Blind adaptive Volterra system identification using barrier function methods for constrained optimisation

This paper forms a part of a series of studies we have undertaken, in which the problem of adaptive Volterra system identification is examined. We assume that we have an observed "output" signal 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 formulate equations that relate the unknown parameters of the Volterra model with the statistical parameters of the "output" signal. These equations are highly nonlinear and their solution is achieved through a constrained optimisation formulation. We attempt to interpret the constrained problem as an unconstrained one by incorporating various types of the so called "barrier functions". The barrier function (or interior point) methods are believed to have properties which are theoretically or computationally desirable for constrained optimisation. The results of the entire modelling scheme are compared with other contributions.