Stability Conditions for the Leaky LMS Algorithm Based on Control Theory Analysis

• Autorzy: Bismor D. , Pawelczyk M.

Identyfikatory

DOI

10.1515/aoa-2016-0070

• Języki publikacji: EN

Abstrakty

EN

The Least Mean Square (LMS) algorithm and its variants are currently the most frequently used adaptation algorithms; therefore, it is desirable to understand them thoroughly from both theoretical and practical points of view. One of the main aspects studied in the literature is the influence of the step size on stability or convergence of LMS-based algorithms. Different publications provide different stability upper bounds, but a lower bound is always set to zero. However, they are mostly based on statistical analysis. In this paper we show, by means of control theoretic analysis confirmed by simulations, that for the leaky LMS algorithm, a small negative step size is allowed. Moreover, the control theoretic approach alows to minimize the number of assumptions necessary to prove the new condition. Thus, although a positive step size is fully justified for practical applications since it reduces the mean-square error, knowledge about an allowed small negative step size is important from a cognitive point of view.

Słowa kluczowe

EN

adaptive filtering; leaky LMS; stability; negative step size; identification; adaptive line enhancer; active noise control

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2016
• Tom: Vol. 41, No. 4
• Strony: 731--739
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Bismor D.

• Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

autor

Pawelczyk M.

• Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.