A Fast Labeled Multi-Bernoulli Filter Using Belief Propagation

Abstract

We propose a fast labeled multi-Bernoulli (LMB) filter that uses belief propagation for probabilistic data association. The complexity of our filter scales only linearly in the numbers of Bernoulli components and measurements, while the performance is comparable to or better than that of the Gibbs sampler-based LMB filter.

Trajectory Poisson Multi-Bernoulli Filters

“…IV]. The MBM 01 form is avoided in the fast LMB in [47]. The TPMB avoids these drawbacks by creating Bernoulli components directly from the measurements, performing the update in PMBM form, without MBM 01 , and estimating trajectories directly from the posterior.…”

An Efficient Labeled/Unlabeled Random Finite Set Algorithm for Multiobject Tracking

“…A widely used approach to achieving track continuity is to model the multiobject state by a labeled RFS [9]- [16]. Related tracking filters include the generalized labeled multi-Bernoulli (GLMB) filter [9], [10], which is based on the GLMB RFS, and the labeled multi-Bernoulli (LMB) filter [11]- [13], which is based on the LMB RFS. Compared to the GLMB filter, the LMB filter incorporates certain approximations resulting in a much lower complexity.…”

“…Compared to the GLMB filter, the LMB filter incorporates certain approximations resulting in a much lower complexity. Recently, (G)LMB methods for large-scale tracking scenarios [13]- [15] and multi-scan problems [16] have been proposed. On the other hand, the track-oriented marginal multi-Bernoulli/Poisson (TOMB/P) filter [17] is based on the union of two unlabeled RFSs, namely, a Poisson RFS and an MB RFS.…”

“…Algorithms based on this approach comprise the trajectory PHD and CPHD filters [23], the trajectory multi-Bernoulli mixture filter [21], and the trajectory Poisson multi-Bernoulli mixture filter [22]. These methods can have performance advantages over the methods proposed in [13]- [15], [17]- [20], but also a significantly increased computational complexity.…”

“…In summary, the exact update step transforms the predicted posterior pgfl G Xk ,X k [ h, h|Z 1:k−1 ] in (13), which is approximately the product of an LMB pgfl and a Poisson pgfl, into the new posterior pgfl G Xk ,X k [ h, h|Z 1:k ], which, according to (18) and our discussion above, is the product of the LMB-MB mixture pgfl G Xk ,X k [ h, h] in (19) and the Poisson pgfl G X k [h] in (30). The exact update step also takes into account the detection of objects that are unlikely to exist.…”