On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

TL;DR

This paper investigates the stability and approximation properties of measure-valued equations in nonlinear multi-target filtering, demonstrating convergence of stochastic algorithms like particle filters, with applications to Bernoulli and PHD filters.

Contribution

It provides the first stability and convergence analysis for a broad class of nonlinear multi-target filtering algorithms, including sequential Monte Carlo methods.

Findings

Exponential stability of measure-valued equations established.

Uniform convergence of stochastic filtering algorithms proved.

Applications to Bernoulli and PHD filters demonstrated.

Abstract

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject.