Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering

• URL: http://arxiv.org/abs/2211.16041v2
• Date: Thu, 28 Dec 2023 02:11:27 GMT
• Title: Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering
• Authors: Changbeom Shim, Ba-Tuong Vo, Ba-Ngu Vo, Jonah Ong, Diluka Moratuwage
• Abstract summary: Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. We propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $mathcalO(T(P+M))$ complexity. This innovation enables the GLMB filter implementation to be reduced from an $mathcalO(TP2M)$ complexity to $mathcalO(T(P+M+log T)+PM)
• Score: 4.186094981300538
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\mathcal{O}(T(P+M))$ 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 $\mathcal{O}(TP^{2}M)$ complexity to $\mathcal{O}(T(P+M+\log T)+PM)$. 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.

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