A Linear Approach for Parameters Estimation of Multivariable Models in a Parameter Matrix Form

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When a model output is a linear function of the model parameters, the estimation process is significantly simplified, since the optimal estimates can be determined without the usage of a numerical optimization method. Moreover, some types of nonlinear models w.r.t. their parameters can be interpreted as linear (obviously introducing a discrepancy). This is the main premise behind the linear approach for parameter estimation, where the Least Squares (LS) method is used for parameters estimation. As this assumption contradicts with the non-linear parameterized model structure, the estimation process becomes iterative. In spite of this, the linear approach is frequently preferable due to the reduced number of computations, compared with the non-linear approach, where the model is correctly considered as non-linear. Moreover, some issues with the starting point selection, stuck at a local minima, etc., natural for the non-linear approach, are avoided. In this paper estimators are presented, based on the linear approach, for both MIMO linear and non-linear parameterized models in a parameter matrix form. The representatives of the first group are LS and Weighted LS (WLS). For non-linear models, this approach is presented in terms of Extended LS (ELS). The topic regarding the efficient realizations of the estimators is also discussed


  • 1. Atanassov, A. Advanced Software Architecture of an Automatic Number Plate Recognition System. - Journal of the University of Chemical Technology and Metallurgy, 47, 2012, issue 1, ISSN 1311-7629.

  • 2. Atanassov, A. Algorithm for Synthesis of Process-Oriented Software and its Distribution on a Single and Multiprocessor Systems. - Journal of the University of Chemical Technology and Metallurgy, 2012, ISSN 1311-7629.

  • 3. Atanasov, À. CSP Oriented Software Architecture of an Automatic Number Plate Recognition System. International Conference Automatics and Informatics, Sofia, 3-7 October 2013.

  • 4. Efremov, A. Multivariable System Identification. Monograph. Dar-RH, 2014, ISBN 978-954-9489-42-2.

  • 5. Nelles, O. Nonlinear System Identification. From Classical Approaches to Neural Networks and Fuzzy Models. Springer- Verlag, Berlin Heidelberg, 2001.

  • 6. Tellinghuisen, J. Least Squares with Non-Normal Data: Estimating Experimental Variance Functions. - The Royal Society of Chemistry, 133, 2008, 161-166

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