Robust signal estimation using H∞ criteria

Kalman and Weiner filters are used extensively for implementation of optimal filters. These filters try to minimize variance of error when input signal and noise power spectral density (PSD) is known. Here we consider filters under H_∞ setting. This paper shows the robust performance of H_∞ filters under noise uncertainty. Optimization criteria for H_∞ filters is represented in the time and frequency domain. From this representation it is shown that optimal H_∞ filters place an upper bound on error PSD and error variance for a certain class of noise perturbations. It is shown that the estimation problem can be reduced to the model matching problem, which can be solved using γ-iteration in the frequency domain. Simulations results are included to confirm the robust performance of these filters for noise PSD belonging to a certain class