# phd approach for multi-target tracking nikki hu nikki hu

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- Slide 1
- PHD Approach for Multi-target Tracking Nikki Hu Nikki Hu
- Slide 2
- Outline Acknowledgement Acknowledgement Review of PHD filter Review of PHD filter Simulation Simulation Further work Further work
- Slide 3
- Acknowledgements Much of this work is from Tracking and Identifying of Multiple Targets Much of this work is from Tracking and Identifying of Multiple Targets Code modified from Matlab codes Code modified from Matlab codes
- Slide 4
- Review of PHD Filter Multitarget Bayes Filter Multitarget Bayes Filter M.T. 1 st -Moment Filter M.T. 1 st -Moment Filter PHD Filter Implementation PHD Filter Implementation Particle-System Equations for PHD Mass Updates for Particles
- Slide 5
- Multitarget Bayes Filter sensors Z k+1 targets data Z k = T k C k multitarget motion T k+1 = T k B k multitarget Markov motion model multitarget time prediction f k+1|k (Y|Z (k) ) = f k+1|k (Y|X) f k|k (X|Z (k) ) X multisensor-multitarget Bayes update multisensor -multitarget likelihood function f k+1|k+1 (X|Z (k+1) ) f(Z k+1 |X) f k+1|k (X|Z (k) ) X k+1 ^ multitarget state estimation
- Slide 6
- M.T. 1 st -Moment Filter f k|k (X|Z (k) ) f k+1|k+1 (X|Z (k+1) ) f k+1|k (X|Z (k) ) k|k k+1|k+1 k+1|k multitarget Bayes filter use filter that propagates multitarget first-moment densities observation space single-target state space Time-update step Data-update step 1 st moment (PHD)Fillter
- Slide 7
- time-update step data-update step D k+1|k (x|Z (k) )D k+1|k+1 (x|Z (k+1) )D k|k (x|Z (k) ) 1st-moment (PHD) filter compress to first moment compress to first moment compress to first moment
- Slide 8
- PHD Implementation Strong convergence properties Strong convergence properties for every observation sequence, particle distribution converges a.s. to posterior for every observation sequence, particle distribution converges a.s. to posterior computationally efficient ( O(N), N = no. of particles) computationally efficient ( O(N), N = no. of particles) PHD, time k PHD, time k+1 particles = samples Delta functions propagation of particles Sequential Monte-Carlo (Particle Filters)
- Slide 9
- Particle-System Equations for PHD Mass mean no. births probability of survival mean no. of offspring Time Update: Observation Update: observation likelihood prob. detection clutter density mean no. false alarms Monte Carlo samples PHD mass
- Slide 10
- Motion Update Motion Update Assume no target spawning and death probability is independent of target state. Assume no target spawning and death probability is independent of target state. Update particles using Markov density. Update particles using Markov density. Resample particles using spontaneous birth distribution Resample particles using spontaneous birth distribution Updates for Particles
- Slide 11
- Observation Update Observation Update Assume single sensor, and p D is independent of X. Assume single sensor, and p D is independent of X. Compute a weight for each particle (using below) and resample particles according to the induced distribution Compute a weight for each particle (using below) and resample particles according to the induced distribution
- Slide 12
- Problem 1 How to extract state from a PhD? How to extract state from a PhD? User wants to know target positions. User wants to know target positions. Does not want to see a Poisson process density function. Does not want to see a Poisson process density function. Are there efficient algorithms for Particle Filter implementation of PHD? Are there efficient algorithms for Particle Filter implementation of PHD?
- Slide 13
- Example 1 Current techniques rely on peak and/or cluster detection algorithms. Current techniques rely on peak and/or cluster detection algorithms.
- Slide 14
- Example 2 Peak detection algorithms are not a universal solution: Peak detection algorithms are not a universal solution:
- Slide 15
- Two Targets Tracking
- Slide 16
- Three Targets Tracking
- Slide 17
- Graphs Get from Matlab Codes System Mass
- Slide 18
- System Particles
- Slide 19
- System Targets
- Slide 20
- System Targets(. ) and estimated System Targets(x)
- Slide 21
- Further work Change Observation Model Change Observation Model Change Interacting Particle implementation to SERP Change Interacting Particle implementation to SERP