# Second order multi-object filtering with target interaction using determinantal point processes

## TL;DR

This paper introduces a second-order PHD filter based on Determinantal Point Processes to model target interactions, specifically repulsion, improving multi-target tracking accuracy over traditional independent-target assumptions.

## Contribution

It develops a novel second-order PHD filter using DPPs that captures target interactions by propagating variance and covariance, extending beyond first-order methods.

## Key findings

- Successfully models target repulsion with DPPs
- Provides Monte Carlo simulations demonstrating improved tracking
- Estimates correlation between targets in measurement domains

## Abstract

The Probability Hypothesis Density (PHD) filter, which is used for multi-target tracking based on sensor measurements, relies on the propagation of the first-order moment, or intensity function, of a point process. This algorithm assumes that targets behave independently, an hypothesis which may not hold in practice due to potential target interactions. In this paper, we construct a second-order PHD filter based on Determinantal Point Processes (DPPs) which are able to model repulsion between targets. Such processes are characterized by their first and second-order moments, which allows the algorithm to propagate variance and covariance information in addition to first-order target count estimates. Our approach relies on posterior moment formulas for the estimation of a general hidden point process after a thinning operation and a superposition with a Poisson Point Process (PPP), and on suitable approximation formulas in the determinantal point process setting. The repulsive properties of determinantal point processes apply to the modeling of negative correlation between distinct measurement domains. Monte Carlo simulations with correlation estimates are provided.