Blind identifiability of quadratic non-linear systems in higher-order statistics domain

Abstract

Quadratic non-linear systems are widely used in various engineering fields such as signal processing, system filtering, predicting and identification. Some conditions to blindly estimate kernels of any discrete and finite extent quadratic system in the higher-order cumulants domain are introduced in this paper. The input signal is assumed as an unobservable i.i.d. random sequence which is viable for engineering practice. Due to properties of the output third-order cumulant functions, identifiability of the non-linear system holds even if the system's output measurement is corrupted by a Gaussian random disturbance. It provides a useful starting point for implementating the identification of a truncated Volterra non-linear system using conventional techniques or neural network methodologies. © 1998 John Wiley & Sons, Ltd.