Recursive Filter Design for Discrete-Time Systems with Sparsity Constraint and Correlated Noises

This paper is concerned with the recursive filtering problem for the discrete-time linear systems with correlated noises and sparsity constraint. The process and measurement noises are one-step autocorrelated, two-step cross-correlated, respectively. Based on the Kalman filtering idea, an improved filtering algorithm with sparsity constraint is proposed. Com-pared with the classical Kalman filter, inversion calculation of the large-scale matrix sequence is avoided. In order to demonstrate the efficiency of the suggested filter design strategy, a simulation example is also provided.