## 5 Conclusions  
Currently, the GNSS-based PPP technology plays an important role in remote time transfer, and the performance of time transfer is continuously improved with the GNSS modernization. This contribution rigorously assesses the time transfer performance of PPP technology with almost fully deployed GNSS and RNSS constellations, including BDS (BDS-3 and BDS-2), GPS, GLONASS, Galileo, and QZSS, in terms of the availability, the accuracy of time transfer, and the frequency stability of time transfer under open-sky environments and at locations with limited sky view. In addition, the a priori ISB constraints are used to further enhance the time transfer performance of the five-system integrated PPP. Theoretically, the average number of visible satellites on a global scale for the five-system combination is 38.9, with a minimum statistic of 29.7. In terms of TDOP value (average results over three stations), the numerical value for GPS, GLONASS, Galileo, and BDS single-GNSS cases is 0.90, 1.73, 1.38, and 0.87, respectively, while the average TDOP value for the five-system combination is 0.42, with a significant improvement. These results imply the reliable PPP time transfer of five-system combination. Under open-sky environment (at an elevation mask of 10\({}^{\circ}\)), the time transfer accuracy of GPS-only, GLONASS-only, Galileo-only, and BDS-only PPP can be 0.074, 0.359, 0.068, and 0.346 ns, respectively, while the corresponding accuracy of the five-system integrated PPP time transfer is improved to 0.061 ns. The frequency stability of five-system combination case 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. The average improvement rate of the five-system combination case over the four single-GNSS cases on the frequency stability is 18.4-82.2%, 19.4-94.0%, and 21.3-85.9% when the average time is 10\({}^{2}\), 10\({}^{3}\), and 10\({}^{4}\) s, respectively. For the PPP time transfer under environments with limited sky view, the service rate is 100.0%, 70.6%, 79.3%, and 91.3% for GPS-only, GLONASS-only, Galileo-only, and BDS-only PPP time transfer, respectively, when the cut-off elevation angle is set to 20\({}^{\circ}\). In this case, the time transfer accuracy degrades to 0.234, 0.849, 0.254, and 0.571 ns for the four single-GNSS cases, respectively. When the elevation mask angle is set to 30\({}^{\circ}\), for the four single-GNSS cases, the service rate is 88.9%, 30.0%, 37.4%, and 40.5%, respectively, and the time transfer accuracy is 0.368, 1.029, 0.318, and 0.725 ns, respectively. When the cut-off elevation angle further increases to 40\({}^{\circ}\), the service rate of each single-GNSS case is below 36%. Hence, the single-GNSS cases cannot provide stable and reliable time transfer service. In contrast, the service rate of the five-system integrated PPP time transfer always remains at 100.0% when the elevation mask increases from 20\({}^{\circ}\) to 40\({}^{\circ}\), and the corresponding time transfer accuracy can be 0.227, 0.264, and 0.376 ns, respectively. Under the cut-off elevation of 20\({}^{\circ}\), 30\({}^{\circ}\), and 40\({}^{\circ}\) for the five-system combination case, the frequency stability can be 1.17 \(\times\) 10\({}^{-13}\), 9.64 \(\times\) 10\({}^{-13}\), and 8.42 \(\times\) 10\({}^{-12}\) at an average time of 10\({}^{2}\) s, 2.19 \(\times\) 10\({}^{-14}\), 1.29 \(\times\) 10\({}^{-13}\), and 4.80 \(\times\) 10\({}^{-13}\) at an average time of 10\({}^{3}\) s, and 8.85 \(\times\) 10\({}^{-15}\), 2.40 \(\times\) 10\({}^{-14}\), and 3.46 \(\times\) 10\({}^{-14}\) at an average time of 10\({}^{4}\) s, respectively. We propose a method to mitigate the day-boundary jumps of ISB estimates by considering the difference of satellite clock datums between two adjacent days. This creates a precondition for the enhanced multi-system PPP time transfer with a priori ISB constraints.