## 4 Experiments and Analysis
### Performance Analysis for the BDS System  
Considering the fact that the BDS system includes three types of orbital satellites, they were compared and analyzed separately. First, Figure 4 presents the results of the satellite repeat shift time by the three methods for BDS GEO during DOY:161-181, 2018. Consistent with the theoretical derivation, the mean shift time of the GEO satellites is about 236 s. For the same satellite, the difference between the three methods performs in different ways, and the maximum difference is found in the C04 satellite between the CCM and ARTM, which is about 4 s. However, for the C05 satellite, the results are almost identical to the three methods. In addition, for the same method, the difference of the mean shift time between satellites is not significant, and the maximum difference is only 4 s, which appeared between C04 and C01 for CCM. Figure 3: The STD of the satellite repeat shift time for the three methods for each satellite during the period DOY:161–181, 2018. Figure 2: The mean shift time for GPS satellites calculated by the three methods during DOY: 161–181, 2018. Similarly, Figure 5 demonstrates the STD of the repeat shift time of the three methods for each satellite during DOY:161-181, 2018. Obviously, the STD of each BDS GEO satellite is relatively high, and the values of the STD are more than 6 for all satellites and methods. This phenomenon indicates that the satellite repeat shift time of GEO satellites obviously fluctuates during this period. In addition, comparing the three methods, it is clear that the STD of CCM is higher than the other two methods for most satellites. This is mainly because the change of the elevation and azimuth is not obvious, since the GEO satellite is almost stationary relative to the ground user. Although the GEO and IGSO satellites have similar repeat periods, their orbital operation track is different. Hence, the characteristic of the satellite repeat shift time for IGSO is also different from the GEO satellite. From Figure 6, it is apparent that the mean repeat shift time for the BEM, CCM, and ARTM is almost similar for the same satellite during this period. On the contrary, the mean shift time varies with different satellites, such as C08 and C10; the maximum difference between them is approximately 25 s. In particular, the mean shift time of C08 is much shorter than other IGSO satellites, which is only 225 s during these days. Figure 4: The mean shift time for BDS GEO satellites calculated by the three methods during DOY: 161–181, 2018. Figure 5: The STD of the satellite repeat shift time for the three methods for each satellite during the period DOY:161–181, 2018. Figure 7 demonstrates the results of the STD of the three methods, which was used to evaluate the fluctuation of the BDS IGSO satellites. It is obvious that although the STD of the CCM method is slightly higher than those of the other two methods, the difference is negligible. In addition, compared to the BDS GEO satellite, the STD of IGSO is much smaller, which is only about 2. This result indicates that the fluctuation of the satellite repeat shift time of IGSO is more stable than GEO satellites. The BDS MEO satellite operation track is also different from the IGSO satellite, whose satellite repeat period is about 7 days and the satellite repeat shift time is about 1700 s. Figure 8 presents the results of the mean shift time of the three methods for the three MEO satellites. From Figure 8, it can be seen that for the same satellite, the mean shift time of the three methods is not much different, especially for the C11 satellite. The maximum difference between the BEM and CCM for C14 is about 4 s. However, for different satellites, the mean shift time is also different. Additionally, the maximum difference is about 7 s, such as the C12 and C14 for the CCM and ARTM methods.