# Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering

arXiv: https://arxiv.org/abs/2211.16041 · HTML: https://mlsanity.com/paper/2211.16041/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much](https://mlsanity.com/paper/1606.03432/) (2016)
- [Scalable Importance Tempering and Bayesian Variable Selection](https://mlsanity.com/paper/1805.00541/) (2018)
- [Tracking Cells and their Lineages via Labeled Random Finite Sets](https://mlsanity.com/paper/2104.10964/) (2021)
- [Multi-sensor Joint Adaptive Birth Sampler for Labeled Random Finite Set Tracking](https://mlsanity.com/paper/2109.04355/) (2021)
- [Robust Distributed Fusion with Labeled Random Finite Sets](https://mlsanity.com/paper/1710.00501/) (2017)
- [Multi-Sensor Control for Multi-Object Bayes Filters](https://mlsanity.com/paper/1702.05858/) (2017)
- [Multi-Objective Multi-Agent Planning for Jointly Discovering and Tracking Mobile Object](https://mlsanity.com/paper/1911.09807/) (2019)
- [Multi-object Tracking for Generic Observation Model Using Labeled Random Finite Sets](https://mlsanity.com/paper/1604.01202/) (2016)
- [Online UAV Path Planning for Joint Detection and Tracking of Multiple Radio-tagged Objects](https://mlsanity.com/paper/1808.04445/) (2018)
- [Multi-Scan Multi-Sensor Multi-Object State Estimation](https://mlsanity.com/paper/2205.15516/) (2022)

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

- [A Low-Code Methodology for Developing AI Kiosks: a Case Study with the DIZEST Platform](https://mlsanity.com/paper/2511.17853/) (2025)

## Abstract (arXiv)

Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an O(T(P+M)) complexity, where T is the number of iterations of the algorithm, P and M are the number hypothesized objects and measurements. This innovation enables the GLMB filter implementation to be reduced from an O(TP2M) complexity to O(T(P+M+log T)+PM). Moreover, the proposed framework provides the flexibility for trade-offs between tracking performance and computational load. Convergence of the proposed Gibbs sampler is established, and numerical studies are presented to validate the proposed GLMB filter implementation.