Core Concepts
The core message of this article is to develop a novel set-type belief propagation (BP) algorithm that can efficiently compute approximate marginal probability densities of random finite sets (RFSs) with unknown cardinalities. The authors show that the proposed set-type BP is a generalization of the standard vector-type BP, and they apply it to derive a Poisson multi-Bernoulli (PMB) filter for simultaneous localization and mapping (SLAM).
Abstract
The article presents a novel set-type belief propagation (BP) algorithm for efficiently computing approximate marginal probability densities of random finite sets (RFSs) with unknown cardinalities. The key highlights are:
- The authors derive set-type BP update rules and introduce special factors, such as a partition and merging factor and a conversion factor, to handle sets with unknown cardinalities.
- They show that the standard vector-type BP is a special case of the proposed set-type BP, where each RFS follows a Bernoulli process.
- The authors apply the developed set-type BP to derive a Poisson multi-Bernoulli (PMB) filter for simultaneous localization and mapping (SLAM), which naturally leads to a set-type BP PMB-SLAM method.
- The set-type BP PMB-SLAM method is shown to be algorithmically equivalent to the existing vector-type BP-SLAM filters, but the proposed approach avoids certain heuristics required in the vector-type methods.
- Simulation results demonstrate that the set-type BP PMB-SLAM filter outperforms the vector-type BP-SLAM filter, especially in scenarios with informative Poisson point process (PPP) birth.