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. 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

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.  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

8. 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)

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. 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

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