# Set-Type Belief Propagation with Applications to Poisson Multi-Bernoulli SLAM

arXiv: https://arxiv.org/abs/2305.04797 · HTML: https://mlsanity.com/paper/2305.04797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 58 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 15 of 15)

- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [Poisson multi-Bernoulli mixture filter: direct derivation and implementation](https://mlsanity.com/paper/1703.04264/) (2017)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Trajectory Poisson multi-Bernoulli filters](https://mlsanity.com/paper/2003.12767/) (2020)
- [A Scalable Algorithm for Tracking an Unknown Number of Targets Using Multiple Sensors](https://mlsanity.com/paper/1607.07647/) (2016)
- [Gaussian implementation of the multi-Bernoulli mixture filter](https://mlsanity.com/paper/1908.08819/) (2019)
- [A Belief Propagation Algorithm for Multipath-Based SLAM](https://mlsanity.com/paper/1801.04463/) (2018)
- [5G mmWave Cooperative Positioning and Mapping using Multi-Model PHD Filter and Map Fusion](https://mlsanity.com/paper/1908.09806/) (2019)
- [PMBM-based SLAM Filters in 5G mmWave Vehicular Networks](https://mlsanity.com/paper/2205.02502/) (2022)
- [Data Fusion for Multipath-Based SLAM: Combining Information from Multiple Propagation Paths](https://mlsanity.com/paper/2211.09241/) (2022)
- [5G mmWave Downlink Vehicular Positioning](https://mlsanity.com/paper/1901.01931/) (2019)
- [Trajectory PMB Filters for Extended Object Tracking Using Belief Propagation](https://mlsanity.com/paper/2207.10164/) (2022)
- [Poisson multi-Bernoulli mixture filter with general target-generated measurements and arbitrary clutter](https://mlsanity.com/paper/2210.12983/) (2022)
- [Multisensor Poisson Multi-Bernoulli Filter for Joint Target-Sensor State Tracking](https://mlsanity.com/paper/1712.08146/) (2017)
- [A Computationally Efficient EK-PMBM Filter for Bistatic mmWave Radio SLAM](https://mlsanity.com/paper/2109.03561/) (2021)

## Abstract (arXiv)

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.