Adaptive Filtering for Stochastic Systems With Generalized Disturbance Inputs

This letter presents a new class of discrete-time linear stochastic systems with the statistically-constrained disturbance input, which can represent an arbitrary linear combination of dynamic, random, and deterministic disturbance inputs to generalize the complicated modeling error encountered in actual applications. An adaptive filtering scheme is proposed for such systems by recursively constructing and adaptively minimizing the upper-bounds of covariance matrices of the state predictions, innovations, and estimates. The minimum-upper-bound filter is then obtained via online scalar convex optimization. The experiment on maneuvering target tracking shows that the proposed filter can significantly reduce the peak estimation errors due to maneuvers, compared with the well-known IMM method.