## 1 Introduction  
For global navigation systems, the satellite has the characteristic of a repeat period, which means that the satellite will appear in the same position with a period for the ground static user. Not only can this feature of the satellite be used to predict the satellite position, but it can also mitigate multipath errors and observation noise effectively. Besides, the repeat period characteristic of the satellite can also reflect the status of satellite operation and assess the stability of the whole system operation to a certain extent. In order to calculate the orbital repeat shift time of the satellite, some effective methods have been proposed in the literature. The satellite repeat shift time was first pointed out by [PERSON] et al. [1] which was mainly used to reduce multipath disturbance. After that, authors [2; 3; 4; 5] also used the satellite repeat shift time to reduce the noise for long baselines or isolate signals from multipath error. However, all of them assumed that the shift time between two consecutive days for the same satellite was about 4 min for a GPS satellite. [PERSON] et al. [6] pointed out that the satellite repeat shift time of the GPS satellite is slightly different for each satellite between 240 and 256 s instead of the assumed 236 s, but the calculation process was not given. [PERSON] et al. [7] adopted broadcast ephemeris values and Kepler's third law to estimate the satellite repeat period of the GPS satellite, and the results showed that the repeat periods of the satellites are not precisely a sidereal day and are distinct from each satellite. This method was also adopted by [PERSON] and [PERSON] [8] and [PERSON] et al. [9]. Moreover, [PERSON] et al. [10] and [PERSON] et al. [11] used the broadcast ephemeris to analyze the satellite repeat shift time for the Beidou satellite. [PERSON] et al. [12] analyzed the GPS satellite by applying the broadcast ephemeris method, which showed that the mean shift time of each satellite is different. Particularly, for a satellite undergoing a maneuver, the mean shift time is significantly different from that of other satellites. Taking advantage of the correlation method, [PERSON] et al. [13] observed the repeat shift time by the correlation coefficient method for the GPS satellite first. [PERSON] et al. [14] proposed the use of the auto-correlation technique to determine the repeat shift time for a GPS satellite. [PERSON] et al. [15] analyzed the repeat shift time of a Beidou GEO satellite by utilizing the Fourier transform, correlation, and wavelet transform methods. The results indicated that the satellite repeat shift time ranges from 220 to 270 s. Similarly, [PERSON] et al. [16] employed correlation analysis, Fourier transformation, and wavelet decomposition methods to estimate the repeat shift time for Beidou IGSO and MEO satellites. [PERSON] et al. [17] developed the cross-correlation method to determine the repeat shift time for the GPS satellite. Furthermore, [PERSON] et al. [18] also introduced this method to analyze the characteristics of the Beidou satellite's orbit. Moreover, [PERSON] and [PERSON] [19] proposed the aspect repeat time method to determine the repeat shift time for the GPS satellite, and the experiment results indicated that the mean repeat shift time calculated by this method is 246 s and the fluctuations through the day are as much as 2.5 s at high latitudes. [PERSON] et al. [17] utilized the aspect repeat time method to estimate time-varying and site-dependent shifts for the GPS satellite. [PERSON] [20] compared the broadcast ephemeris method with the aspect repeat time method. [PERSON] et al. [21] also used the aspect repeat time method to calculate the repeat shift time for the Galileo satellite. In addition, [PERSON] et al.