Distributed consensus filtering for discrete-time nonlinear systems with non-Gaussian noise

This paper studies the problem of distributed estimation for a class of discrete-time nonlinear non-Gaussian systems in a not fully connected sensor network environment. The non-Gaussian process noise and measurement noise are approximated by finite Gaussian mixture models. A distributed Gaussian mixture unscented Kalman filter (UKF) is developed in which each sensor node independently calculates local statistics by using its own measurement and an average-consensus filter is utilized to diffuse local statistics to its neighbors. A main difficulty encountered is the distributed computation of the Gaussian mixture weights, which is overcome by introducing the natural logarithm transformation. The effectiveness of the proposed distributed filter is verified via a simulation example involving tracking a target in the presence of glint noise.