Set-membership adaptive filtering algorithm based on hyperbolic tangent kernel fractional p-power method

Abstract

A well know problem in Kernel Adaptive Filtering (KAF) algorithm is the growing network, where Quantized Kernel Adaptive Filtering (QKAF) is one of the most outstanding solutions. However, the most existing QKAF’s have the problem of large steady-state error. In this paper, based on the sparse perceptual data selection characteristic of Set Membership (SM) algorithm, a kernel member adaptive filtering algorithm is proposed. The proposed kernel SM algorithm features an adaptive step based on the hyperbolic tangent form of instantaneous error, in which the hyperbolic tangent function can compress the scale of the variable, thus weakening the collinearity of the model and further improving the stability of the algorithm. The simulation results show that the proposed algorithm has lower steady-state error and better steady-state performance when the convergence rate is close.