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PHD Approach for Multi-target Tracking

PHD Approach for Multi-target Tracking. Nikki Hu. Outline. Acknowledgement Review of PHD filter Simulation Further work. Acknowledgements. Much of this work is from Tracking and Identifying of Multiple Targets Code modified from Matlab codes.

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PHD Approach for Multi-target Tracking

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  1. PHD Approach for Multi-target Tracking Nikki Hu

  2. Outline • Acknowledgement • Review of PHD filter • Simulation • Further work

  3. Acknowledgements • Much of this work is from Tracking and Identifying of Multiple Targets • Code modified from Matlab codes

  4. Review of PHD Filter • Multitarget Bayes Filter • M.T. 1st-Moment Filter • PHD Filter Implementation • Particle-System Equations for PHD Mass • Updates for Particles

  5. multisensor-multitarget likelihood function multisensor-multitarget Bayes update multitarget state estimation ^ fk+1|k+1(X|Z(k+1))  f(Zk+1|X) fk+1|k(X|Z(k)) Xk+1 Multitarget Bayes Filter data Zk = Tk Ck sensors multitarget Markov motion model Zk+1 multitarget time prediction targets fk+1|k(Y|Z(k)) =  fk+1|k(Y|X) fk|k(X|Z(k))dX multitarget motion Tk+1= Tk Bk

  6. M.T. 1st-Moment Filter use filter that propagates multitarget first-moment densities observation space single-target state space Xk|k Xk+1|k Xk+1|k+1 multitarget Bayes filter  fk|k(X|Z(k)) fk+1|k(X|Z(k)) fk+1|k+1(X|Z(k+1))  1st –moment (PHD)Fillter Time-update step Data-update step

  7. compress to first moment compress to first moment compress to first moment  Dk|k(x|Z(k)) Dk+1|k(x|Z(k)) Dk+1|k+1(x|Z(k+1))  time-update step data-update step 1st-moment (PHD) filter

  8. PHD Implementation Sequential Monte-Carlo (Particle Filters) PHD, timek PHD, timek+1 “particles” = samples Delta functions propagation of particles • Strong convergence properties • for every observation sequence, particle distribution converges a.s. to posterior • computationally efficient (  O(N), N = no. of particles)

  9. Particle-System Equations for PHD Mass Time Update: mean no. births mean no. of offspring probability of survival PHD mass Monte Carlo samples Observation Update: prob. detection mean no. false alarms observation likelihood clutter density

  10. Motion Update Assume no target spawning and death probability is independent of target state. Update particles using Markov density. Resample particles using spontaneous birth distribution Updates for Particles

  11. Observation Update • Assume single sensor, and pD is independent of X. • Compute a weight for each particle (using below) and resample particles according to the induced distribution

  12. Problem 1 • How to extract state from a PhD? • User wants to know target positions. • Does not want to see a Poisson process density function. • Are there efficient algorithms for Particle Filter implementation of PHD?

  13. Example 1 • Current techniques rely on peak and/or cluster detection algorithms.

  14. Example 2 • Peak detection algorithms are not a universal solution:

  15. Two Targets Tracking

  16. Three Targets Tracking

  17. Graphs Get from Matlab Codes • System Mass

  18. System Particles

  19. System Targets

  20. System Targets(.) and estimated System Targets(x)

  21. Further work • Change Observation Model • Change Interacting Particle implementation to SERP

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