cndcgs Challenges to national defence in contemporary geopolitical situation 2538-8959 2669-2023 LKA 63_NAKONECHNYI 10.47459/cndcgs.2026.63 Article Guaranteed RMS Estimates of Spectral Functions and Radiation Sources from Observations with Random Disturbances Nakonechnyi Oleksandr oleksandrnakonechny@knu.ua ∗ Department of System Analysis and Decision Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Ukraine Zinko Petro Department of System Analysis and Decision Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Ukraine Zinko Taras Department of System Analysis and Decision Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Ukraine Losieva Mariia Department of System Analysis and Decision Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Ukraine Corresponding author. 2026 1 549 558 09 07 2026 Creative Commons Attribution International License (CC BY)

In this article, we investigate the problem of estimating the spectral characteristics of the intensity of moving objects under stochastic uncertainty based on the results of measuring the magnitudes of wave fields at separate points. We assume that the unknown spectral functions belong to known sets from the functional space, and certain restrictions are given for the unknown correlation matrices. For linear guaranteed estimates of the set of linear functionals from spectral functions, we prove that the guaranteed mean square estimates are expressed in terms of solutions of a certain system of linear algebraic equations.

 linear estimate of the vector guaranteed estimate of the vector vector estimation error spectral function moving radiation source stochastic uncertainty observation