An Improved Robust Kernel Adaptive Filtering Method for Time-Series Prediction

Time-series prediction is a popular application that relies on the collection of historical data via sensors, which is then leveraged by predictive models to forecast future values or trends. As an important online predictive model, kernel adaptive filtering (KAF) has attracted much attention over the past decade. The traditional kernel least-mean square (KLMS) is derived based on minimizing the mean square error (MSE) criterion, which inevitably suffers from performance deterioration for nonlinear regression tasks corrupted by non-Gaussian noise. To this end, we, in this article, propose a novel robust KAF algorithm, namely a robust variable step-size kernel normalized LMS (RVSS-KNLMS) algorithm. The fundamental idea of our design is to prevent large outliers from perturbing the model training by limiting the energy of the weight update within a dynamic threshold. By establishing the energy conservation relation, we perform a rigorous analysis of the mean square convergence properties of the proposed algorithm. This analysis allows us to derive a sufficient condition for determining the appropriate step size. In addition, with the pretuned dictionary strategy that serves to simplify the nonlinear system model, we investigate the steady-state excess MSE (EMSE) of the proposed algorithm and arrive at a closed-form solution for prediction. Simulations on synthetic data and real-world data have confirmed the advantages of RVSS-KNLMS. Moreover, the theoretical steady-state analysis has been validated to provide good prediction results.