Guaranteed root mean square estimates of linear matrix equations solutions under conditions of uncertainty

2023;
: pp. 474–486
https://doi.org/10.23939/mmc2023.02.474
Received: October 12, 2022
Revised: April 20, 2023
Accepted: May 02, 2023

Mathematical Modeling and Computing, Vol. 10, No. 2, pp. 474–486 (2023)

1
Taras Shevchenko National University of Kyiv
2
Taras Shevchenko National University of Kyiv
3
Taras Shevchenko National University of Kyiv
4
Taras Shevchenko National University of Kyiv
5
Kyiv National Economic University named after Vadym Hetman

The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions of linear matrix equations with the right-hand sides belonging to bounded sets.  The random errors of the observation vector have zero mathematical expectation, and the correlation matrix is unknown and belongs to one of two bounded sets.  Explicit expressions of the guaranteed root mean square errors of estimates for linear operators acting from the space of rectangular matrices into some vector space are given.  Guaranteed quasi-minimax root mean square errors of linear estimates are obtained.  As the test examples, two options for solving the problem are considered, taking into account small perturbations of known observation matrices.

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