Gauss Hermite Fourier Features Based on Maximum Correntropy Criterion for Adaptive Filtering

Kernel adaptive filters (KAFs) are a class of nonlinear adaptive filters developed in the reproducing kernel Hilbert space, and are particularly suitable for addressing signal processing issues involving data streams and unknown nonlinearities. However, KAFs endure the issue of network structure growth as the number of training samples increases. To this end, a novel structural sparsification method for KAFs, i.e., Gauss Hermite Fourier features (GHFF) method, is first proposed by combining Gauss Hermite quadrature integration rule and Fourier transform. Subsequently, the GHFF method is integrated with the maximum correntropy criterion in filter design, leading to the development of two new adaptive filtering algorithms, i.e., GHFF maximum correntropy (GHFFMC) algorithm and stochastic batch GHFFMC (SB-GHFFMC) algorithm. The proposed GHFFMC and SB-GHFFMC algorithms are expected to exhibit excellent capabilities in characterizing the unknown nonlinear relationships within the data, along with robustness to outliers. Meanwhile, SB-GHFFMC is anticipated to exhibit superior filtering performance in comparison with GHFFMC, as it leverages a general and flexible batch gradient descent method for model optimization. Simulations on nonlinear system identification and time-series prediction of Chua’s circuits confirm the performance superiorities of the proposed algorithms compared to other robust KAFs and RFF-based filters.