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

Authors:
Levente Hunyadi;István Vajk
Affiliations:
Budapest University of Technology and Economics, Department of Automation and Applied Informatics, Budapest, Hungary;Budapest University of Technology and Economics, Department of Automation and Applied Informatics, Budapest, Hungary
Venue:
WSEAS TRANSACTIONS on SYSTEMS
Year:
2009

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Abstract

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 Monte- Carlo simulations.