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

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

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 multisensor-multitarget Bayes update likelihood function fk+1|k+1(X|Z(k+1))  f(Zk+1|X) fk+1|k(X|Z(k)) Tk+1= Tk  Bk Xk+1 ^ multitarget state estimation

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

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

PHD Implementation Sequential Monte-Carlo (Particle Filters) PHD, time k PHD, time k+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)

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

Updates for Particles 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

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

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?

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

Example 2 Peak detection algorithms are not a universal solution:

Two Targets Tracking

Three Targets Tracking

Graphs Get from Matlab Codes System Mass

System Particles

System Targets

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

Further work Change Observation Model Change Interacting Particle implementation to SERP