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

Abstract

For the standard point target model with Poisson birth process, the Poisson Multi-Bernoulli Mixture (PMBM) is a conjugate multi-target density. The PMBM filter for sets of targets has been shown to have state-of-the-art performance and a structure similar to the Multiple Hypothesis Tracker (MHT). In this paper we consider a recently developed formulation of multiple target tracking as a random finite set (RFS) of trajectories, and present three important and interesting results. First, we show that, for the standard point target model, the PMBM density is conjugate also for sets of trajectories. Second, based on this we develop PMBM trackers (trajectory RFS filters) that efficiently estimate the set of trajectories. Third, we establish that for the standard point target model the multi-trajectory density is PMBM for trajectories in any time window, given measurements in any (possibly non-overlapping) time window. In addition, the PMBM trackers are evaluated in a simulation study, and shown to yield state-of-the-art performance.

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

“…Closed-form PMBM filtering recursions based on the sets of trajectories framework have been derived in [31], which enables us to leverage on the benefits of the PMBM filter recursion based on sets of targets, while also obtaining track continuity. Assuming standard point target dynamic [32,Sec 13.2.4] and measurement models (defined in Section 2-A), two different trajectory PMBM filters were proposed in [31]: one in which the set of current (i.e., alive) trajectories is tracked, and one in which the set of all trajectories (dead and alive) up to the current time step is tracked. In both cases, finite trajectories, i.e., trajectories of finite length in time, are considered.…”

“…The implementation of the trajectory PMBM filter in [31] considers the single-scan data association problem, and the best global hypotheses are found using Murty's algorithm [33]. As a complement to [31], an approximation to the exact trajectory PMBM filter that considers multi-scan data association was developed in [34].…”

“…The implementation of the trajectory PMBM filter in [31] considers the single-scan data association problem, and the best global hypotheses are found using Murty's algorithm [33]. As a complement to [31], an approximation to the exact trajectory PMBM filter that considers multi-scan data association was developed in [34]. It operates by performing track-oriented N-scan pruning [5] to limit computational complexity, and using dual decomposition [17] to solve the involved multiframe assignment problem.…”

“…In this paper, we present the trajectory PMBM and the trajectory MBM filter with multi-scan data association. The main novelties of the proposed algorithms, compared to previous work based on sets of trajectories [27], [31], [38], [39], are that they consider the multi-scan data association problem. The main novelties of the proposed algorithms, compared to TOMHT, are that they produce full trajectory estimates, i.e., smoothed estimates, upon receipt of each new set of measurements, and that the filters based on sets of trajectories model the targets that remain to be detected and the target death subsequent to the final detection.…”

“…A multi-Bernoulli RFS is the union of a finite number of independent Bernoulli RFSs. In previous work [27], [31], [38], [39] two different birth models have been used. In this paper we present multi-scan trajectory filter implementations for both birth models: the Poisson birth model defined in Assumption 1; and the multi-Bernoulli birth model defined in Assumption 2.…”