An approach to identifying linearizable dynamic errors-in-variables systems

We consider an important class of dynamic singleinput single-output nonlinear systems where the system model is polynomial in observations but linear in parameters. The investigation is done in the errors-in-variables framework, i.e. both input and output are observed with noise. Assuming white Gaussian measurement noise that is characterized by a magnitude and a covariance structure, we propose a nonlinear extension to the generalized Koopmans–Levin method that can estimate parameters of dynamic nonlinear systems with polynomial nonlinearities given a priori knowledge on the noise covariance structure. In order to estimate noise structure, we apply a covariance matching objective function. Combining the extended Koopmans–Levin and the covariance matching approaches, an identification algorithm to estimate both model and noise parameters is proposed. The feasibility of the approach is demonstrated by Monte-Carlo simulations. Keywords—dynamic system identification; linearizable nonlinear systems; polynomial eigenvalue problem; covariance matching