Sequential monte carlo implementation of the phd filter for multi-target tracking

TLDR

Random finite sets provide a natural representation for multi‑target states and observations, enabling multi‑sensor tracking within the unifying random set framework, yet optimal Bayesian filtering remains impractical and SMC approximations are computationally expensive; the PHD filter offers a practical alternative by propagating only the first moment, though its integrals lack closed form. The study proposes to approximate the PHD using weighted random samples propagated over time via a generalized SMC method. The authors approximate the PHD by propagating weighted random samples over time with a generalized SMC method, addressing the integrals that lack closed form. The resulting algorithm handles nonlinear, non‑Gaussian dynamics and maintains computational complexity independent of the time‑varying number of targets.

Abstract

Random finite sets are natural represen- tations of multi-target states and observations that al- low multi-sensor multi-target tmcking to fit in the uni- fying random set framework for Data fision. Although a rigorous foundation has been developed in the form of Finite Set Statistics, optimal Bayesian multi-target filtering is not yet practical. Sequential Monte Carlo (SMC) approzimations of the optimal filter are compu- tationally ezpensive. A practical altemative to the opti- mal filter is the Probability Hypothesis Density (PHD) filter, which propagates the PHD or first moment in- stead of the full multi-target posterior. The propagation of the PHD involves multiple integrals which do not ad- mit closed form. We propose to approzimate the PHD by a set of weighted random samples which are propa- gated over time using a generalised SMC method. The resulting algorithm is very attractive as it is general enough to handle non-linear non-Gaussian dynamics and the computational complezity is independent of the (time-varying) number of targets.