Relativistic Effects on Satellite-Ground Two-Way Precise Time Synchronization

An ultrahigh precise clock (space optical clock) will be installed onboard a low-orbit spacecraft (a usual expression for a low-orbit satellite operating on an orbit at an altitude of less than 1000 km) in the future, which will be expected to obtain better time-frequency performance in a microgravity environment, and provide the possible realization of ultrahigh precise long-range time synchronization. The advancement of the microwave two-way time synchronization method can offer an effective solution for developing time-frequency transfer technology. In this study, we focus on a method of precise satellite-ground two-way time synchronization and present their key aspects. For reducing the relativistic effects on two-way precise time synchronization, we propose a high-precision correction method. We show the results of tests using simulated data with fully realistic effects such as atmospheric delays, orbit errors, and earth gravity, and demonstrate the satisfactory performance of the methods. The accuracy of the relativistic error correction method is investigated in terms of the spacecraft attitude error, phase center calibration error (the residual error after calibrating phase center offset), and precise orbit determination (POD) error. The results show that the phase center calibration error and POD error contribute greatly to the residual of relativistic correction, at approximately 0.1 similar to 0.3 ps, and time synchronization accuracy better than 0.6 ps can be achieved with our proposed methods. In conclusion, the relativistic error correction method is effective, and the satellite-ground two-way precise time synchronization method yields more accurate results. The results of Beidou two-way time synchronization system can only achieve sub-ns accuracy, while the final accuracy obtained by the methods in this paper can improved to ps-level.