# Poisson Multi-Bernoulli Mapping Using Gibbs Sampling

arXiv: https://arxiv.org/abs/1811.03154 · HTML: https://mlsanity.com/paper/1811.03154/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [A comparison between PMBM Bayesian track initiation and labelled RFS adaptive birth](https://mlsanity.com/paper/2207.06156/) (2022)

## Abstract (arXiv)

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multi-object posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.