Minimum Variance FIR Smoother for Model-based Signals

In this paper, finite impulse response (FIR) smoothers are proposed for discrete-time systems. The proposed FIR smoother is designed under the constraints of linearity, unbiasedness, FIR structure, and independence of the initial state information. It is also obtained by directly minimizing the performance criterion with unbiased constraints. The approach to the MVF smoother proposed in this paper is logical and systematic, while existing results have heuristic assumption, such as infinite covariance of the initial state. Additionally, the proposed MVF smoother is based on the general system model that may have the singular system matrix and has both system and measurement noises. Thorough simulation studies, it is shown that the proposed MVF smoother is more robust against modeling uncertainties numerical errors than fixed-lag Kalman smoother which is infinite impulse response (IIR) type estimator.