DOI 10.17586/0021-3454-2024-67-8-670-677
UDC 681.5
METHOD OF ESTIMATION OF PARAMETERS OF LINEAR REGRESSION MODEL WITH LINEARLY DEPENDENT ELEMENTS
ITMO University, Faculty of Control Systems and Robotics; Head of a Laboratory
A. A. Vedyakov
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate Professor
Reference for citation: Ovcharov A. O., Vedyakov A. A. Method of estimation of parameters of linear regression model with linearly dependent elements. Journal of Instrument Engineering. 2024. Vol. 67, N 8. P. 670–677 (in Russian). DOI:
10.17586/0021-3454-2024-67-8-670-677.
Abstract. The problem of online estimation of parameters of linear regression models in the presence of linearly dependent elements in the regressor is considered. To solve the problem, a method is proposed that allows estimating the parameters corresponding to independent elements of the regressor. The method includes two stages. At the first stage, the original regression model with unknown vector parameters is transformed into a model with a new unknown vector method. Thus, the problem of measuring parameters leads to the problem of synthesizing an observer. At the second stage, an adaptive observer of the new vector of variables is synthesized, which allows simultaneously estimating the desired vector of parameters.
Abstract. The problem of online estimation of parameters of linear regression models in the presence of linearly dependent elements in the regressor is considered. To solve the problem, a method is proposed that allows estimating the parameters corresponding to independent elements of the regressor. The method includes two stages. At the first stage, the original regression model with unknown vector parameters is transformed into a model with a new unknown vector method. Thus, the problem of measuring parameters leads to the problem of synthesizing an observer. At the second stage, an adaptive observer of the new vector of variables is synthesized, which allows simultaneously estimating the desired vector of parameters.
Keywords: parameter estimation, linear regression, linear dependence, convergence, dynamic regressor extention,
Gram-Schmidt orthogonalization
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