Generalized eigenvector algorithm for nonlinear system identification with non-white inputs

Traditional methods for nonlinear system identification require a white, Gaussian, test input, a restriction that has limited their usability in many fields. In this study, we address the problem of identifying the dynamics of a nonlinear system when the input is highly colored—a restriction commonly encountered in the study of physiological systems. An extension of the parallel cascade method is developed that is optimal in a constrained minimum mean squared error sense and exactly corrects for the distortion induced by the non-white input spectrum. However, this correction is a deconvolution, which may become extremely ill-conditioned if the input spectrum depart significantly from whiteness; to confront this, we develop a low-rank projection operation that stabilizes the deconvolution. The overall algorithm is robust and places few requirements on the nature of the test input. Practical application of this new method is demonstrated by using it to identify a known analog nonlinear system from experimental data.