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

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

**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**

**What is a Multitarget
First-Order Moment?**

**Indirect Expected Values of
a Random State-Set**

**PHD for a Discrete State
Space (Picture)**

**Example of a PHD on 2-D
Euclidean Space**

**PHD Functional Derivative
Formula**

**PHD Filter Assumptions: Motion Model**

**PHD Filter Assumptions: Sensor Model**

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

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

**Proof, III: Choice of Likelihood Function**

**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**

**Branching Particle-System
Filters
fast and rapidly convergent**