A Practical Form of Exponentially-Weighted H∞ Adaptive Filters

Abstract

This paper examines the problem of exponentially-weighted H ∞ adaptive filtering and shows that its suboptimal solution reduces to a recursive algorithm which is slightly different from the RLS algorithm. Based on this similarity, its fast array form is immediately obtained by following the derivation of the fast RLS array algorithm. Also a theoretical expression for its steady-state mean-square error is provided. Several numerical examples indicate that the exponentially-weighted H ∞ filter can achieve a proper balance between H ∞ and H 2 (least squares) filtering criteria.

An Improved Adaptive Compensation H∞ Filtering Method for the SINS’ Transfer Alignment Under a Complex Dynamic Environment

“…When the mathematical model or the priori information on the external noise is not exactly known or is unavailable in the transfer alignment system, the Kalman filtering scheme is no longer applicable [14,15,16]. In contrast, the H∞ filter does not make assumptions about the statistical characteristics of the input signal, and it has good robustness against the model uncertainties, such as measurement noise, external disturbance, and structural uncertainty [17,18,19,20]. The main purpose of the H∞ filter is to design an estimator to minimize the H∞ norm of the error system in order to ensure that the L2-induced gain from the disturbance input to the filter error output is less than a prescribed level [14,21,22,23].…”