An Approach to Optimal Filtering of Time-Variant Systems via Finite Measurements

摘要

Fast optimal estimates are often required in control and signal processing. In this paper, we discuss an approach to optimal finite impulse response (OFIR) filtering for discrete time-variant systems using finite measurements. The mean square error is minimized to obtain the batch OFIR algorithm which requires measurements on an a finite horizon of N points. Fast iterative algorithm is found using recursions. It is shown that each recursion has a predictor/corrector Kalman filter (KF)-like format with special initial conditions. In this sense, the KF is considered as a special case of the proposed iterative OFIR filtering algorithm when N approaches infinity for known initial conditions. It has been confirmed by simulation that the iterative form of the OFIR filter operates much faster than the batch form.