Receding horizon filtering for discrete-time linear systems with state and observation delays

In this study, the authors consider the receding horizon filtering problem for discrete-time linear systems with state and observation time delays. Novel filtering algorithm is proposed based on the receding horizon strategy in order to achieve high estimation accuracy and stability under parametric uncertainties. New receding horizon filter uses a set of recent observations with appropriately chosen initial horizon conditions. The key contribution is the derivation of Lyapunov-like equations for receding horizon mean and covariance of system state with an arbitrary number of time delays. The authors demonstrate how the proposed algorithm robust against dynamic model uncertainties comparing with Kalman and Lainiotis filters with time delays. Superior performance of the proposed filter is illustrated through two numerical examples when the system modelling uncertainties appear.