priborИзвестия высших учебных заведений. ПриборостроениеJournal of Instrument Engineering0021-34542500-0381Национальный исследовательский университет ИТМО10.17586/0021-3454-2024-67-8-670-677pribor-73Research ArticleСИСТЕМНЫЙ АНАЛИЗ, УПРАВЛЕНИЕ И ОБРАБОТКА ИНФОРМАЦИИSYSTEM ANALYSIS, MANAGEMENT AND INFORMATION PROCESSINGМетод оценивания параметров линейных регрессионных моделей с линейно зависимыми элементамиMethod of Estimation of Parameters of Linear Regression Model with Linearly Dependent ElementsОвчаровА. О.OvcharovA. O.

Алексей Олегович Овчаров – аспирант; факультет систем управления и робототехники; заведующий лабораторией

Санкт-Петербург

Alexey O. Ovcharov – Post-Graduate Student; Faculty of Control Systems and Robotics; Head of a Laboratory

St. Petersburg

ovcharov.alex.o@gmail.comВедяковА. А.VedyakovA. A.

Алексей Алексеевич Ведяков – канд. техн. наук, доцент; факультет систем управления и робототехники; доцент

Санкт-Петербург

Alexey A. Vedyakov – PhD, Associate Professor; Faculty of Control Systems and Robotics; Associate Professor

St. Petersburg

vedyakov@gmail.comУниверситет ИТМОITMO University,Университет ИТМОITMO University202426112024678670677Copyright © Национальный исследовательский университет ИТМО, 20242024Национальный исследовательский университет ИТМОНациональный исследовательский университет ИТМОhttps://pribor.ifmo.ru/jour/about/submissions#copyrightNoticehttps://pribor.ifmo.ru/jour/article/view/73

Рассмотрена задача онлайн-оценивания параметров моделей линейной регрессии при наличии линейно зависимых элементов в регрессоре. Однако из-за линейной зависимости оценить все параметры не представляется возможным. Предложен метод, позволяющий оценить параметры, соответствующие линейно независимым элементам регрессора. Метод включает два этапа. На первом этапе выполняется преобразование исходной модели регрессии с неизвестным вектором параметров к модели с новым неизвестным вектором переменных. Таким образом, задача оценивания параметров приводится к задаче синтеза наблюдателя. На втором этапе синтезируется адаптивный наблюдатель нового вектора переменных, позволяющий одновременно оценить искомый вектор параметров.

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.

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The authors declare that there are no conflicts of interest present.