Kernel Based Learning for Nonlinear System Identification

In this paper, an efficient Kernel based algorithm is developed with application in nonlinear system identification. Kernel adaptive filters are famous for their universal approximation property with Gaussian kernel, and online learning capabilities. The proposed adaptive step-size KLMS (ASS-KLMS) algorithm can exhibit universal approximation capability, irrespective of the choice of reproducing kernel. Performance evaluation of proposed nonlinear adaptive filter is carried out for an unknown plant with an additive white Gaussian noise in the expected output. In comparative study, learning parameters are computed using KLMS, NKLMS and ASS-KLMS algorithms for polynomial and Gaussian kernels. Simulation results are presented for the performance analysis of the algorithm in terms of signal to noise ratio (SNR) and MSE [dB], showing preference of ASS-KLMS algorithm over the rest.