Robustness of the filtered-X LMS algorithm— Part II: robustness enhancement by minimal regularization for norm bounded uncertainty

Fraanje, R., Elliott, S.J. and Verhaegen, M. (2007) Robustness of the filtered-X LMS algorithm— Part II: robustness enhancement by minimal regularization for norm bounded uncertainty. IEEE Transactions on Signal Processing, 55 (8), 4038-4047. (doi:10.1109/TSP.2007.896086).

Record type: Article

Abstract

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.

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