DOI
10.34229/KCA2522-9664.25.5.8
UDC 519.711
O.G. Nakonechnyi
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
oleksandrnakonechny@knu.ua
P.M. Zinko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
petro.zinko@knu.ua
T.P. Zinko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
taras.zinko@knu.ua
LINEAR RMS ESTIMATES OF SPECTRAL FUNCTIONS OF AVERAGE VALUES
OF NON-STATIONARY RANDOM PROCESSES UNDER CONDITIONS OF UNCERTAINTY
Abstract. Based on observations of the implementation of a non-stationary random process on a finite interval and at individual points, the problem of estimating linear functionals from spectral functions of signals that are included in the average values of such processes was investigated. Under the conditions that the correlation function of the random process and the spectral function of the signal are unknown and belong to certain bounded sets, expressions for guaranteed mean-square linear estimates of a set of linear functionals from spectral functions were found. In a particular case, it is shown that such estimates are expressed in terms of solutions of certain linear integral and linear algebraic equations. The use of a guaranteed approach for finding linear mean-square estimates of the corresponding linear functionals is illustrated by test examples.
Keywords: Implementation of a scalar random process, matrix function, signal spectrum, linear functional, linear vector estimate, guaranteed mean-square vector estimate, vector estimate error.
full text
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