Optimal selection of free parameters in expansions of Volterra models using Kautz functions

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models of any order is proposed. The usual large number of parameters required to represent the Volterra kernels can be reduced by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. The resulting model can be truncated into fewer terms if the Kautz functions are properly designed. The underlying problem is how to select the arbitrary complex poles that fully parameterize these functions. This problem is approached by minimizing an upper bound for the error resulting from the truncation of the kernel expansion when each multidimensional kernel is decomposed into a set of independent Kautz bases, each of which is parameterized by an individual pair of conjugate Kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension. An analytical solution for one of the Kautz parameters is derived.