Set-membership kernel adaptive algorithms

Abstract

Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless, these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper, we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernel-based affine projection (SM-KAP) algorithm. Finally, several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to existing methods.