A Finite Memory Filter for Discrete-Time Stochastic Linear Delay Systems

In this paper, we propose a finite memory filter (estimator) for discrete-time stochastic linear systems with delays in state and measurement. A novel filtering algorithm is designed based on finite memory strategies, to achieve high estimation accuracy and stability under parametric uncertainties. The new finite memory filter uses a set of recent observations with appropriately chosen initial horizon conditions. The key contribution is the derivation of Lyapunov-like equations for finite memory mean and covariance of system state with an arbitrary number of time delays. A numerical example demonstrates that the proposed algorithm is more robust and accurate than the Kalman filter against dynamic model uncertainties.