Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM
This work addresses a bottleneck in probabilistic inference for robotics and multi-target tracking by extending BP to set-type variables, though it is incremental as it builds on existing PMB and BP frameworks.
The paper tackles the problem of belief propagation (BP) for random finite sets (RFSs) with an unknown number of elements, developing set-type BP rules and applying them to Poisson multi-Bernoulli (PMB) SLAM, resulting in a performance gain over vector-type BP-SLAM filters.
Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random variables with a fixed and known number of vector elements, while certain applications rely on RFSs with an unknown number of vector elements. In this paper, we develop BP rules for factor graphs defined on sequences of RFSs where each RFS has an unknown number of elements, with the intention of deriving novel inference methods for RFSs. Furthermore, we show that vector-type BP is a special case of set-type BP, where each RFS follows the Bernoulli process. To demonstrate the validity of developed set-type BP, we apply it to the PMB filter for SLAM, which naturally leads to new set-type BP-mapping, SLAM, multi-target tracking, and simultaneous localization and tracking filters. Finally, we explore the relationships between the vector-type BP and the proposed set-type BP PMB-SLAM implementations and show a performance gain of the proposed set-type BP PMB-SLAM filter in comparison with the vector-type BP-SLAM filter.