Poisson Multi-Bernoulli Approximations for Multiple Extended Object Filtering

Xia, Yuxuan; Granström, Karl; Svensson, Lennart; Fatemi, Maryam; García-Fernández, Ángel F.; Williams, Jason L.

doi:10.1109/taes.2021.3111720

Cited by 26 publications

(14 citation statements)

References 53 publications

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“…1 for an example. These two different local hypothesis representations lead to the same PMBM posterior, but the one in Proposition 2 facilitates the development of efficient PMB approximation methods [40].…”

Section: Filtering Recursionsmentioning

confidence: 99%

“…The PMB is a special case of PMBM with a single MB component. We can form PMB approximations using different techniques, see, e.g., [40], [52], [55]. In this work, we follow [52] where the best TPMB approximation is defined by using Kullback-Leibler divergence (KLD) minimization, on a trajectory space with auxiliary variables [52].…”

Section: E Trajectory Pmb Approximationmentioning

confidence: 99%

“…The first category contains methods based on random vectors, including, e.g., the multiple hypothesis tracker (MHT) [11], the probabilistic MHT [12], the joint (integrated) probabilistic data association filter [9], [13]- [18], graph-based filters [19]- [21] using belief propagation (also known as the sum-product algorithm (SPA)), and the box particle filter [22]. The second category contains methods based on random finite sets (RFSs) [23], including the probability hypothesis density (PHD) filter [24]- [29], the cardinalized PHD filter [30], filters based on labelled RFSs [31]- [34], the Poisson multi-Bernoulli mixture (PMBM) filter [35]- [38], and its approximation the Poisson multi-Bernoulli (PMB) filter [39], [40].…”

Section: Introductionmentioning

confidence: 99%

“…Common to all the multiple extended object filters is that the data association problem, due to the unknown correspondences between measurements and objects, needs to be efficiently addressed to keep the computational complexity at a tractable level. A common way is to handle the data association problem in two stages: first, clustering algorithms are used to find a set of reasonable measurement partitions; second, for each partition, the explicit assignment of measurement clusters to objects is either avoided using the principle approximation [25], [26], [28], [30] or obtained using a 2D assignment algorithm [31]- [33], [35], [37]- [40]. These two-step approaches based on clustering and assignment (C&A) usually work well in scenarios with well-spaced objects, but they may suffer from a decreased performance in scenarios where objects move in close proximity.…”

Section: Introductionmentioning

confidence: 99%

“…To leverage 1) the PMBM filtering recursions on the pos-terior of sets of trajectories built on the standard extended object models, and 2) the efficient data association method in [20] using BP, we present the trajectory PMB (TPMB) filters for EOT using particle BP. Compared to the extended object PMB filter in our previous work [40], where the PMB approximation is obtained by marginalizing out the data association uncertainties using truncated global hypotheses, the proposed TPMB filter considers the posterior on sets of trajectories, and the marginal association probabilities and Bernoulli densities in the update step are jointly obtained using BP.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory PMB Filters for Extended Object Tracking Using Belief Propagation

Xia¹,

García-Fernández²,

Meyer³

et al. 2022

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In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) posterior after the update step is approximated as a PMB. The efficient PMB approximation relies on several important theoretical contributions. First, we present a PMBM conjugate prior on the posterior of sets of trajectories for a generalized measurement model, in which each object generates an independent set of measurements. The PMBM density is a conjugate prior in the sense that both the prediction and the update steps preserve the PMBM form of the density. Second, we present a factor graph representation of the joint posterior of the PMBM set of trajectories and association variables for the Poisson spatial measurement model. Importantly, leveraging the PMBM conjugacy and the factor graph formulation enables an elegant treatment on undetected objects via a Poisson point process and efficient inference on sets of trajectories using BP, where the approximate marginal densities in the PMB approximation can be obtained without enumeration of different data association hypotheses. To achieve this, we present a particle-based implementation of the proposed filter, where smoothed trajectory estimates, if desired, can be obtained via single-object particle smoothing methods, and its performance for EOT with ellipsoidal shapes is evaluated in a simulation study.

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Section: Filtering Recursionsmentioning

confidence: 99%