Novel procedure for characterizing nonlinear systems with memory and combating the curse of dimensionality

A well-known mathematical model for characterizing nonlinear systems was originally proposed by Vito Volterra (1860-1940) and later developed by Norbert Wiener (1894-1964). More recently, Albert Nuttall, working with coauthors, has made substantial improvements to Wiener’s approach, in which kernel estimates are modeled directly rather than computed from Wiener functionals. Other enhancements made include kernel estimation using a least-square approach for obtaining a best fit to the measured system response, and procedural methods to obtain uncorrelated column-wise basis vectors in the design matrix. These techniques, among others, include: maximally-sparse sampling of the kernels (for first-, second- and third-order), combatting ill-conditioning on its own terms, and realizing an exponential decrease of the growth of the number of kernel coefficients.