PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.

[1]  Ba-Ngu Vo,et al.  The Gaussian Mixture Probability Hypothesis Density Filter , 2006, IEEE Transactions on Signal Processing.

[2]  Hedvig Kjellström,et al.  Multi-target particle filtering for the probability hypothesis density , 2003, ArXiv.

[3]  S. Singh,et al.  Novel data association schemes for the probability hypothesis density filter , 2007, IEEE Transactions on Aerospace and Electronic Systems.

[4]  A. El-Fallah,et al.  Regularized multitarget particle filter for sensor management , 2006, SPIE Defense + Commercial Sensing.

[5]  R. Mahler.  PHD filters of higher order in target number , 2007 .

[6]  Aaron D. Lanterman,et al.  Multitarget tracking using multiple bistatic range measurements with probability hypothesis densities , 2004, SPIE Defense + Commercial Sensing.

[7]  R.P.S. Mahler,et al.  "Statistics 101" for multisensor, multitarget data fusion , 2004, IEEE Aerospace and Electronic Systems Magazine.

[8]  Ronald P. S. Mahler,et al.  Random Set Theory for Target Tracking and Identification , 2001 .

[9]  Ba-Ngu Vo,et al.  Sequential Monte Carlo methods for static parameter estimation in random set models , 2004, Proceedings of the 2004 Intelligent Sensors, Sensor Networks and Information Processing Conference, 2004..

[10]  Simon Ahlberg,et al.  The IFD03 Information Fusion Demonstrator , 2004 .

[11]  Ronald Mahler,et al.  Multitarget Moments and their Application to Multitarget Tracking , 2001 .

[12]  Abhijit Sinha,et al.  A distributed implementation of a sequential Monte Carlo probability hypothesis density filter for sensor networks , 2006, SPIE Defense + Commercial Sensing.

[13]  D. Clark,et al.  PHD filter multi-target tracking in 3D sonar , 2005, Europe Oceans 2005.

[14]  R. Mahler.  Random Sets : Unification and Computation for Information Fusion — A Retrospective Assessment , 2004 .

[15]  Aaron D. Lanterman,et al.  Probability hypothesis density-based multitarget tracking with bistatic range and Doppler observations , 2005 .

[16]  Ba-Ngu Vo,et al.  Performance of PHD Based Multi-Target Filters , 2006, 2006 9th International Conference on Information Fusion.

[17]  A. El-Fallah,et al.  Advancements in situation assessment sensor management , 2006, SPIE Defense + Commercial Sensing.

[18]  B. Vo,et al.  Improved Probability Hypothesis Density (PHD) Filter for Multitarget Tracking , 2005, 2005 3rd International Conference on Intelligent Sensing and Information Processing.

[19]  Thiagalingam Kirubarajan,et al.  Data association combined with the probability hypothesis density filter for multitarget tracking , 2004, SPIE Defense + Commercial Sensing.

[20]  D.E. Clark,et al.  Data Association for the PHD Filter , 2005, 2005 International Conference on Intelligent Sensors, Sensor Networks and Information Processing.

[21]  Ba-Ngu Vo,et al.  Closed Form PHD Filtering for Linear Jump Markov Models , 2006, 2006 9th International Conference on Information Fusion.

[22]  N. Ikoma,et al.  Tracking of feature points in image sequence by SMC implementation of PHD filter , 2004, SICE 2004 Annual Conference.

[23]  A. Doucet,et al.  Sequential Monte Carlo methods for multitarget filtering with random finite sets , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[24]  A.D. Lanterman,et al.  A probability hypothesis density-based multitarget tracker using multiple bistatic range and velocity measurements , 2004, Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the.

[25]  Ba-Ngu Vo,et al.  Probability hypothesis density filter versus multiple hypothesis tracking , 2004, SPIE Defense + Commercial Sensing.

[26]  Ronald P. S. Mahler,et al.  Particle-systems implementation of the PHD multitarget-tracking filter , 2003, SPIE Defense + Commercial Sensing.

