Performance analysis of adaptive step-size sign-Newton algorithm

This paper first proposes to combine the Sign Algorithm (SA) with an estimate of the inverse covariance matrix of the filter input calculated using the Newton´s method. We further propose a new adaptive step-size (ASS) control algorithm to improve the filter convergence speed, yielding an adaptation algorithm named Adaptive Step-Size Sign-Newton (ASS-Sign-Newton) algorithm. A performance analysis of the ASS-Sign-Newton algorithm is developed for calculating theoretical convergence behavior. In experiments with some examples, we demonstrate effectiveness of the proposed ASS-Sign-Newton algorithm in realizing faster convergence, while preserving the robustness against impulsive observation noise. The calculated theoretical convergence curves are generally in good agreement with the simulated ones which shows that the analysis is valid.