Fast Computation of Discrete Optimal FIR Estimates in White Gaussian Noise

Abstract

We propose a fast iterative algorithm for optimal finite impulse response (OFIR) filtering of linear discrete time-invariant state-space models in white Gaussian noise. The OFIR filter is known to have the BIBO stability and better robustness against the Kalman filter (KF). The iterative OFIR algorithm is KF-like; that is, its estimate appears much faster than in the batch OFIR filter. A dramatic reduction of computation time is demonstrated in the full-horizon iterative OFIR algorithm which operates as fast as KF. We also notice a considerable reduction of the computational resources allowed by iterations.