## 3 Results
### Performance of Five-System PPP Time Transfer at Locations with Limited Sky View  
In the previous section, we assess the PPP time transfer performance under good observation conditions, but in the practical applications, the users also have the requirement of high-accuracy time transfer at locations with limited sky view. Therefore, this section focuses on the PPP time transfer performance of the BDS/GPS/GLONASS/Galileo/QZSS five-system combination under the environments with limited satellite visibility. To simply simulate the environments with limited sky view, the cut-off elevation angles are set from \(20^{\circ}\) to \(40^{\circ}\) in steps of \(10^{\circ}\). For comparative analysis, the results of the four single-GNSS cases are also given. Table 5 shows the service rates of each PPP time transfer case under observation conditions with limited sky view. The service rate for a time link is roughly defined as the ratio of the number of epochs in which the receiver clock differences between two stations can be successfully solved over the total number of epochs during the whole analysis period. The average results over all the 12 time links are computed and provided in Table 5. Under an elevation cut-off angle of \(20^{\circ}\), the seven-day service rate of the GPS \begin{table}
\begin{tabular}{c c c c} \hline \hline
**System Combination** & **BRUX-MGUE** & **BRUX-PTBB** & **BRUX-SPT0** \\ \hline GPS & 2.2\% & 8.7\% & 12.1\% \\ GLO & 11.2\% & 35.2\% & 45.2\% \\ GAL & 5.9\% & 16.5\% & 8.4\% \\ BDS & 4.4\% & 10.1\% & 15.6\% \\ GRECJ & 1.6\% & 6.7\% & 6.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average value of day-to-day variation ratios of MDEV statistics over seven days (DOY 248 to 254, 2021) and three specific average times (\(10^{2}\), \(10^{3}\), and \(10^{4}\) s) for three time links. Figure 11: Average MDEV values over a week and all 12 time links at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s.  
only case, GLONASS-only case, Galileo-only case, and BDS-only case is 100.0%, 70.6%, 79.3%, and 91.3%, respectively. After further setting the elevation cut-off angle to 30\({}^{\circ}\), the corresponding service rate of the GLONASS-only case, Galileo-only case, and BDS-only case significantly decreases. When the elevation cut-off angle is further set to 40\({}^{\circ}\), the service rate is reduced to less than 36% for the GPS-only case, and less than 6% for the other three single-GNSS cases. In contrast, the service rate of the five-system combination case can still maintain 100.0%. For further analysis, the service rates of single-GNSS PPP time transfer cases for each time link are detailed in Figure 12. It is seen that the service rates dramatically vary among the 12 time links. Actually, the low service rates of single-GNSS PPP time transfer cases are related to the number of visible satellites. Table 6 further provides the success rates of each PPP time transfer case under observation conditions with limited sky view. The success rate is defined as the ratio of the number of epochs with successfully solved receiver clock differences over the number of epochs with sufficient satellites (at least four satellites) using the datasets of all the stations and days. Similar to the service rates (see Table 5), the success rates always maintain 100.0% for the five-system combination case, and decrease with the increasing cut-off elevation angles for the four single-GNSS cases. When using the cut-off elevation angle of 40\({}^{\circ}\), the success rates are still larger than 90% for the GPS-only, Galileo-only, and BDS-only cases, while those of the GLONASS-only case are reduced to only 37.6%, which may be attributed to the worse quality of observations and the lower accuracy of precise satellite products in comparison with other satellite systems. Figure 12: Service rates of single-GNSS PPP time transfer cases for each time link using the cut-off elevation angle of 20\({}^{\circ}\), 30\({}^{\circ}\), and 40\({}^{\circ}\).