## 3 Results
### Performance of the Five-System PPP Time Transfer under Open Sky
Figure 10 displays the average MDEV values over a week for 12 time links at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s. It is seen that the difference in the MDEV statistics among different time links is most obvious for the GLONASS-only case, followed by the Galileo-only and BDS-only cases, which may be attributed to the distinct number of visible satellites for the stations located in different latitude and longitude regions. In contrast, the MDEV values of the five-system combination case at an average time of \(10^{2}\) and \(10^{3}\) s seem to be at the same level for different time links. Except for GLONASS-only PPP time transfer, the average MDEV values for most of the time links are on the order of \(10^{-13}\) when the average time is \(10^{2}\) s; the corresponding values are on the order of \(10^{-14}\) when the average time increases to \(10^{3}\) s; and the corresponding values are on the order of \(10^{-14}\) to \(10^{-15}\) when the average time is as long as \(10^{4}\) s. As for the GLONASS-only case, the average MDEV values are usually on the order of \(10^{-12}\) to \(10^{-13}\), \(10^{-13}\) to \(10^{-14}\), and \(10^{-13}\) to \(10^{-14}\) when the average time is \(10^{2}\), \(10^{3}\), and \(10^{4}\) s, respectively. Figure 7: MDEV values of the time link BRUX-MGUE at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s on DOY 248 to 254, 2021. Figure 8: MDEV values of the time link BRUX-PTBB at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s on DOY, 248 to 254, 2021. Figure 9: MDEV values of the time link BRUX-SPT0 at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s on DOY, 248 to 254, 2021. Figure 10: Average MDEV values over a week for 12 time links at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s. The MDEV results for the time links with CEBR, CRO1, KOKB, MATE, MGUE and TID1 stations are provided in (**a**), and those for the time links with PTBB, ROAG, SPT0, USN7, WTZR and ZIM3 stations are provided in (**b**). Figure 11 further shows the average MDEV results over a week and all 12 time links at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s. The frequency stability of the five-system integrated PPP time transfer can be \(1.24\times 10^{-13}\), \(2.28\times 10^{-14}\), and \(8.74\times 10^{-15}\) at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s, respectively. Compared with the GPS-only case, GLONASS-only case, Galileo-only case, and BDS-only case, the average improvement rates of the five-system combination case on the frequency stability are \(18.4\%\), \(82.2\%\), \(34.7\%\), and \(54.1\%\) when the average time is \(10^{2}\) s; the corresponding improvement rates are \(19.4\%\), \(94.0\%\), \(62.6\%\), and \(71.6\%\) when the average time is \(10^{3}\) s; and the average improvement rates are \(21.3\%\), \(85.9\%\), \(23.3\%\), and \(59.7\%\) when the average time is \(10^{4}\) s. It is concluded that even under an open-sky environment, the five-system combination case can significantly improve the time transfer performance (in terms of the frequency stability as well as the time transfer accuracy) compared with the single-GNSS cases.