Algoritmo recursivo não quadrático autorregulado

Abstract

Adaptive filtering has been extensively studied for a wide range of applications such as

economics, biomedical engineering, channel equalization, control systems, and telecommu- nications. The problem of non-stationary signals constitutes one of the greatest challenges

in the context of adaptive filters, since it simultaneously requires high convergence speed, good tracking capability, and stability, motivating the proposal of new filtering algorithms

and variants of well-established algorithms. The variability of the signal’s statistical prop- erties imposes the need for detection mechanisms for abrupt statistical variations in the

input signal, increasing the computational complexity of the algorithm. This work presents the Recursive Non-Quadratic Self-Regulated (RNQA) algorithm, which derives from a family of algorithms based on even-power errors where the dynamic regularization of the autocorrelation matrix is continuously performed by the square of the instantaneous error of the algorithm, characterizing an adaptive adjustment mechanism in the matrix update phase, capable of responding effectively in non-stationary environments. A system identification configuration was performed in a non-stationary environment, characterized by abrupt changes in the unknown parameter, allowing the evaluation of the tracking capability of the proposed algorithm. RNQA showed better performance results in terms of convergence speed compared to the standard RNQ and Kalman filter algorithm in a system identification framework.