Identifying dynamic systems with polynomial nonlinearities in the errors-in-variables context

Many practical applications including speech and audio processing, signal processing, system identification, econometrics and time series analysis involve the problem of reconstructing a dynamic system model from data observed with noise in all variables. We consider an important class of dynamic single-input single-output nonlinear systems where the system model is polynomial in observations but linear in parameters, which captures a wide range of such systems. 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 MonteCarlo simulations. Key–Words: system identification; discrete-time dynamic systems; errors-in-variables; linearizable systems; polynomial eigenvalue problem; covariance matching