Distributed Information Filter for Linear Systems with Colored Measurement Noise

This paper considers the distributed filtering problem for discrete-time linear systems with colored measurement noise obeying an autoregressive process in sensor networks. For the considered system in the centralized fusion framework, a novel information-type filter is proposed based on the measurement difference approach. Here, the dimension of the estimate error covariance (i.e., the information matrix) in the proposed information filter is the same as that of the original system state, with the help of the block matrix inverse operation. Then, the average consensus-based distributed implementation is designed, to ensure that the final state estimate in each sensor node is asymptotically consistent with the centralized filtering result as closely as possible. An example about target tracking with colored measurement noise in sensor networks validates the proposed method.