Introducing Stochastic Functional Link Polynomial Filters

The class of Functional Link Polynomials (FLiP) filters is very broad and includes many popular nonlinear filters, as the well-known Volterra and the Wiener nonlinear filters. They are linear in the parameters and can approximate arbitrarily well any discrete-time, time invariant, finite memory, continuous nonlinear system. This work extends the approximation capability of FLiP filters to systems that together with the previous properties have random parameters. This is achieved by extending the FLiP representation to random coefficients and applying the Kosambi–Karhunen–Loève theorem to the coefficients.