Robust Cauchy Kernel Conjugate Gradient Algorithm for Non-Gaussian Noises

Abstract

The Cauchy loss (CL) is a high-order loss function which has been successfully used to overcome large outliers in kernel adaptive filters. The squared error in the CL is then transformed into a reproducing kernel Hilbert space (RKHS) to generate the Cauchy kernel loss (CKL). However, due to its non-convexity, the CKL optimized by the stochastic gradient descent (SGD) suffers from poor performance in the presence of non-Gaussian noise. To improve the performance of CKL, the kernel conjugate gradient (KCG) method combining the half-quadratic (HQ) method twice is used to transform it into a globally convex function. A novel Cauchy kernel loss conjugate gradient (CKCG) algorithm is therefore proposed in the transformed CKL. Simulations on nonlinear system identification in non-Gaussian noises confirm the superiorities of the proposed CKCG from the aspects of robustness and filtering accuracy.