Nonlinear System Identification Using Varying Exponential Even Mirror Fourier Nonlinear Filters

Adaptive exponential functional link neural network (AeFLNN) based on functional link architecture is a recently added member in the family of linear-in-parameter nonlinear filters. However, AeFLNN does not fulfill the criteria of universal approximate due to the absence of cross-terms in its functional expansion. Therefore, a new nonlinear filter based on even mirror Fourier nonlinear filters (EMFN) and exponentially varying sinusoidal basis functions named varying exponential EMFN (VeEMFN) is presented in this paper. To further improve the modeling accuracy, an independently varying exponential EMFN (IVeEMFN) filter is designed to allow each sinusoid in the basis function to grow or decay independently. A suitable update rule for updating the filter coefficients and exponential parameters are derived with the bounds on the learning rates is also presented. The simulation study demonstrates the enhanced modeling accuracy of the proposed filters.