Distributed particle filtering via optimal fusion of Gaussian mixtures

We propose a distributed particle filtering algorithm based on optimal fusion of local posterior estimates. We derive an optimal fusion rule from Bayesian statistics, and implement it in a distributed and iterative fashion via an average consensus algorithm. We approximate local posterior estimates as Gaussian mixtures, and fuse Gaussian mixtures through importance sampling. We prove that under certain conditions the proposed distributed particle filtering algorithm converges to a global posterior estimate locally available at every sensor in the network. Numerical examples are presented to demonstrate the performance advantages of the proposed method in comparison with other posterior-based distributed particle filtering algorithms.