Minimum Variance FIR Smoothers for Continuous-Time State Space Signal Models

In this letter, we propose a fixed-lag finite impulse response (FIR) smoother for a class of continuous-time state space signal models. The proposed fixed-lag FIR smoother is linear with respect to outputs on the recent finite time interval and has a kernel function depending only on given system parameters. It is optimal in the sense that the variance of the estimation error is minimized with the unbiased constraint. The fixed-lag minimum variance FIR (MVF) smoother has a closed-form solution and can be easily extended to an FIR filter by setting the lag size to zero. A simulation example is presented to illustrate the performance of the proposed MVF smoother by comparing with a conventional fixed-lag Kalman infinite impulse response (IIR) smoother.