ПСЕВДОПРОЕКЦІЙНІ АЛГОРИТМИ ОЦІНЮВАННЯ, ЩО ВИКОРИСТОВУЮТЬ ЗВАЖУВАННЯ ІНФОРМАЦІЇ

• Дата: 2020
• Автори: Liberol, B.D., Rudenko, O.G., Bezsonov, A.A.
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Теми: алгоритм Качмажа; проекційний алгоритм; рекурентна процедура; асимптотична оцінка; точність ідентифікації
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/478
• Назва журналу: Problems of Control and Informatics

The Kaczmarz algorithm, which is now widely used due to its simplicity and efficiency in solving various technical problems, was proposed in [3] for solving systems of linear algebraic equations. Analytical studies carried out in [8–10] allowed to obtain non–asymptotic and asymptotic convergence rate estimates of this algorithm in the presence of measurement interference. In [11–14], the problem of acceleration of the Kaczmarz algorithm by using not one but a number of previous measurements was considered. In [12–16], multi-step projection algorithms were proposed, which used information about L of the previous steps when constructing the estimate at the next n-th step. In [15, 16], the speed of convergence of these algorithms was determined and it was shown that the use of information in the multi-step projection algorithms of information about the previous steps is equivalent in the sense of the speed of convergence to reducing the dimension of the output space N by L. A significant positive effect of using information about the previous steps from one side and the need of the matrix inversion on the other side, indicate the feasibility of developing algorithms that have properties similar to multi-step projection algorithms, but which are simpler to implement. One such approach is approximation of the orthogonal projection operation of the estimation error vector onto the input vectors linear shell, carried out on the basis of a one-step Kaczmarz projection algorithm, was studied in [17]. This article discusses a modification of the Kaczmarz algorithm that uses the weighting of the estimates obtained in a number of previous steps.The properties of pseudoprojection estimation algorithms that use information weighing and are based on the one-step adaptive Kaczmarz algorithm are investigated. Estimates of the algorithms convergence rate were obtained and it is shown that the use of the information weighting operation in the estimation algorithms allows to reduce the size of their convergence region (in comparison with the Kaczmarz algorithm with g = const = 1), which is determined by the ratio of signal and interference dispersions, with a slight decrease in the convergence rate.