Prediction of a Quasi-Periodic Processes in the Formation of Satellite Time Scale

A. V. Saltsberg, E. A. Roshchina

Transactions of IAA RAS, issue 76, 8–16 (2026)

DOI: 10.32876/ApplAstron.76.8-16

Keywords: GNSS, time-frequency support, onboard frequency standard, satellite time scales, relativisticgravitational effects, quasi-periodic processes, time series prediction

Abstract

The aim of this work is to investigate approaches for predicting the periodic component of satellite clock time offset caused by relativistic-gravitational effects on the onboard frequency standard when calculating frequency-time corrections in the onboard computing system. Predicting such quasi-periodic processes requires a combination of analytical methods and numerical modeling. Although long-term predictions are limited due to the incommensurability of frequencies, accurately defining the mathematical model and selecting the most effective forecasting methods can achieve sufficiently low errors over short- and medium-term intervals. It is equally important to strike a balance between model complexity with interpretability. The article compares various algorithms for predicting quasi-periodic processes based on the least squares method, the Kalman filter, and the Seasonal AutoRegressive Integrated Moving Average (SARIMA) model. The study examines the number of frequencies that need to be accounted for, depending on required prediction accuracy, and explores optimal ratios between observation and prediction intervals for both continuous initial data and data sampled according to the radio visibility zones of measuring instruments. It is shown that using the least squares method with a trigonometric component in the model allows us to predict the contribution of relativistic-gravitational effects to the satellite clock time offset with an error of less than 200 ps over intervals of up to 30 days. This result holds for both continuous measurement series of satellite position and velocity (with observation intervals of 1–5 days), as well as data containing gaps due to radio visibility constraints. The simplicity of the prediction algorithm for quasi-periodic processes using this method and trigonometric modeling makes it feasible for implementation in satellite onboard computing systems for accurate frequency-time correction calculations.

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