Um algoritmo não quadrático baseado no RLS estendido

Abstract

Filters are used for the general purpose of separating different elements. When these elements form electrical signals, Filters are devices that change the frequency content of the input signal. In order to remove unwanted parts (Noise, interference) or separate one signal from another, the filters restrict the passage of specific frequencies. An adaptive filter is a filter whose coefficients are adjusted adaptively, in function of objectives or conditions in time and translated into an error signal. The typical practical criterion for adapting coefficients of the filter and optimization of its performance is the minimization of the mean square value of the error signal. The applications of adaptive algorithms are important in several areas, such as telecommunications, control systems and others. How the objective function of an adaptive algorithm is presented can provide important information about performance or behavior of the algorithm. In adaptive filtering, new structures and new adaptation algorithms Accelerate the convergence of the mean square error (MSE) and / or decrease the computational complexity, Especially in applications that require the use of a large number of adaptive coefficients. Several algorithms for updating the adaptive filter shape coefficients developed in recent years. We can mention some: the conventional LMS (Least-MeanSquare) algorithm, which has low complexity But its behavior during convergence varies according to the characteristics of the signal Leading to slow convergence for correlated input signals; The algorithm RLS (Recursive-Least-Square), which has high convergence speed but high complexity computational and, in certain cases, numerical instability; The Least-Mean-Fourth (LMF) algorithm Minimize the average fourth error, which is a function of the convex weight vector. There are several methods to derive adaptive filtering algorithms, which can be based on concepts stochastic or deterministic, or even in the mathematical formulation of a system in a problem of optimization. In spite of the great diversityof the iterative algorithms that can result from the solution of a problem using the MSE as a cost function, most lead to a response that has a direct relation with the given response by the Wiener filter. In this work, we present an algorithm based on the even error, motivated by the exponentially weighted EX-RLS (Extended Recursive Least Squares) algorithm. We will show simulations based on convergence and mismatch comparing the algorithms cited with the proposed algorithm.