An Implementation of the Poisson Multi-Bernoulli Mixture Trajectory Filter via Dual Decomposition

Abstract

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target 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 multi-target tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multi-scan trajectory PMBM filter and a multi-scan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multi-scan 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 multi-frame assignment problem. The performance of the presented multi-target trackers, applied with an efficient fixed-lag smoothing method, are evaluated in a simulation study.

Poisson Multi-Bernoulli Mixture Trackers: Continuity Through Random Finite Sets of Trajectories

“…For a fair comparison, the Gaussian densities in the MB birth were the same as the Gaussian densities in the PPP birth. All compared trackers process the measurements sequentially, one measurement set after another; comparison with trackers that involve multi-scan data association, see, e.g., [24], [36], [42], [43], is outside the scope of this work.…”

Trajectory Poisson Multi-Bernoulli Filters

“…The above track building problems can be solved by computing (multi-object) densities on sets of trajectories [23], rather than sets of labelled targets. This approach has led to the following filters: trajectory PMBM (TPMBM) filter [25], [26], trajectory MBM (TMBM) filter [27], trajectory MBM 01 (TMBM 01 ) filter [23], and trajectory PHD (TPHD) and CPHD (TCPHD) filters [28]. These filters are analogous to their set of targets counterparts, but have the ability to estimate trajectories from first principles, and the possibility of improving the estimation of past states in the trajectories.…”

Decentralized Poisson Multi-Bernoulli Filtering for Vehicle Tracking

“…The PMBM conjugate prior [25] was originally developed for point targets; a PMBM conjugate prior for extended targets was presented in [3], [4]. In several simulation studies it has been shown that, compared to tracking filters built upon labeled random finite set (RFS), the PMBM conjugate prior has good performance for tracking the set of present target states, for both point targets [26]- [28] and extended targets [3], [4], [29]. The PMBM conjugate priors for point targets and extended targets have been shown to be versatile, and have been used with data from Lidars [30]- [33], radars [31], [32], and cameras [32], [34].…”