## 3 Results
### Performance of the Five-System PPP Time Transfer under Open Sky
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Time Links** & **GPS** & **GLO** & **GAL** & **BDS** & **GRECJ** \\ \hline BRUX-CRO1 & 0.091 & 0.428 & 0.088 & 0.507 & 0.086 \\ BRUX-PTBB & 0.093 & 0.164 & 0.042 & 0.110 & 0.064 \\ BRUX-SPT0 & 0.036 & 0.236 & 0.060 & 0.158 & 0.029 \\ BRUX-USN7 & 0.074 & 0.608 & 0.082 & 0.610 & 0.064 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average STD statistics of the time link differences over a week for the five-system combination case and the four GNSS single-system cases (unit: ns). on stability. Therefore, this contribution adopts the Modified Allan Deviation (MDEV) to evaluate the frequency stability of PPP time transfer. Figure 6 illustrates the MDEV values of three time links, BRUX-MGUE, BRUX-PTBB, and BRUX-SPT0, using a cut-off elevation angle of \(10^{\circ}\) on DOY 252, 2021. The frequency stability of the GLONASS-only and BDS-only PPP time transfer is obviously inferior to other time transfer cases, and the MDEV statistics of the five-system combination case are superior to the four single-GNSS cases. When the average time is larger than \(2\times 10^{4}\) s, the MDEV values are not reliable, which can be attributed to the small number of data samples, and thus they are not presented in the figure. To investigate the effects of the selected datum of the receiver clock offset on the five-system combined PPP time transfer performance, we compared the MDEV values of the time link BRUX-MGUE taking the receiver clock offset of GPS and BDS-3 as the datum on DOY 252, 2021. The frequency stability for the five-system combined PPP time transfer with GPS datum can be \(1.14\times 10^{-13}\), \(1.70\times 10^{-14}\), and \(9.88\times 10^{-15}\) at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s, respectively, while the corresponding frequency stability for that with BDS-3 datum can be \(1.25\times 10^{-13}\), \(1.48\times 10^{-14}\), and \(9.99\times 10^{-15}\), respectively. The difference in the MDEV values between the two datums is not significant. Therefore, the receiver clock offset of GPS is taken as the datum in all other five-system combined PPP time transfer results. Figures 7, 8 and 9 illustrate the MDEV values of three time links, BRUX-MGUE, BRUX-PTBB, and BRUX-SPT0, on DOY 248 to 254, 2021, when the average time is \(10^{2}\), \(10^{3}\), and \(10^{4}\) s, respectively. The MDEV values at the average time \(10^{2}\), \(10^{3}\), and \(10^{4}\) s are taken as typical results to reflect the short-term, medium-term, and long-term frequency stability, respectively [26]. It is seen that the GLONASS-only PPP time transfer shows the largest day-to-day scattering of the MDEV values, followed by the Galileo-only and BDS-only cases, which may be attributed to the relatively lower accuracy of precise satellite products or the insufficient number of available satellites. In contrast, the day-to-day scattering of the MDEV values is not obvious for GPS-only and five-system integrated PPP time transfer, especially for the five-system combination case. For further analysis, Table 4 provides the average value of day-to-day variation ratios of MDEV statistics over seven days (DOY 248  
Figure 6: MDEV values of three time links under a cut-off elevation angle of \(10^{\circ}\) on DOY 252, 2021.  
to 254, 2021) and three specific average times (\(10^{2}\), \(10^{3}\), and \(10^{4}\) s) for the three employed time links. According to the average results over the three time links, the variation ratios of frequency stability between two adjacent days for the GLONASS-only PPP time transfer can be up to 30.5%, while the corresponding variation ratios under the GPS, Galileo, and BDS single-GNSS cases are 7.7%, 10.3%, and 10.0%, respectively. As for the five-system combination case, the average variation ratios of frequency stability are only 4.8%, implying its ability to provide a steady time transfer service.