Distributed Gaussian sum filter for discrete-time nonlinear systems with Gaussian mixture noise

This paper studies the problem of distributed estimation for discrete-time nonlinear systems with Gaussian mixture noise. A merge-fusion-split strategy has been proposed to develop a distributed Gaussian sum filter (GSF) over a sensor network. In the proposed filter, the GSF is implemented for each sensor to generate local estimates and the local estimates of Gaussian components are merged as a single Gaussian distribution by using the moment-matching approach. Then the merged estimates are exchanged between neighboring sensors and are fused by using the weighted Kullback-Leibler divergence. To maintain the feature of Gaussian mixture models, the fused estimates for each sensor are splitted into multiple Gaussian components as the inputs of the local GSF at the next step. Compared with the consensus-based distributed GSF, much lower computational complexity and communication cost are required in the proposed filter. The performance of the proposed filter is demonstrated for a target tracking problem in the presence of glint noise.