## 5 Conclusions
The single-day prediction residuals of daily ISBs (within the same group) for the stations with various receiver types are comparable to each other. The single-day prediction accuracy of daily ISBs for GLONASS, Galileo, BDS-2, and BDS-3 with respect to GPS can be 1.055, 0.640, 1.242, and 0.849 ns, respectively. The prediction accuracy of daily ISBs degrades with the increasing time span of prediction and a prediction accuracy of 1.767, 1.954, 2.982, and 2.580 ns can still be achieved for the four groups of daily ISBs when the time span of prediction is increased to seven days, respectively. The correction rates of predicted daily ISBs between Galileo and GPS are only 78.0% even when the time span of prediction is set to a day and decrease to 32.8% with a time span of prediction of a week, whereas the corresponding correction rates for the other three groups of daily ISBs keep over 93.0% with the increasing time span of ISB prediction. The accuracy improvements that benefit from the a priori ISB constraints are marginal (less than 10%) when the cutoff elevations are lower than or equal to 30\({}^{\circ}\). The accuracy improvements coming with the a priori ISB constraints become significant when the elevation masks are further increased to 40\({}^{\circ}\) and 50\({}^{\circ}\). The accuracy improvements after introducing the a priori ISB constraints can be 22%, 27%, 24%, and 24% and 25%, 26%, 23%, and 23% at an elevation mask of 40\({}^{\circ}\) and 50\({}^{\circ}\) with a time span of ISB prediction of a day in the east, north, up, and 3D directions, respectively. Under a cutoff elevation of 40\({}^{\circ}\) and 50\({}^{\circ}\), the improvement rates decrease with the increasing time span of ISB prediction, and the corresponding accuracy improvements attributed to the a priori ISB constraints with a time span of ISB prediction of seven days can still be 8%, 20%, 12%, and 13% and 12%, 17%, 6%, and 7% in the four directions, respectively. The availability starts to decrease at an elevation mask of 40\({}^{\circ}\) and is reduced to only 64.0% at an elevation mask of 50\({}^{\circ}\) for the four-system SPP ignoring a priori ISB constraints (traditional four-system SPP). By contrast, the availability still keeps 100.0% when the cutoff elevation is increased to 40\({}^{\circ}\) and can be up to approximately 90.0% at an elevation mask of 50\({}^{\circ}\) for the four-system SPP considering a priori ISB constraints. In addition, we also characterize the ISB estimates derived from the low-cost u-blox M8T receiver and two Xiaomi Mi8 smartphones and also investigate the performance enhancement of a priori ISB constraints for the multisystem SPP solutions. Although both the short-term stability of epochwise ISBs and the single-day prediction accuracy of daily ISBs with these devices are worse than those with the geodetic-type receivers, the position accuracy as well as the availability of the multisystem integrated SPP can be improved after introducing the a priori ISB constraints, especially for the SPP results with the smartphones. Usually, the receiver hardware delay is considered to change with the temperatures. However, the epochwise ISBs obtained with the u-blox M8T receiver and the Xiaomi Mi8 smartphone do not show obvious fluctuations in the first half an hour (with increased temperatures), which may be attributed to the worse ISB estimates with the low-cost SPP receivers. Conceptualization, L.P. and W.Y. ; methodology, L.P.; software, L.P.; validation, L.P.; formal analysis, L.P.; investigation, L.P.; resources, L.P.; data curation, L.P.; writing--original draft preparation, L.P.; writing--review and editing, Z.Z., W.Y. and W.D. ; visualization, L.P.; supervision,L.P. ; project administration, L.P.; funding acquisition, L.P. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (Grant No. 41904030), Natural Science Foundation of Hunan Province, China (Grant No.