Study of Set-Membership Adaptive Kernel Algorithms

TL;DR

This paper introduces data-selective adaptive kernel algorithms that enhance learning speed and reduce computational costs in nonlinear filtering, with proven superior performance in system identification and time series prediction.

Contribution

The paper presents novel data-selective KNLMS algorithms with adaptive step-size, improving convergence and efficiency in kernel-based nonlinear adaptive filtering.

Findings

Outperform existing algorithms in nonlinear system identification.

Efficiently balance convergence speed and steady-state performance.

Reduce computational complexity through data-selective updates.

Abstract

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation.