  Kernel adaptive filters (KAF) are a class of powerful nonlinear filters
developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is
usually the default kernel in KAF algorithms, but selecting the proper kernel
size (bandwidth) is still an open important issue especially for learning with
small sample sizes. In previous research, the kernel size was set manually or
estimated in advance by Silvermans rule based on the sample distribution. This
study aims to develop an online technique for optimizing the kernel size of the
kernel least mean square (KLMS) algorithm. A sequential optimization strategy
is proposed, and a new algorithm is developed, in which the filter weights and
the kernel size are both sequentially updated by stochastic gradient algorithms
that minimize the mean square error (MSE). Theoretical results on convergence
are also presented. The excellent performance of the new algorithm is confirmed
by simulations on static function estimation and short term chaotic time series
prediction.
