## 3 Results
### Enhanced Performance with a Priori ISB Constraints Considering Satellite Clock Datums  
As both BDS-2 and QZSS constellations mainly provide the services over Asia-Pacific areas, only the ISBs of the GLONASS, Galileo, and BDS-3 against GPS are employed to  
Figure 16: Epoch-wise average number of visible satellites and TDOP value over all the employed days and stations under the elevation cut-off angle of \(20^{\circ}\), \(30^{\circ}\), and \(40^{\circ}\).  
Figure 17: MDEV value of three time links derived from five-system integrated PPP under the elevation cut-off angle of \(20^{\circ}\), \(30^{\circ}\), and \(40^{\circ}\) on DOY 252, 2021.  
investigate the performance enhancement owing to a priori ISB constraints for time transfer. The elevation mask angle is set to \(10^{\circ}\). Figure 19 illustrates the time series of original ISB estimates at station BRUX on DOY 248 to 254, 2021. It is seen that the day-boundary jumps of original ISB estimates are dramatic. For comparison, the adjusted ISBs with the estimated differences of satellite clock datums between two adjacent days are also provided in Figure 19. After considering the effects of satellite clock datums, the consistency of ISBs is significantly improved. This creates a precondition for the multi-system integrated PPP time transfer with a priori ISB constraints.  
Figure 19: Time series of original ISB estimates and those considering satellite clock datums at station BRUX on DOY 248 to 254, 2021.  
Figure 18: Average MDEV values over a week and all the 12 time links at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s under environments with limited sky view.  
Figure 20 illustrates the difference of the time link BRUX-SPT0 between PPP estimates and IGS final products for the five-system combination case with and without ISB constraints on DOY 249, 2021. The MDEV values of the time link BRUX-SPT0 derived from five-system integrated PPP with and without ISB constraints on DOY 249, 2021, are provided in Figure 21. After taking the a priori ISB constraints into account, both the time transfer accuracy and frequency stability can be significantly improved.  
The a priori ISB estimates of the previous day are introduced into the data processing of the five-system integrated PPP time transfer of the next day. The time transfer results for three time links, BRUX-PTBB, BRUX-SPT0, and BRUX-USN7, on DOY 249 to 254, 2021, are obtained. Table 9 lists the average STD statistics of daily time link differences between PPP estimates and IGS final products over six days for the five-system combination case with and without ISB constraints for three time links. Table 10 presents the average MDEV values over six days for three time links derived from the five-system integrated PPP with and without ISB constraints at an average time of \(10^{2}\), \(10^{3}\), and \(10^{4}\) s. The time transfer  
Figure 21: MDEV values of the time link BRUX-SPT0 derived from the five-system integrated PPP with and without ISB constraints on DOY 249, 2021.  
Figure 20: Difference of the time link BRUX-SPT0 between PPP estimates and IGS final products for the five-system combination case with and without ISB constraints on DOY 249, 2021.  
accuracy can be improved by 51.6%, 37.9%, and 45.3% for the three time links, respectively, after considering ISB constraints. As for the frequency stability, it can be improved by 14.8%, 21.6%, and 15.0% at an average time of \(10^{2}\) s, 6.1%, 5.3%, and 7.6% at an average time of \(10^{3}\) s, and 29.6%, 20.0%, and 29.5% at an average time of \(10^{4}\) s, respectively, for the three time links for the five-system integrated PPP with ISB constraints over that without ISB constraints.