Receding horizon estimators for systems with delayed state and measurement

In this paper we propose a receding horizon estimator (filter) for discrete-time stochastic linear systems with delays in state and measurement. A novel filtering algorithm is designed based on the receding horizon strategy in order to achieve high estimation accuracy and stability under parametric uncertainties. The 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 numerical example demonstrates the proposed algorithm is more robust and more accurate than Kalman filter against dynamic model uncertainties.