Kernel least mean square with tracking

Based on the Gaussian process (GP) regression, the relationship between the input-output pair can be modeled by the sum of the Gaussian noise and an unknown latent function evaluated on an input (LFEI). The acquisition of LFEI is thus essentially required. In this paper, a novel algorithm called kernel least mean square with tracking (KLMS-T) is proposed to estimate LFEI. Based on the existing kernel least mean square (KLMS) that is a simple and efficient kernel adaptive filtering algorithm, the proposed KLMS-T utilizes the framework of Bayesian inference to estimate LFEI from the function-space view. Simulations show that compared with LMS and KLMS, KLMS-T achieves better filtering performance in terms of the convergence rate and the steady state mean square error.