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

Author

Assistant Professor, Imam Hossein University (AS), Tehran, Iran

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


[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.
  • Receive Date: 27 April 2015
  • Revise Date: 21 June 2023
  • Accept Date: 19 September 2018
  • Publish Date: 20 February 2016