Tracking in High Target Densities Using a
First-Order Multitarget Moment Density

Problem

Approach:  “Bulk Tracking”

Approach (Ctd.): 1^st-Order Multitarget Moment Filter

Topics

Slide 6

Multi-Sensor/Target Problem:  Point Process Formulation

Geometric Point Processes (= Random Finite Sets)

Integral and Derivative for Simple Point Processes

Probability Law of a Geometric Point Process

Slide 11

Slide 12

What is a Multitarget First-Order Moment?

Two Possible Choices for   f

Indirect Expected Values of a Random State-Set

PHD for a Discrete State Space (Picture)

The PHD (Ctd.)

Example of a PHD on 2-D Euclidean Space

Slide 19

PHD Functional Derivative Formula

PHD Filter Assumptions:  Motion Model

PHD Filter Assumptions:  Sensor Model

Slide 23

Slide 24

Proof, I:  Transform PHD into p.g.fl. Form

Proof, II:  Transform PHD into p.g.fl. Form

Proof, III:  Choice of Likelihood Function

Proof, IV:  Simplification

Slide 29

Example:  Six Targets, Two Clusters

Two Clusters:  PHD at 3^rd Observation

Two Clusters :  PHD at 9^th Observation

Two Clusters:  PHD at 17^th Observation

Two Clusters:  PHD at 27^th Observation

Two Clusters:  PHD at 31^st Observation

Slide 36

Branching Particle-System Filters
fast and rapidly convergent

Simple Simulation:  Multitarget Tracking in Clutter

Summary / Conclusions