An efficient kernel adaptive filtering algorithm with adaptive alternating filtering mechanism

Abstract

To effectively reduce the kernel conjugate gradient (KCG) algorithm's network size, this paper proposes an improved algorithm based on an adaptive alternating filtering mechanism (AAFM) called AAFM-KCG. The algorithm utilizes a clustering sparse strategy and the orthogonality of nearest instance centroid estimate subspaces to decompose the complex KCG filter into multiple nearly independent sub-filters. By alternately activating only the most relevant sub-filters for updates, it significantly reduces computational complexity and storage requirements while ensuring high filtering accuracy. Then, to establish a fixed-scale network structure, the random Fourier feature (RFF) technique is integrated, yielding the AAFM-RFFCG algorithm. Furthermore, for scenarios with non-Gaussian noise interference, we introduce a truncated generalized exponential hyperbolic tangent (TGEHT) function and embed it into the AAFM framework, refined into the T-AAFM-KCG and T-AAFM-RFFCG algorithms. The simulation results demonstrate that the proposed algorithm achieves excellent computational efficiency and noise robustness in Lorenz chaotic time series prediction, nonlinear system identification, and sunspots time series prediction tasks.