M-estimate affine projection spline adaptive filtering algorithm: Analysis and implementation

Abstract

This paper investigates the M-estimate affine projection spline adaptive filtering (MAPSAF) algorithm, which utilizes a modified Huber function with robustness against impulsive interference, and employs historical regression data to update the weight and the knot vector estimates for nonlinear filtering tasks. The detailed convergence and steady-state analyses of MAPSAF are also carried out in the mean and mean-square senses. In addition, an improved MAPSAF by exploiting the combined step sizes, called the CSS-MAPSAF algorithm, is derived to speed up the convergence on the premise of low steady-state misalignment. Numerical experiments in nonlinear system identification and nonlinear acoustic echo cancellation problems corroborate the theoretical performance analysis and the superiority of the proposed algorithms.