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Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm

Parreira, Wemerson D. and Bermudez, José Carlos M. and Richard, Cédric and Tourneret, Jean-Yves Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm. (2012) IEEE Transactions on Signal Processing, vol. 60 (n° 5). pp. 2208-2222. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2012.2186132

Abstract

The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application.

Item Type:Article
Additional Information:Thanks to IEEE. The original publication is available at http://ieeexplore.ieee.org
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Other partners > Université Nice Sophia Antipolis (FRANCE)
Other partners > Observatoire de la Côte d'Azur (FRANCE)
Other partners > Federal University of Santa Catarina - UFSC (BRAZIL)
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
Laboratory name:
Statistics:download
Deposited By: Jean-yves TOURNERET

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