Set JPDA Filter for Multitarget Tracking

Abstract

In this article we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the Joint Probabilistic Data Association (JPDA) filter, which we call the Set JPDA (SJPDA) filter. Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, KLSJPDA, which provides optimal Gaussian approximations in the Kullback-Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean Optimal Subpattern Assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture CPHD filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter.

Track-before-detect labeled multi-bernoulli particle filter with label switching

“…This minimisation was solved in [31, Appendix C] and its result is provided in Theorem 4. A quite similar proof for a two-target case with Gaussian PDFs is found in [42].…”

“…This is the main reason why the set integrals in (2) are easier to compute than in (1). Based on [6], we make the following definition. …”

“…Importantly, at any time step, we can change the labelled RFS density π − with another labelled density ϕ − ∈ [π − ] at our convenience. These ideas were first used in [6] to provide more accurate Gaussian approximations in MTT with fixed and known number of targets.…”

“…This kind of idea, which we refer to as label switching improvement, was first introduced for fixed and known number of targets and Gaussian approximations in [6]. It can lead to benefits in performance if there is mixed labelling [7], i.e., when targets get in close proximity for a sufficiently long time and then separate.…”

“…It can lead to benefits in performance if there is mixed labelling [7], i.e., when targets get in close proximity for a sufficiently long time and then separate. An extension of [6] for MTT, with Gaussian multi-Bernoulli PDFs, has been proposed in [8].…”