Distributed Particle Filtering via Optimal Fusion of Gaussian Mixtures

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