Robustness of the Filtered-X LMS Algorithm— Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty

摘要

The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-x LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [“Robustness of the Filtered-X LMS Algorithm—Part I: Necessary Conditions for Convergence and the Asymptotic Pseudospectrum of Toeplitz Matrices” of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set.