Features of practical application of the method of regressor dynamic expansion and mixing with desired indicators of parameters estimation quality

Abstract

The features of the dynamic regressor expansion and mixing method and its modifications used in estimating the parameters of a linear regression equation for systems with different properties are analyzed. The objectives of the study are to identify key aspects of the practical application of the dynamic regressor expansion and mixing method, compare the patterns of application of its modifications, and select the most effective solutions. Numerical modeling is used to compare various modifications of the original algorithm aimed at overcoming the following problems: a relatively large number of adjustable parameters, weak excitation of the regressor, the need to select gradient descent coefficients to ensure convergence for each parameter in a comparable time, and the presence of outliers in the estimate for piecewise constant parameters. It is shown that the use of expansion schemes allows to reduce the number of adjustable parameters, adding a regularizing matrix to the expanded regressor provides an estimate for cases with weak excitation, normalization of the excitation of the regressor ensures the agreement of the convergence time of the estimate for different degrees of excitation of the regressor, and an interval integral filter with resetting is effective against outliers in the parameter estimate in the case of their piecewise constant assignment.