Extended Random Fourier Features Recursive Non-quadratic Algorithm

The extended recursive non-quadratic (EX-RNQ) algorithm can improve the filtering performance of the extended recursive least-squares (EX-RLS) algorithm in the state-space model. To improve the filtering performance of EX-RNQ, a novel extended random Fourier features recursive non-quadratic (EX-RFFRNQ) algorithm is proposed by transforming the input data into a high-dimensional feature space with the random Fourier features (RFF) method under the non-quadratic error criterion. In comparison with the kernel adaptive filters (KAFs), the proposed EX-RFFRNQ algorithm can achieve the performance improvement in a fixed-dimensional network structure and thus require no sparsification. Monte Carlo simulations on channel tracking and short-term chaotic time-series prediction validate the superiority of the proposed EX-RFFRNQ algorithm.