Minimum Variance FIR Smoothers for Discrete-Time State Space Models

We propose a fixed-lag finite-impulse-response (FIR) smoother for a discrete-time state space model. The proposed FIR smoother estimates the state at the fixed-lag time using measured output samples on the recent finite time horizon so that the variance of the estimation error is minimized. The minimum variance FIR (MVFIR) smoother is unbiased and independent of any a priori information of the state on the horizon. A numerical example shows that the proposed MVFIR smoother has better performance than the fixed-lag Kalman smoother based on the infinite impulse response structure when transitory modeling uncertainties exist.