Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering
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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 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 an 𝒪(T(P+M+log(T))+PM) complexity implementation of the GLMB filter. Convergence of the proposed Gibbs sampler is established and numerical studies are presented to validate the proposed GLMB filter implementation.
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