Variable learning rates kernel adaptive filter with single feedback

Abstract

In this paper, we propose a novel kernel adaptive filtering algorithm, which called variable learning rates kernel adaptive filter with single feedback (SF-VLRKAF). Based on a feedback structure, the past information can be used to estimate current output to improve the filtering performance, because of a momentum term existing in the weight update equation. A switch ON–OFF normalized variable learning rate is developed to obtain a tradeoff between convergence rate and filtering accuracy of the proposed algorithm. The weights, in the SF-VLRKAF, are updated at each iteration to avoid local minimum, and the analysis of mean square convergence is performed. Furthermore, a sufficient condition ensuring mean square convergence is obtained by applying the energy conservation relation. Moreover, we derive the lower and upper bounds on a theoretical result of the steady-state excess mean square error. Simulations for nonlinear regression, chaotic time-series predictions and real-world applications are presented to illustrate the effectiveness of the new algorithm.