Multiple Object Trajectory Estimation Using Backward Simulation

TL;DR

This paper introduces a general method for estimating multiple object trajectories from multi-object filtering densities, enabling trajectory estimation even when filters do not explicitly estimate trajectories, and demonstrates superior performance through simulations.

Contribution

It derives a general multi-trajectory backward smoothing equation and develops a tractable sampling method for Poisson multi-Bernoulli filters, advancing multi-object trajectory estimation.

Findings

Proposed multi-trajectory backward smoothing equation.

Developed a tractable backward simulation sampling method.

Demonstrated superior performance in simulations.

Abstract

This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate trajectories. In this paper, we first derive a general multi-trajectory backward smoothing equation based on random finite sets of trajectories. Then we show how to sample sets of trajectories using backward simulation for Poisson multi-Bernoulli filtering densities, and develop a tractable implementation based on ranked assignment. The performance of the resulting multi-trajectory particle smoothers is evaluated in a simulation study, and the results demonstrate that they have superior performance in comparison to several state-of-the-art multi-object filters and smoothers.