Particle approximation of the intensity measures of a spatial branching point process arising in multi-target tracking

TL;DR

This paper analyzes the stability and long-term behavior of intensity measures in a spatial branching point process for multi-target tracking and introduces a novel particle scheme with strong theoretical guarantees.

Contribution

It provides the first sharp theoretical results for this class of spatial branching point processes and proposes a new particle approximation method.

Findings

Established stability and long-term behavior of intensity measures.

Developed a particle scheme with uniform and non-asymptotic error estimates.

Proved a functional central limit theorem for the particle approximation.

Abstract

The aim of this paper is two-fold. First we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple target tracking context. We study its stability properties, characterize its long time behavior and provide a series of weak Lipschitz type functional contraction inequalities. Second we design and analyze an original particle scheme to approximate numerically these intensity measures. Under appropriate regularity conditions, we obtain uniform and non asymptotic estimates and a functional central limit theorem. To the best of our knowledge, these are the first sharp theoretical results available for this class of spatial branching point processes.