Identification of an univariate function in a nonlinear dynamical model

This paper addresses the problem of estimating, from measurement data corrupted by highly correlated noise, the shape of an unknown scalar and univariate function hidden in a known phenomenological model of the system. The method makes use of the Vapnik’s support vector regression to find the structure of a parametrized black box model of the unknown function. Then the parameters of the black box model are identified using a maximum likelihood estimation method specially well suited to cope with correlated noise. The ability of the method to provide an accurate confidence bound for the unknown function is clearly illustrated from a simulation example. Keywords—Hybrid Identification; Support Vector Machine; Nonlinear System; Correlated Residuals; Maximum Likelihood.