Multiple Object Trajectory Estimation Using Backward Simulation

Authors:
  • YXYuxuan Xia
    Yuxuan Xia
  • LSLennart Svensson
    Lennart Svensson
  • ÁGÁngel F. García-Fernández
    Ángel F. García-Fernández
  • JWJason L. Williams
    Jason L. Williams
  • DSDaniel Svensson
    Daniel Svensson
  • KGKarl Granström
    Karl Granström
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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.
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