PHD Approach PHD Approach for Multi-target for Multi-target

TrackingTracking

Nikki HuNikki Hu

OutlineOutline

AcknowledgementAcknowledgement Review of PHD filterReview of PHD filter SimulationSimulation Further workFurther work

AcknowledgementsAcknowledgements

Much of this work is from Tracking Much of this work is from Tracking and Identifying of Multiple Targetsand Identifying of Multiple Targets

Code modified from Matlab codesCode modified from Matlab codes

Review of PHD FilterReview of PHD Filter

Multitarget Bayes FilterMultitarget Bayes Filter M.T. 1M.T. 1stst-Moment Filter-Moment Filter PHD Filter ImplementationPHD Filter Implementation

Particle-System Equations for PHD Particle-System Equations for PHD MassMass

Updates for ParticlesUpdates for Particles

Multitarget Bayes Multitarget Bayes FilterFilter

sensors

Zk+1targets

data

Zk = Tk Ck

multitarget motion

Tk+1= Tk Bk

multitarget Markov motionmodel

multitarget time prediction

fk+1|k(Y|Z(k)) = fk+1|k(Y|X) fk|k(X|Z(k))X

multisensor-multitargetBayes update

multisensor-multitarget

likelihoodfunction

fk+1|k+1(X|Z(k+1)) f(Zk+1|X) fk+1|k(X|Z(k))Xk+1^

multitarget state estimation

M.T. 1M.T. 1stst-Moment -Moment FilterFilter

fk|k(X|Z(k)) fk+1|k+1(X|Z(k+1)) fk+1|k(X|Z(k))

k|k k+1|k+1k+1|k

multitargetBayes filter

use filter that propagates multitarget first-moment densities

observation space

single-target state space

Time-update step

Data-update step

1st –moment (PHD)Fillter

)|( )(|

kkk ZXD )|( )(

|1k

kk ZXD )|( )1(1|1

kkk ZXD

time-updatestep

data-updatestep

Dk+1|k(x|Z(k)) Dk+1|k+1(x|Z(k+1))Dk|k(x|Z(k))1st-moment(PHD) filter

compress tofirst moment

compress tofirst moment

compress tofirst moment

PHD PHD ImplementationImplementation

Strong convergence propertiesStrong convergence properties for every observation sequence, particle for every observation sequence, particle distribution converges a.s. to posteriordistribution converges a.s. to posterior

computationally efficient ( computationally efficient ( OO((NN), ), NN = no. of particles) = no. of particles)

PHD, time k PHD, time k+1

“particles”= samples

Deltafunctions

propagation of particles

Sequential Monte-Carlo (Particle Filters)

Particle-System Particle-System Equations for PHD Equations for PHD

MassMass

N

1i

ikkk1kN

MN

1i

ikkk1kN

Mk1kk1k XBXqBM kkkk

||||||||

mean no. birthsprobability of survival mean no. of

offspring

N

i

ikkD

kk

ZzN

i

ikk

ikkD

kkkk

ikk

N

i

ikkD

kk

kk XpN

M

XzfXpN

Mzc

XzfXpN

M

Mk 1

|1|1

1|1|1

|111

|11

|1|1

1|1 1|

|

Time Update:

Observation Update:

observation likelihood

prob. detection

clutter densitymean no. false alarms

Monte Carlo samplesPHD mass

Motion UpdateMotion UpdateAssume no target spawning and Assume no target spawning and death probability is independent of death probability is independent of target state.target state.

Update particles using Markov Update particles using Markov density.density.

Resample particles Resample particles using spontaneous birth distributionusing spontaneous birth distribution

Updates for Updates for ParticlesParticles

Observation UpdateObservation Update Assume single sensor, and Assume single sensor, and ppDD is is

independent of independent of XX..

Compute a weight for each particle Compute a weight for each particle (using below) and resample particles (using below) and resample particles according to the induced distributionaccording to the induced distribution

Problem 1Problem 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 Does not want to see a Poisson process

density function.density function.

Are there efficient algorithms for Particle Are there efficient algorithms for Particle Filter implementation of PHD?Filter implementation of PHD?

Example 1Example 1

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

2 dxZxD kk

Example 2Example 2

Peak detection Peak detection algorithms are not algorithms are not a universal a universal solution:solution: 2 dxZxD k

k

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 workFurther work

Change Observation ModelChange Observation Model Change Interacting Particle Change Interacting Particle

implementation to SERPimplementation to SERP