Zero-attracting Chebyshev Functional Link Adaptive Filter for Nonlinear System Identification

Abstract

Identification of nonlinear system in sparse environment employing a functional link adaptive filter based on Chebyshev polynomial expansion and l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm regularization is introduced in this paper. Mostly trigonometric FLAFs are used to identify the unknown nonlinear systems. Here the input signal is expanded into Chebyshev polynomial expansion as it is easy to compute and also has faster convergence rate. The proposed zero attracting Chebyshev FLAF (ZA-CFLAF) and reweighted ZA-CFLAF (RZA-CFLAF) with l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm constraint are employed in case of sparse nonlinear system. The derivation of the introduced algorithm is also accomplished. The results of the simulation indicate better steady state performance and fast convergence rate with good tracking ability as compared with respective TFLAFs.