Bias Compensation for Kernel Least-Mean-Square Algorithms

This letter addresses the challenge of input noise in nonlinear system identification using kernel adaptive filtering (KAF) techniques. Conventional kernel least-mean-square (KLMS) algorithms are susceptible to input noise, which introduces bias into the estimated weights, degrading performance. To mitigate this issue, we propose a bias-compensated KLMS (BC-KLMS) algorithm. By employing a finite-order nonlinear regression model and leveraging Taylor series expansion, we analyze the bias terms generated by input noise and incorporate them into a modified cost function. The resulting BC-KLMS algorithm effectively reduces noise-induced bias, leading to improved accuracy in nonlinear system identification tasks. Simulation results demonstrate that BC-KLMS outperforms traditional KLMS methods, achieving substantial bias compensation even in low signal-to-noise ratio conditions. This approach enhances the robustness of KAFs in real-world applications where input noise is prevalent.