# PMBM-based SLAM Filters in 5G mmWave Vehicular Networks

**Authors:** Hyowon Kim, Karl Granström, Lennart Svensson, Sunwoo Kim, Henk Wymeersch  
**arXiv:** [2205.02502](https://arxiv.org/abs/2205.02502)  
**Date:** 2022-05-05  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2205.02502v1/

## Key points

- Radio-based vehicular SLAM goal: accurately locate vehicles and create a map of surrounding landmarks
- Proposed approach: sequence of three Poisson multi-Bernoulli mixture (PMBM) based filters
- Filters progressively reduce complexity while maintaining high accuracy
- Key innovation: deriving SLAM density approximation by marginalizing nuisance parameters
- First filter: PMBM SLAM filter based on Rao-Blackwellized particle filter
- Second filter: PMB SLAM filter with novel interpretation using auxiliary variables and relation to Bethe free energy
- Third filter: marginalized PMB SLAM filter using low-complexity cubature Kalman filter instead of particles
- Evaluation compared to PHD SLAM filter in 5G mmWave vehicular networks
- Computation-performance trade-off between filters demonstrated, highlighting effectiveness in real-world scenarios

## Summary

In the field of radio-based vehicular simultaneous localization and mapping (SLAM), the goal is to accurately locate vehicles while simultaneously creating a map of the surrounding landmarks. The authors propose a novel approach to SLAM using a sequence of three Poisson multi-Bernoulli mixture (PMBM) based filters. These filters are designed to handle the entire SLAM problem in an optimal manner, progressively reducing complexity while maintaining high accuracy. The key innovation of the proposed approach lies in deriving SLAM density approximation by marginalizing nuisance parameters such as vehicle state or data association. The first filter in the sequence is the PMBM SLAM filter which serves as the foundation. The authors provide a comprehensive description of this filter based on a Rao-Blackwellized particle filter. The second filter in the sequence is the Poisson multi-Bernoulli (PMB) SLAM filter which builds upon the standard reduction from PMBM to PMB but introduces a novel interpretation using auxiliary variables and their relation to Bethe free energy. Finally, leveraging the same auxiliary variable argument, they derive a marginalized PMB SLAM filter that avoids particles and instead utilizes a low-complexity cubature Kalman filter. This marginalized approach further reduces computational complexity while maintaining accuracy. To evaluate their proposed filters, they compare them with probability hypothesis density (PHD) SLAM filter in 5G mmWave vehicular networks and demonstrate a computation-performance trade-off between these filters highlighting their effectiveness in handling SLAM tasks in real world scenarios. Overall, this paper presents a significant contribution to radio-based vehicular SLAM by introducing a sequence of three PMBM based filters that offer theoretical optimality and progressively reduced complexity without compromising accuracy.