Backward Simulation for Sets of Trajectories

TL;DR

This paper introduces a backward simulation method for sets of trajectories, enabling full trajectory recovery from multitarget filtering densities without explicit trajectory estimation, demonstrated through simulations.

Contribution

It derives a general multitrajectory smoothing equation and proposes a backward simulation sampling method for multi-Bernoulli processes.

Findings

Effective trajectory recovery demonstrated in simulations

New smoothing equation for sets of trajectories

Backward simulation enables trajectory sampling in multitarget filters

Abstract

This paper presents a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories, from a sequence of multitarget (unlabelled) filtering densities and the multitarget dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multitarget filters that do not explicitly estimate trajectories. In this paper, we first derive a general multitrajectory forward-backward smoothing equation based on sets of trajectories and the random finite set framework. Then we show how to sample sets of trajectories using backward simulation when the multitarget filtering densities are multi-Bernoulli processes. The proposed approach is demonstrated in a simulation study.