Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation

TL;DR

This paper introduces a novel Gaussian multi-target filtering approach that models target dynamics with stochastic differential equations, providing closed-form solutions and extensions to nonlinear dynamics for improved multi-target tracking.

Contribution

It develops a Gaussian continuous-discrete PMBM filter with closed-form expressions for target birth and motion, extending to nonlinear stochastic differential equations.

Findings

Derivation of closed-form mean and covariance for target birth

Introduction of a Gaussian continuous-discrete PMBM filter

Extensions to nonlinear target dynamics

Abstract

This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. In particular, targets appear according to a Poisson point process (PPP) in time with a given Gaussian spatial distribution, targets move according to a general time-invariant linear stochastic differential equation, and the life span of each target is modelled with an exponential distribution. For this multi-target dynamic model, we derive the distribution of the set of new born targets and calculate closed-form expressions for the best fitting mean and covariance of each target at its time of birth by minimising the Kullback-Leibler divergence via moment matching. This yields a novel Gaussian continuous-discrete Poisson multi-Bernoulli mixture (PMBM) filter, and its approximations based on Poisson multi-Bernoulli and probability hypothesis density filtering. These continuous-discrete multi-target filters are also extended to target dynamics driven by nonlinear stochastic differential equations.