Geodesic
A two-stage approach to forecasting the divergence of time scales based on an adjusted linear model
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2023), pp. 80-93

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This paper presents the results of a study of the accuracy of a two-stage approach to forecasting the divergence of time scales of GLONASS spacecraft relative to the system time scale for intervals of up to 2 h. At the first stage a linear model is constructed on the results of measurements of the divergence of time scales on the selected dimensional interval based on the least squares method, the offset of the smoothed estimate of the divergence of time scales at the end of the dimensional interval relative to the linear trend found over the entire dimensional interval is determined, the constant coefficient of the linear model is corrected. At the second stage the unaccounted residual component of the time series of the time scale divergence values is determined and an AR model describing it is constructed. A comparative analysis of the accuracy of the forecast of the divergence of time scales according to a linear model with an adjusted constant coefficient and the forecast using its combination with an AR model is carried out. The analysis of the numerical results obtained during the annual observation interval showed that for all spacecraft, the use of a two-stage approach makes it possible to reduce the standard deviation of the forecast of time scale divergence, as well as to increase the number of forecast implementations for which the standard deviation does not exceed 0.3– 0.5 ns.
Keywords: divergence of time scales; onboard time scale; synchronisation; time measurement; least squares method; time-frequency corrections; forecasting. 
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     title = {A two-stage approach to forecasting the divergence of time scales based on an adjusted linear model},
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O. S. Chernikova; T. A. Marareskul. A two-stage approach to forecasting the divergence of time scales based on an adjusted linear model. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2023), pp. 80-93. http://geodesic.mathdoc.fr/item/BGUMI_2023_2_a7/