Fixed-lag Minimum Variance FIR Smoothers for Continuous-time Systems

In this paper, we consider the fixed-lag finite impulse response (FIR) smoother problem for a class of continuous-time systems. The proposed fixed-lag FIR smoother is represented linearly with inputs and outputs on the recent time interval, and has coefficients without respect to any state information. It is optimal in view of the minimum variance performance criterion with unbiased constraints. The approach to the minimum variance fixed-lag FIR (MVF) smoother provides a closed-form solution and can be easily extended to an FIR filter by setting a lag size to zero. A simulation example is presented to validate the effectiveness of the proposed approach by comparing to a traditional fixed-lag Kalman smoother