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Information Technologies and Control

The Journal of Institute of Information and Communication Technologies of Bulgarian Academy of Sciences

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

A. Efremov
Published Online: 2014-12-30 | DOI: https://doi.org/10.2478/itc-2013-0014


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

Keywords : LS; WLS; ELS; MIMO model; parameter matrix; tensors; GPU


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About the article

Received: 2013-12-18

Published Online: 2014-12-30

Published in Print: 2014-09-01

Citation Information: Information Technologies and Control, Volume 11, Issue 3, Pages 36–44, ISSN (Online) 1312-2622, DOI: https://doi.org/10.2478/itc-2013-0014.

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© 2015. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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