Poisson Conjugate Prior for PHD Filtering based Track-Before-Detect Strategies in Radar Systems

TL;DR

This paper derives a new Poisson conjugate prior for PHD filters in track-before-detect radar systems, providing a rigorous, closed-form solution and demonstrating improved performance in low SNR conditions.

Contribution

It introduces a principled derivation of the TBD-PHD filter based on Kullback-Leibler divergence and establishes the conjugacy of PHD filters to Poisson priors in TBD strategies.

Findings

Effective in Rayleigh noise and low SNR scenarios

Provides a closed-form solution for TBD-PHD filter

Demonstrates improved target tracking performance

Abstract

A variety of filters with track-before-detect (TBD) strategies have been developed and applied to low signal-to-noise ratio (SNR) scenarios, including the probability hypothesis density (PHD) filter. Assumptions of the standard point measurement model based on detect-before-track (DBT) strategies are not suitable for the amplitude echo model based on TBD strategies. However, based on different models and unmatched assumptions, the measurement update formulas for DBT-PHD filter are just mechanically applied to existing TBD-PHD filters. In this paper, based on the Kullback-Leibler divergence minimization criterion, finite set statistics theory and rigorous Bayes rule, a principled closed-form solution of TBD-PHD filter is derived. Furthermore, we emphasize that PHD filter is conjugated to the Poisson prior based on TBD strategies. Next, a capping operation is devised to handle the divergence of target number estimation as SNR increases. Moreover, the sequential Monte Carlo implementations of dynamic and amplitude echo models are proposed for the radar system. Finally, Monte Carlo experiments exhibit good performance in Rayleigh noise and low SNR scenarios.