[27]  Ronald P. S. Mahler,et al.  Multitarget filtering using a multitarget first-order moment statistic , 2001, SPIE Defense + Commercial Sensing.

[28]  A. Cantoni,et al.  The Cardinalized Probability Hypothesis Density Filter for Linear Gaussian Multi-Target Models , 2006, Annual Conference on Information Sciences and Systems.

[29]  Sumeetpal S. Singh,et al.  Sequential monte carlo implementation of the phd filter for multi-target tracking , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[30]  Ronald Mahler,et al.  MULTITARGET SENSOR MANAGEMENT OF DISPERSED MOBILE SENSORS , 2004 .

[31]  Syed Ahmed Pasha,et al.  A Gaussian Mixture PHD Filter for Jump Markov System Models , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[32]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[33]  Ronald P. S. Mahler,et al.  Statistical Multisource-Multitarget Information Fusion , 2007 .

[34]  Ronald Mahler,et al.  PHD filters of second order in target number , 2006, SPIE Defense + Commercial Sensing.

[35]  Sumeetpal S. Singh,et al.  Random finite sets and sequential Monte Carlo methods in multi-target tracking , 2003, 2003 Proceedings of the International Conference on Radar (IEEE Cat. No.03EX695).

[36]  Hedvig Kjellström,et al.  Tracking Random Sets of Vehicles in Terrain , 2003, 2003 Conference on Computer Vision and Pattern Recognition Workshop.

[37]  I. R. Goodman,et al.  Mathematics of Data Fusion , 1997 .

[38]  Ba-Ngu Vo,et al.  The GM-PHD Filter Multiple Target Tracker , 2006, 2006 9th International Conference on Information Fusion.

[39]  Ba-Ngu Vo,et al.  Convergence Analysis of the Gaussian , 2007 .

[40]  Daniel E. Clark,et al.  Bayesian multiple target tracking in forward scan sonar images using the PHD filter , 2005 .

[41]  B. Vo,et al.  Bayesian approaches to track existence - IPDA and random sets , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[42]  Ashraf A. Kassim,et al.  Tracking a Variable Number of Human Groups in Video Using Probability Hypothesis Density , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[43]  Y. Bar-Shalom,et al.  Probability hypothesis density filter for multitarget multisensor tracking , 2005, 2005 7th International Conference on Information Fusion.

[44]  Raman K. Mehra,et al.  Joint tracking and identification with robustness against unmodeled targets , 2003, SPIE Defense + Commercial Sensing.

[45]  K. Punithakumar,et al.  Multiple-model probability hypothesis density filter for tracking maneuvering targets , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[46]  A. El-Fallah,et al.  Unified Bayesian situation assessment sensor management , 2005, SPIE Defense + Commercial Sensing.

[47]  Yaakov Bar-Shalom,et al.  A physical-space approach for the probability hypothesis density and cardinalized probability hypothesis density filters , 2006, SPIE Defense + Commercial Sensing.

[48]  Ba-Ngu Vo,et al.  Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter , 2007, IEEE Transactions on Signal Processing.

[49]  Ronald P. S. Mahler,et al.  Multisensor-multitarget sensor management with target preference , 2004, SPIE Defense + Commercial Sensing.

[50]  R. Mahler.  Multitarget Bayes filtering via first-order multitarget moments , 2003 .

[51]  B. Vo,et al.  A closed-form solution for the probability hypothesis density filter , 2005, 2005 7th International Conference on Information Fusion.

[52]  T. Kirubarajan,et al.  PHD filtering for tracking an unknown number of sources using an array of sensors , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[53]  Ba-Ngu Vo,et al.  GM-PHD filter multitarget tracking in sonar images , 2006, SPIE Defense + Commercial Sensing.

[54]  Daniel E. Clark,et al.  Convergence results for the particle PHD filter , 2006, IEEE Transactions on Signal Processing.