Kernel Online Learning Algorithm with Scale Adaptation

Kernel adaptive filtering is implemented by evaluating the inner product between the kernel function-based vector and the coefficient vector. In this brief, the coefficient vector is decomposed into the direction vector and the scale, which are updated using the steepest descent method and thus generate a novel online learning method, namely kernel online learning algorithm with scale adaptation (KOL-SA). In addition, the convergence of KOL-SA is proved and an upper bound of steady-state mean square error is therefore obtained. Simulation results confirm that the proposed KOL-SA achieves desirable filtering performance from the aspects of the filtering accuracy and stability.