Adaptive nonlinear Wiener-Laguerre-lattice models

In this work we develop an adaptive nonlinear estimation technique, polynomial model-based, that has guaranteed stability and makes parsimonious use of coefficients. Our approach to the development of reduced-complexity adaptive nonlinear filters is based on a combination of: (a) The Wiener model of nonlinear systems (both FIR and IIR) and its application to nonlinear estimation from white Gaussian signals; (b) Wiener´s notion of fixed (Laguerre) pre-orthogonalization, which we have extended to include adaptive pre-orthogonalization with respect to arbitrary (non-white and non-Gaussian) input signals; (c) Efficient implementation of memoryless nonlinear maps for uncorrelated inputs based on (Hermite) orthogonal polynomials; (d) Application of suitably modified RLS and LMS adaptation techniques to determine the coefficients of such nonlinear maps