This paper proposes a novel distributed particle filtering algorithm for acoustic source tracking in distributed microphone networks within the Bayesian filtering framework. The core innovation leverages multiple tempering Stein variational gradient descent to efficiently fuse probability density functions of the local posteriors across the network, minimizing Kullback-Leibler divergence. At each sensor node, the probability density functions of local posteriors are first approximated using particles via sequential Monte Carlo sampling. To enable communication-efficient distributed consensus, these particles model local posteriors as Gaussian mixture distributions. Neighboring nodes exchange these local Gaussian mixture posteriors. Within each average consensus iteration, a multiple tempering Stein variational gradient descent sampler generates samples approximating the fused posterior, defined as the product of fractional powers of the received Gaussian mixture posteriors. This process yields a consistent approximation of the global posterior probability density on every node from the fused samples. The algorithm’s effectiveness is validated through both distributed acoustic source tracking simulations and a real-world recording experiment.
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