Model Identification and Data Fitting

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Model Identification and Data Fitting is centered around the estimation of a mathematical model based on previous observations. This course is devoted to the various practical and theoretical aspects of such estimations (identifications) of mathematical models from several model classes. The course starts by addressing distance measures, norms, and criterion functions. After this the prediction error identification of linear regression models will be discussed. The emphasis will be on the various interpretations of these models such as deterministic, stochastic with Gaussian white noise and maximum likelihood estimation, stochastic in a Bayesian estimation context. Additionally several numerical implementation aspects such as: recursion, numerical complexity, numerical conditioning, and square root filtering will be highlighted. Next the focus will be on identification within the class of auto-regressive dynamical models, to which the Levinson algorithm applies. Other topics that will be discussed include identifiability, model reduction and model approximation. Several of the techniques that will be discussed are illustrated in Matlab. After completing this course the student will have obtained insight into the various aspects that play a key role in building a mathematical model from measurement data. The student will be able to apply the techniques learned to real world problems to construct models from observed data. The student will be able to judge and predict the quality of such models.