IDENTIFICACION DE SISTEMAS DINAMICOS LINEALES MEDIANTE MAXIMA VEROSIMILITUD CON MEZCLA FINITA DE DISTRIBUCIONES NORMALES
BITTNER HOFFMANN, GUSTAVO JUAN ESTEBAN
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This Thesis addresses the identification problem of output-error systems with nonGaussian measurement noise. Initially the problem is restricted to minimum phase noise zeros, i.e. the roots of the numerator associated with the noise transfer function lies within the unit circle. The noise distribution is approximated by a finite Gaussian mixture, whilst the parameters of the system and the parameters that approximate the noise distribution are simultaneously estimated using the principle of Maximum Likelihood. To this end, a global optimization algorithm is utilized to solve the resulting nonconvex optimization problem. It is shown that our approach improves the accuracy of the estimates, when compared with classic estimation techniques such as the Prediction Error Method (PEM), in terms of covariance of the estimation error, while also obtaining an approximation of the noise distribution. The benefits of the proposed technique are illustrated by numerical simulations. Later, a Maximum Likelihood estimation algorithm for a non-minimum-phase linear dynamic system with Gaussian mixture noise distribution is developed. Based on the Expectation-Maximization algorithm, we propose an identification technique to estimate the system model parameters and the Gaussian mixture parameters. We show that the estimates obtained by using this approach exhibit good accuracy. The benefits of our proposal are illustrated via numerical simulations. The work hereby presented is divided in three main parts. First, an overview of classical system identification and the state of the art technique, given by the Method of Moments, for solving the problem of interest is discussed. The second part of the thesis presents a solution based on a global optimization method, given by the Pattern Search algorithm, to solve the Maximum Likelihood estimation problem. A Gaussian Mixture Model is considered to approximate the noise distribution and its parameters are simultaneously estimated with the system parameters. The third part of the thesis addresses an extension by considering non-minimum phase noise zeros. An ExpectationMaximization based algorithm is proposed to estimate the system model arameters and the Gaussian mixture parameters.