An evaluation method of GPS satellite clock in-orbit with periodic terms deducted

The performance of the atomic clock in orbit is of terrific significance for the Global Navigation Satellite System (GNSS). With the rapid development of satellite navigation and atomic clock technology, the periodic error of satellite clocks caused by the environment is more prominent. This paper focuses on the analysis and quantification of the systematic periodic error in the clock offset and proposes a more accurate evaluation method for GPS satellite clocks. The fact that the J2 relativistic effect and orbit radial error are the main sources of the systematic periodic term has been revealed. Then, the Fast Fourier Transform (FFT) is employed using the sliding window to investigate the periodic influence caused by satellite orbit and the J2 relativistic effect on clock offset through six GPS satellites with different orbital planes, these satellites also cover all four types of GPS satellite blocks. The results show that there is an obvious relationship between the sun elevation and orbit radial error, clock offset fitting precision, frequency stability and amplitude. The different geometric configurations of the satellite and the varying environment make this relationship different. Based on the clock offset provided by European Space Agency (ESA), the period of clock offset is extracted and quantized, with the period of 24 h, 12 h, 8 h, 6 h, 4 h, and 3 h. According to the daily extraction results of the time-varying periodic terms, the two most noticeable terms correction on satellite clock offset has been proven to be effective in eliminating periodic errors. Compared to those without periodic correction, the fitting precision and frequency stability can improve by 48.5% and 42.6%, respectively. In addition, all GPS satellite clocks in orbit are evaluated by this periodic correction method, and the results are more approach to the actual performance of the satellite clock. Furthermore, this method can also be adapted to evaluate satellite clocks of other GNSS systems. Therefore, when we evaluate the high-precision atomic clock flying on board GNSS satellites and compare them with the manufacturers' specifications, the periodic error cannot be neglected.