Recursive functional link polynomial filters: An introduction

In this paper, we first introduce a novel sub-class of recursive linear-in-the-parameters nonlinear filters, called recursive functional link polynomial filters, which are derived by using the constructive rule of Volterra filters. These filters are universal approximators, according to the Stone-Weierstrass theorem, and offer a remedy to the main drawback of their finite memory counterparts, that is the curse of dimensionality. Since recursive nonlinear filters become, in general, unstable for large input signals, we then consider a simple stabilization procedure by slightly modifying the input-output relationship of recursive functional link polynomial filters. The resulting filters are always stable and, even though no more universal approximators, still offer good modeling performance for nonlinear systems.