Multiscan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

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1 December 2019
Yuxuan Xia, Karl Granstrom, Lennart Svensson, Ángel F. Garcia-Fernandez, Jason L. Williams

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The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multitarget distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multitarget tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multiscan trajectory PMBM filter and a multiscan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multiscan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multiframe assignment problem. The performance of the presented multitarget trackers, applied with an efficient fixed-lag smoothing method, is evaluated in a simulation study.