## 5 Conclusions  
The satellite repeat shift time can be used to mitigate the multipath for GNSS static applications, and the stability of satellite operation can also be reflected to some extent. Two methods were introduced to estimate the approximate satellite repeat period in solar days, named the orbit shift coefficient method and the simplest fraction method. After that, three methods for calculating the satellite repeat shift time were also demonstrated. The recent GNSS observations collected from two stations in Australia were used to evaluate the characteristics of the shift time of the three global systems: GPS, BDS, and GAL.  
The experimental results indicated that the satellite repeat shift time calculated by the three methods is almost identical for the same satellite. It was shown that all three methods can be applied to sidereal filtering multipath correction without much difference. However, for the same method, the mean shift time of each satellite was obviously different. Concretely, the maximum difference between satellites was about 10 s for the GPS system, 25 s for the BDS system IGSO satellite, and 12 s for the GAL system, respectively. Moreover, the STD of the shift time for the satellite and the inter-systems was also estimated to investigate the fluctuation of the satellite and systems. In addition, the mean STD of the ARTM was more stable than the other two methods, which is mainly due to the fact that the ARTM method adopts the precise ephemeris to estimate the shift time.  
Considering the characteristic of the satellite repeat shift time as a whole, the GPS system is more stable than the BDS and GAL systems. Both the BS (the STD between the satellites for the same system) and MS (the STD of the mean shift time for the same satellite) of the GPS system were much smaller than the other two systems, which indicates that the fluctuation of the satellite orbit track is more stable and the stability of the whole system is also much better than the other systems. In addition, since the broadcast ephemeris of the GLONASS system is different from other global systems, the characteristics of the satellite repeat shift time of the GLONASS system need to be further investigated in the future.  
Conceptualization, Y.Y. and M.S.; Methodology, J.J.; Software, M.S.; Validation, Y.Y.; Formal analysis, Y.Y.; Investigation, Y.Y.; Resources, Y.Y.; Data curation, Y.Y.; Writing--original draft preparation, Y.Y.; Writing--review and editing, Y.Y.; Visualization, M.S.; Supervision, M.S.; Project administration, J.J.; Funding acquisition, J.J.  
This research was funded by the National Key Research and Development Program of China, grant number 2018 YFB0505200 and 2018 YFB0505201 and funded by the Fundamental Research Funds for the Central Universities, grant number 2042018 kf0253, and also funded by National Natural Science Foundations of China, grant number 41704154.  
Authors would like to thank the editor and the reviewers for their constructive suggestions and comments. This work is supported by the National Key Research and Development Program of China (2018 YFB0505200 and 2018 YFB0505201), and in part by the Fundamental Research Funds for the Central Universities (2042018 kf0253), and the National Natural Science Foundations of China under grant No. 41704154.  
The authors declare no conflict of interest.