Nonlinear spline prioritization optimization generalized hyperbolic secant adaptive filtering against alpha-stable noise

In order to mitigate the interference of impulsive noises in the identification of nonlinear systems using spline prioritization optimization adaptive filtering (SPOAF) algorithm, an enhanced SPOAF based on generalized hyperbolic secant (GHS) function, named SPOAF-GHS, is proposed in this paper. The convergence property of the proposed algorithm has been theoretically analyzed. Two improvements have been made in the proposed algorithm. On the one hand, to improve the convergence speed in the adaptive process, the momentum Nesterov accelerated gradient optimization algorithm has been introduced. In addition, a frequency domain filtering architecture model has been proposed to address the high computational complexity of the filtering algorithm caused by the presence of bigger number of taps during the filtering process. Several numerical experiments are conducted, and the results show that the proposed GHS-type algorithms have superior performance compared to existing spline interpolation filtering algorithms.