A Best Lag Size of Minimum Variance FIR Smoothers

In this paper, we argue that the lag size of half a moving horizon of the minimum variance finite impulse response (MVFIR) smoother is not generally best in the sense of the estimation error variance even though it has been believed to be optimal for a simple input/output (I/O) model with correlated data. For a more general analysis, a state space model is considered in this paper. It is shown via numerical example that the dependency of the lag size on the minimum estimation error variance is asymmetric around half a moving horizon and varies with model parameters. In the case of a scalar system, the best lag size is represented in a closed-form. Some hints on a numerical method are presented for a more general vector system. Considering the lag size as well as the estimation error, we also propose a new performance criterion that puts a penalty on the large lag size while making the estimation error small.