Optimization of Volterra models with asymmetrical kernels based on generalized orthonormal functions

Abstract

An improved approach to determine exact search directions for the optimization of Volterra models based on Generalized Orthonormal Bases of Functions (GOBF) is proposed. The proposed approach extends the work in [7], where a novel, exact technique for optimizing the GOBF parameters (poles) for Volterra models of any order was presented. The proposed extensions take place in two different ways: (i) the formulation here is derived in such a way that each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases (rather than a single, common basis), each of which is parameterized by an individual set of poles intended for representing the dominant dynamic of the kernel along a particular dimension; and (ii) a novel, more computationally efficient method to analytically and recursively calculate the search directions (gradients) for the bases poles is derived. A simulated example is presented to illustrate the performance of the proposed approach. A comparison between the proposed method, which uses asymmetric kernels with multiple orthonormal bases, and the original method, which uses symmetric kernels with a single basis, is presented.