Half-quadratic Student's t-based kernel adaptive filter based on multikernel Nyström method

Abstract

Kernel adaptive filters (KAFs) are effective for nonlinear signal processing. However, the performance of KAFs based on the minimum mean square error (MMSE) criterion can significantly deteriorate in non-Gaussian noise environments. In addition, their computational efficiency decreases as the network size grows, unless an effective sparsification method is employed. To address this issue, this paper introduces a novel Student's t-based KAF based on half-quadratic (HQ) method and multikernel Nyström approach. First, the HQ method transforms the non-convex problem of solving the Student's t-based loss function into a globally convex least squares (LS) problem. Then, the LS problem is solved using the dichotomous coordinate descent (DCD) method, achieving an efficient and low-complexity solution. Moreover, the multikernel Nyström method is leveraged to enhance the algorithm stability and mitigate the impact of network growth, resulting in the Student's t-Based-Multikernel Nyström dichotomous coordinate descent algorithm (ST-MNDCD). The energy conservation argument (ECA) and Taylor expansion are utilized to approximate a range of the steady-state characteristics of ST-MNDCD for performance analysis. Finally, simulations on Mackey-Glass time series prediction and nonlinear system identification demonstrate the advantages of ST-MNDCD.