André R. Flores

Iam Kim de S. Hermont, Andre R. Flores, Rodrigo C. de Lamare

In this work, we propose a robust adaptive filtering approach for active noise control applications in the presence of impulsive noise. In particular, we develop the filtered-x hyperbolic tangent exponential generalized Kernel M-estimate function (FXHEKM) robust adaptive algorithm. A statistical analysis of the proposed FXHEKM algorithm is carried out along with a study of its computational cost. {In order to evaluate the proposed FXHEKM algorithm, the mean-square error (MSE) and the average noise reduction (ANR) performance metrics have been adopted.} Numerical results show the efficiency of the proposed FXHEKM algorithm to cancel the presence of the additive spurious signals, such as \textbf{$α$}-stable noises against competing algorithms.

A. Flores, R. C. de Lamare

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.

R. C. de Lamare, André Flores

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 kernelized affine projection (SM-KAP) algorithm. Finally several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to the existing methods.