Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering
- Publisher:
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Publication Type:
- Journal Article
- Citation:
- IEEE Transactions on Signal Processing, 2023, 71, pp. 1981-1994
- Issue Date:
- 2023-01-01
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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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