High-order system identification with an adaptive recursive second-order polynomial filter

In this letter, an adaptive recursive nonlinear filter based on the Volterra series and an infinite impulse response (IIR) structure is considered. For certain types of nonlinear systems where high-order nonlinearities are recursively generated, we show that the adaptive recursive second-order polynomial filter has improved performance over the well-known (nonrecursive) adaptive second-order Volterra filter and a third-order Volterra filter. This filter represents an alternative to using a traditional Volterra filter whose order has been increased to match that of the system being modeled.