A Fast Distributed Variational Bayesian Filtering for Multisensor LTV System with Non-Gaussian Noise

For multisensor linear time-varying system with non-Gaussian measurement noise, how to design distributed robust estimator to increase the accuracy and robustness to outliers at a relatively low computation and communication cost is a fundamental task. This paper proposes a fast distributed variational Bayesian (VB) filtering algorithm to recursively estimate the state and noise distribution over three conventional sensor networks: 1) incremental-based; 2) diffusion-based; and 3) consensus-based. To be specific, the non-Gaussian measurement noise of each sensor is modeled as Student- ${t}$ distribution, and the system state and the parameters of the distribution are estimated via VB approach in each iteration step. An interaction scheme is then added to obtain the global optimal parameter by fusing the local optimal parameters over incremental, diffusion, and consensus communication topology. An efficient sensor selection criterion under these topologies based on the Cramér-Rao lower bound is proposed to reduce the communication and computation burden. Compared with the existing centralized VB filtering algorithms, the proposed algorithm in this paper can extensively increase the robustness to node or link failure at a lower computation cost with acceptable estimation performance and communication load. The theoretic results and simulation results are given to show the efficiency of our proposed algorithm.