# Multiple Target, Multiple Type Filtering in the RFS Framework

## TL;DR

This paper introduces a novel N-type PHD filter within the RFS framework to effectively handle multiple target types and their confusions, improving tracking accuracy in complex scenarios.

## Contribution

It extends the standard PHD filter to multiple target types with confusions and develops a Gaussian mixture implementation for practical use.

## Key findings

- Improved tracking performance with target confusions.
- Effective discrimination of multiple target types.
- Validation through simulations with 16 targets of 4 types.

## Abstract

A Multiple Target, Multiple Type Filtering (MTMTF) algorithm is developed using Random Finite Set (RFS) theory. First, we extend the standard Probability Hypothesis Density (PHD) filter for multiple types of targets, each with distinct detection properties, to develop a multiple target, multiple type filtering, N-type PHD filter, where $N\geq2$, for handling confusions among target types. In this approach, we assume that there will be confusions between detections, i.e. clutter arises not just from background false positives, but also from target confusions. Then, under the assumptions of Gaussianity and linearity, we extend the Gaussian mixture (GM) implementation of the standard PHD filter for the proposed N-type PHD filter termed the N-type GM-PHD filter. Furthermore, we analyze the results from simulations to track sixteen targets of four different types using a four-type (quad) GM-PHD filter as a typical example and compare it with four independent GM-PHD filters using the Optimal Subpattern Assignment (OSPA) metric. This shows the improved performance of our strategy that accounts for target confusions by efficiently discriminating them.