Adaptive Random Fourier Features Gaussian Kernel Normalized LMS Algorithm

In this paper, we propose an adaptive stochastic Fourier feature Gaussian kernel normalized LMS (ARFF-GKNLMS). Similar to many kernel adaptive filtering algorithms that use stochastic gradient descent, the ARFF-GKNLMS algorithm uses more flexible stochastic Fourier features to reduce computation intensity. The difference is that the algorithm can adjust the inherent core bandwidth online, thereby solving the problem of selecting the core bandwidth in advance to a certain extent. In addition, the ARFF-GKNLMS algorithm has fast convergence performance, low steady-state error and good tracking ability, especially in non-stationary environment with low signal-to-noise ratio or strong noise, which has good robustness and tracking performance. The simulation results show that compared with other kernel adaptive filters with preset core bandwidths, the performance of this method is significantly improved in terms of convergence speed, steady-state error and tracking ability in both transient and steady state.