A robust fixed‐lag receding horizon smoother for uncertain state space models

In this paper, a robust fixed‐lag receding horizon (RH) smoother is proposed for a discrete‐time state space model with bounded uncertainties. The proposed robust RH smoother is based on a set‐valued state estimation method, which produces a set of possible estimates based on inputs and outputs measured over a finite time horizon. The set of possible estimates is represented in an ellipsoidal form, and then the major axis of the ellipsoid is minimized with respect to the preview size. The center of the ellipsoid with the minimum major axis is taken as the estimate of the real state to minimize the possible maximum estimation error under bounded uncertainties. It is illustrated through a numerical example that the proposed robust RH smoother has better performance than the conventional robust Kalman smoothers. Copyright © 2015 John Wiley & Sons, Ltd.