Nonlinearly constrained optimisation using a penalty-transformation method for Volterra parameter estimation

Abstract

This paper forms a part of a series of studies we have undertaken, where the problem of nonlinear signal modelling is examined. We assume that the observed "output" signal is derived from a Volterra filter that is driven by a Gaussian input. Both the filter parameters and the input signal are unknown and therefore the problem can be classified as blind or unsupervised in nature. In the statistical approach to the solution of the above problem we seek for equations that relate the unknown parameters of the Volterra model with the statistical parameters of the "output" signal to be modelled. These equations are highly nonlinear and their solution is achieved through a novel constrained optimisation formulation. The results of the entire modelling scheme are compared with other contributions.