Prediction of time scale divergence based on an adjusted linear model

Abstract

The paper presents the results of a study of the accuracy of a two-stage algorithm for constructing a linear model for predicting the divergence of the time scales of GLONASS spacecraft relative to the system time scale for intervals of up to two hours. At the first stage of the two-stage algorithm, a linear model is constructed based on the least squares method based on the results of the measurement data of the discrepancy of the time scales at the selected dimensional interval. At the second stage, the offset of the smoothed estimate of the discrepancy of the time scales at the end of the dimensional interval (the current session estimate) is determined relative to the linear trend found throughout the dimensional interval, and the constant term of the constructed linear model is refined based on the latest measurements. A comparative analysis of the accuracy of the forecast of the divergence of time scales based on a linear model and a linear model with an adjusted constant coefficient at different forecast intervals is also provided. The analysis of the obtained results of the error estimation of the corrected linear prediction model of the divergence of the GLONASS time scales, constructed using the described two-stage algorithm, allows for all GLONASS spacecraft at the considered prediction intervals to provide a smaller prediction error compared to the linear model without correction. It is also possible to distinguish a group of spacecraft for which the forecast error is noticeably higher than for the rest (the worst forecasts in terms of accuracy were obtained for spacecraft R02, R13, R22).The proposed approach can be used both to predict the divergence of spacecraft time scales and to recover the missing data on a dimensional interval, which is relevant for expanding the class of mathematical models used to describe the divergence of time scales.