Particle Association Measures and Multiple Target Tracking

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


In the last decade, the area of multiple target tracking has witnessed the introduction of important concepts and methods, aiming at establishing principled approaches for dealing with the estimation of multiple objects in an efficient way. One of the most successful classes of multi-object filters that have been derived out of these new grounds includes all the variants of the Probability Hypothesis Density (phd) filter. In spite of the attention that these methods have attracted, their theoretical performances are still not fully understood. In this chapter, we first focus on the different ways of establishing the equations of the phd filter, using a consistent set of notations. The objective is then to introduce the idea of observation path, upon which association measures are defined. We will see how these concepts highlight the structure of the first moment of the multi-object distributions in time, and how they allow for devising solutions to practical estimation problems.


Multiple Target Tracking Association Measures Probability Hypothesis Density Filter Observation Path General Clutter 
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  1. 1.
    Blackman, S.S.: Multiple-Target Tracking with Radar Applications, vol. 463 p. 1. Artech House, Inc., Dedham, MA (1986)Google Scholar
  2. 2.
    Caron, F., Del Moral, P., Doucet, A., Pace, M.: On the conditional distributions of spatial point processes. Adv. Appl. Probab. 43(2), 301–307 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Clark, D.E.: First-moment multi-object forward-backward smoothing. In: 2010 13th Conference on Information Fusion (FUSION), IEEE (2010)Google Scholar
  4. 4.
    Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes, vol. II. Springer, New York (2008)CrossRefzbMATHGoogle Scholar
  5. 5.
    Del Moral, P.: Feynman-Kac Formulae. Springer, Berlin (2004)Google Scholar
  6. 6.
    Del Moral, P.: Mean field simulation for Monte Carlo integration. Chapman and Hall/CRC Monographs on Statistics and Applied Probability (2013)Google Scholar
  7. 7.
    Fortmann, T.E., Bar-Shalom, Y., Scheffe, M.: Sonar tracking of multiple targets using joint probabilistic data association. IEEE J. Oceanic Eng. 8(3), 173–184 (1983)CrossRefGoogle Scholar
  8. 8.
    Goodman, I.R., Mahler, R.P.S., Nguyen, H.T.: Mathematics of Data Fusion, vol. 37. Springer Science & Business Media (1997)Google Scholar
  9. 9.
    Houssineau, J., Del Moral, P., Clark, D.E.: General multi-object filtering and association measure. In: 2013 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), (2013)Google Scholar
  10. 10.
    Jiang, L., Singh, S.S., Yıldırım, S.: arXiv preprint arXiv:1410.2046 (2014)
  11. 11.
    Mahler, R.P.S.: An Introduction to Multisource-Multitarget Statistics and Applications. Lockheed Martin (2000)Google Scholar
  12. 12.
    Mahler, R.P.S.: Multitarget Bayes filtering via first-order multitarget moments. IEEE Trans. Aerosp. Electron. Syst. 39(4), 1152–1178 (2003)Google Scholar
  13. 13.
    Mahler, R.P.S.: PHD filters of higher order in target number. IEEE Trans. Aerosp. Electron. Syst. 43(4), 1523–1543 (2007)Google Scholar
  14. 14.
    Mahler, R.P.S.: Statistical Multisource-Multitarget Information Fusion. Artech House, Boston (2007)zbMATHGoogle Scholar
  15. 15.
    Mahler, R.P.S., Vo, B.T., Vo, B.N.: Forward-backward probability hypothesis density smoothing. IEEE Trans. Aerosp. Electron. Syst. 48(1), 707–728 (2012)Google Scholar
  16. 16.
    Pace, M., Del Moral, P.: Mean-field PHD filters based on generalized Feynman-Kac flow. J. Sel. Top. Signal Process. Special issue on multi-target tracking (2013)Google Scholar
  17. 17.
    Panta, K., Clark, D.E., Vo, B.N.: Data association and track management for the Gaussian mixture probability hypothesis density filter. IEEE Trans. Aerosp. Electron. Syst. 45(3), 1003–1016 (2009)Google Scholar
  18. 18.
    Ristic, B., Clark, D.: Particle filter for joint estimation of multi-object dynamic state and multi-sensor bias. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3877–3880. IEEE (2012)Google Scholar
  19. 19.
    Ristic, B., Clark, D., Vo, B.N.: Improved SMC implementation of the PHD filter. In: 2010 13th Conference on Information Fusion (FUSION), pp. 1–8. IEEE (2010)Google Scholar
  20. 20.
    Singh, S.S., Vo, B.N., Baddeley, A., Zuyev, S.: Filters for spatial point processes. SIAM J. Control Optim. 48(4), 2275–2295 (2009)Google Scholar
  21. 21.
    Vo, B.N., Ma, W.K.: The Gaussian mixture probability hypothesis density filter. IEEE Trans. Signal Process. 54(11), 4091–4104 (2006)Google Scholar
  22. 22.
    Vo, B.N., Singh, S., Doucet, A.: Sequential Monte Carlo methods for multitarget filtering with random finite sets. IEEE Trans. Aerosp. Electron. Syst. 41(4), 1224–1245 (2005)Google Scholar
  23. 23.
    Vo, B.T., Vo, B.N., Cantoni, A.: Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Trans. Signal Process. 55(7), 3553–3567 (2007)Google Scholar
  24. 24.
    Vu, T., Vo, B.N., Evans, R.: A particle marginal Metropolis-Hastings multi-target tracker. IEEE Trans. Signal Process. 62(15), 3953–3964 (2014)Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.School of Engineering and Physical SciencesHeriot-Watt UniversityEdinburghUK

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