Kernel Adaptive Hammerstein Filter

To identify Hammerstein systems, a variety of Hammerstein filters have been proposed. However, most of them assume the nonlinear part in Hammerstein systems to be polynomial in the process of modeling, which restricts their applicability in many practical situations. In this paper, a simple kernel adaptive filter (KAF) called kernel least mean square (KLMS) combined with coherence criterion (CC) is used to approximate the nonlinear part of a Hammerstein system, resulting in the kernel adaptive Hammerstein filter (KAHF). The KAHF can identify various Hammerstein systems well without any prior knowledge of nonlinear part. Simulation results confirm the desirable performance of the new method. Index Terms-Hammerstein system identification, kernel adaptive filter, infinite impulse response system