Finite-time distributed block-decomposed information filter for nonlinear systems with colored measurement noise

This paper considers the distributed filtering problem for discrete-time nonlinear systems with colored measurement noise obeying a nonlinear autoregressive process in sensor networks. A novel block-decomposed information-type filter for such systems is proposed in a centralized fusion structure, by using the statistical linear regression to deal with model nonlinearities and the measurement difference approach to overcome the noise correlation caused by colored measurement noises. Meanwhile, with the help of block matrix inverse operation to realize the high-dimensional block matrix decomposition, the information vector and information matrix of the original system state in the designed information filter is directly estimated recursively, so as to own good numerical stability. Then, the finite-time distributed implementation of the proposed filter is put forward, where the final filtering estimate in each sensor node is consistent with the centralized filtering result, by ensuring that each sensor node directly obtains the average values of shared variables in the sensor network through finite iterations of average consensus. Finally, the posterior Cramér–Rao lower bound is derived to show the proposed filter reaches the optimal theoretical performance bound in the premise of statistical linear regression and Gaussian posterior probability density approximation. A target tracking example with colored measurement noise obeying a linear and a nonlinear autoregressive processes validates the proposed method.