## 4 Experiments and Analysis
### Comparison and Analysis Among Systems  
To further analyze and compare the characteristic of the repeat period for GPS, BDS, and GAL systems, the STD between the satellites (BS) of the same system is presented in Table 2. For convenience of comparison, the mean STD (MS) of all the satellites for each method is also presented. Furthermore, the STD of the BDS system was calculated for different orbital types separately. For the Galileo system, only the normal orbit satellites were counted.  
It is interesting to note that although the MS of the BDS GEO satellite is very high for each method, the STD between the GEO satellites appears to be much smaller than the other satellite types, which is only 0.59 for the BEM method. This is mainly because the GEO satellites are relatively stationary, and the mean shift time for different satellites is almost identical. On the contrary, as for the BDS IGSO satellite, although the MS for each method is very small, the BS of the satellite performs much greater than other system satellites. This result indicates that the shift time of the IGSO satellite is stable for each satellite, but the fluctuation is more serious between the inter-satellites.  
At the same time, the MS of the BDS MEO satellites shows little difference with the IGSO satellites. These results demonstrate that the performance of the BDS satellite orbital repeat track is representative of the whole BDS system. Moreover, it can be seen that the MS of the three methods for the GPS system is much smaller than the other systems. Even for the BS, the GPS system also performs better than the BDS IGSO, BDS MEO, and GAL systems.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Satellite** & \multicolumn{2}{c}{**BEM**} & \multicolumn{2}{c}{**CCM**} & \multicolumn{2}{c}{**ARTM**} \\ \cline{2-7}
**Number** & **Time(s)** & **STD(s)** & **Time(s)** & **STD(s)** & **Time(s)** & **STD(s)** \\ \hline E14 & 4880.07 & 34.82 & 4885 & 33.56 & 4892 & 32.41 \\ \hline E18 & 4875.22 & 35.59 & 4881 & 36.14 & 4878 & 34.13 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The mean shift time and STD for GAL E14 and E18 satellites, which was calculated by the three methods during DOY:161–191, 2018.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**System STD(S) Method**} & \multicolumn{2}{c}{**BEM**} & \multicolumn{2}{c}{**CCM**} & \multicolumn{2}{c}{**ARTM**} \\ \cline{3-8}  & & **BS** & **MS** & **BS** & **MS** & **BS** & **MS** \\ \hline \multirow{2}{*}{BDS} & GPS & 2.74 & 0.35 & 2.68 & 0.35 & 2.67 & 0.34 \\ \cline{2-8}  & GEO & 0.59 & 6.69 & 1.58 & 7.16 & 1.34 & 6.91 \\ \cline{2-8}  & IGSO & 9.40 & 1.98 & 10.52 & 2.08 & 9.46 & 2.02 \\ \cline{2-8}  & MEO & 3.69 & 2.50 & 4.62 & 2.52 & 3.51 & 2.34 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The STD of the GPS, BDS, and GAL systems, which was calculated by the three methods. BS denotes the STD between the satellites for the same system, and MS denotes the STD of the mean shift time for the same satellite.  
Based on the above analysis, in terms of the system as a whole, the mean shift time of the GPS system is more stable than the other systems. Additionally, the BS and MS of the GAL system are significantly greater than the GPS and BDS MEO satellites. However, it should be noted that the characteristics of the shift time can only be used to evaluate the performance of the orbital track of the satellite but does not reflect other aspects of the performance for the satellite or system.