tehran, Iran
Receive Date: 27 April 2015, Revise Date: 21 June 2023, Accept Date: 19 September 2018
Abstract
The PHD filter recursion is introduced to enable the implementation of expensive computational algorithms of multitarget Bayesian filtering. The goal of this recursion is to update and propagate the posterior intensity of a Random Finite Set during time steps. To that end, Cardinalized PHD is introduced as an extension of PHD filter to overcome the PHD’s weakness in estimating the number of targets. In the CPHD filter, the posterior intensity function and the cardinality distribution are updating at the same time. In this paper, we use auxiliary particle filter to implement the CPHD filter. The benefit of the proposed algorithm is to sample at the higher dimensional space compared to the dimensional of the target space in order to generate approximating samples of the CPHD filter and this will improve the estimation accuracy. To that end, we first reformulize the CPHD recursion in a way which is suitable for auxiliary particle filter. Then, to sample in a higher dimensional space, we first use an auxiliary variable which is the index of previously generated samples and then we apply another auxiliary variable which is the index of current measurements to improve the estimation of the number and position of multiple targets. Comparison between mean and variance of estimated cardinality and error of multitarget position estimation obtained from simulation results indicate the superiority of our proposed algorithm compared to the current implementation method of the CPHD filter by using SIR particle filter.
Keywords
Multitarget tracking; Random Finite Set; Probability hypothesis density filter; Cardinalized PHD; Auxiliary particle filter

References
[1] Y. Bar-Shalom, “Multitarget-Multisensor Tracking: Applications and Advances,” Dedham: Artech House, vol. 2, 1992. [2] S. Blackman and R. Popoli, “Design and Analysis of Modern Tracking Systems,” Artech House, 1999. [3] M. Morelande, C. Kreucher, and K. Kastella, “A Bayesian Approach to Multiple Target Detection and Tracking,” Signal Processing, IEEE Transactions on, vol. 55, no. 5, pp. 1589 –1604, 2007. [4] 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, 2006. [5] 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. [6] 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. [7] R. Mahler, “Statistical Multisource Multitarget Information Fusion,” Norwood: Artech House, 2007. [8] J. Mullane and et al., “A Random Finite Set Approach to Bayesian SLAM,” IEEE Transactions on Robotics, vol. 27, no. 2, pp. 268–282, 2011. [9] B. Ristic and B.-N. Vo, “Sensor Control for Multi-object Statespace Estimation using Random Finite Sets”, Automatica, vol. 46, pp. 1812–1818, 2010. [10] 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. [11] M. Tobias and A. Lanterman, “A Probability Hypothesis Density based Multitarget Tracking with Multiple Bistatic Range and Doppler Observations,” Proc. IEE Radar Sonar and Navigation, vol. 152, no. 3, pp. 195–205, 2005. [12] D. Clark, I. T. Ruiz, Y. Petillot, and J. Bell, “Particle Phd Filter Multiple Target Tracking in Sonar Image,” IEEE Transaction on Aerospace and Electronic Systems, vol. 43, no. 1, pp. 409–416, 2007. [13] N. Ikoma, T. Uchino, and H. Maeda, “Tracking of Feature Points in Image Sequence by SMC Implemention of the Phd Filter,” in Proc. SICE Annual Conference., pp. 1696–1701, 2004. [14] D. Clark, and J. Bell, “Bayesian Multiple Target Tracking in Forward Scan Sonar Images using the PHD Filter,” Proc. IEE Radar Sonar Navigation, vol. 152, no. 5, pp. 327–334, 2005. [15] G. Battistelli, L. Chisci, S. Morrocchi, F. Papi, A. Benavoli, A. Farina, and A. Graziano, “Traffic Intensity Estimation Via PHD Filtering,” In Proceedings of the 5th European Radar Conference, Amsterdam, Netherlands, pp. 340–343, 2008. [16] H. Sidenbladh, “Multi-target Particle Filtering for the Probability Hypothesis,” In Proc. Int’l Conf. on Information Fusion, Cairns, Australia, pp. 800–806, 2003. [17] R. R. Juang, A. Levchenko, and P. Burlina, “Tracking Cell Motion using GM-PHD,” In International Symposium on Biomedical Imaging, pp. 1154–1157, 2009. [18] E. Maggio, E. Piccardo, C. Regazzoni, and A. Cavallaro, “Particle PHD Filter for Multi-target Visual Tracking,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Honolulu, Hawaii, pp. 1101–1104, 2007. [19] A. Pasha, B. N. Vo, H. Tuan, and W. K. Ma, “Closed Form Solution to the Phd Recursion for Jump Markov Linear Models,” In Proc. 9th Intl Conf. on Information Fusion, 2006. [20] 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. [21] 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, 2006. [22] M. Ulmke, O. Erdinc, and P. Willett, “GMTI Tracking Via the Gaussian Mixture Cardinalized Probability Hypothesis Density Filter,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 4, pp. 1821–1833, 2010. [23] B. N. Vo and W. K. Ma, “The Gaussian Mixture Probability Hypothesis Density Filter,” IEEE Transactions on Signal Processing, vol. 54, no. 11, pp. 4091–4104, 2006. [24] B. N. V. 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. [25] 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. [26] 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. [27] N. P. Whiteley, S. S. Singh, and S. J. Godsill, “Auxiliary Particle Implementation of the Probability Hypothesis Density Filter,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 3, pp. 1427–1454, 2010. [28] 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. [29] A. Doucet, S. Godsill, and C. Andrieu, “On Sequential Monte Carlo Sampling Methods for Bayesian Filtering,” Statistics and Computing, vol. 10, no. 3, pp. 197–208, 2000. [30] A. Doucet, N. de Freitas, and N. Gordon, “Sequential Monte Carlo Methods in Practice,” Springer 2001. [31] 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. [32] E. Pollard, B. P. Onera, and M. Rombaut, “Hybrid Algorithms for Multitarget Tracking using MHT and GM-CPHD,” IEEE Transactions on Aerospace and Electronic Systems, vol. 47, no. 2, 2011. [33] D. Franken, M. Schmidt, and M. Ulmke, “Spooky Action at a Distance in the Cardinalized Probability Hypothesis Density Filter,” IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 4, pp. 1657–1664, 2009. [34] D. Schuhmacher, B. T. Vo, and B. N. Vo, “A Consistent Metric for Performance Evaluation of Multi-object Filters,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3447–3457, 2008. [35] J. Hartigan, “Clustering Algorithms,” New York: Wiley, 1975.
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On Improvement of Cardinalized Probability Hypothesis Density Filter Implementation by using Auxiliary Particle Filter