Estimation of spectral functions and intensity of point sources of radiation under uncertainty - Nakonechnyi, O. G.; Zinko, P. M.; Zinko, T. P. (Matematychni Studii, 2025)
The paper is dedicated to the study of the problem of estimating the intensity in the frequency domain of point wave sources moving in three-dimensional space. It is assumed that the wave propagation speed is constant, and the point sources move along known trajectories. The frequency characteristics of the moving sources are considered unknown, and to estimate them, values of the wave field with errors are given at certain discrete moments in time or over a given time interval at known points in space. It is also assumed that the frequency characteristics and errors belong to known sets of corresponding spaces. In the case of specifying the wave field at discrete moments in time, guaranteed estimates of the intensity of point wave sources are obtained as solutions to certain matrix linear equations, while in the case of continuous time, guaranteed estimates of the intensity of point wave sources are obtained as solutions to a system of integral equations. The obtained theoretical results are confirmed by test examples.