Laguerre Kernel Adaptive Filter With Arctangent Criterion for Nonlinear System Identification

Kernel adaptive filters (KAF) have emerged as a prominent method for nonlinear system identification (NSI). However, the KAF becomes computationally intensive as the input signal grows. In complex systems, traditional KAF with a unit time-delay structure may struggle with insufficient control capability. Moreover, KAFs adapted to second-order statistics can be susceptible to non-Gaussian noise. In this letter, we introduce the Laguerre kernel adaptive filter (LKAF) for NSI, using a block-oriented nonlinear model. The LKAF leverages the Laguerre series to approximate the linear block, benefiting from infinite impulse response (IIR) characteristics and a simple feedforward structure. To address non-Gaussian noise, the LKAF employs an arctangent (AT) criterion. This integration leads to the development of the Laguerre kernel arctangent least mean square (L-KATLMS) algorithm and its variations, which utilize random Fourier approximation. Simulation results demonstrate the superiority of our proposed algorithms for NSI.