## 3 Results
### Prediction of Daily ISBs  
As the daily ISBs (i.e., the average value of the epochwise ISB estimates over a day) have a good long-term stability (see Figures 7 and 8), they can be used as a priori constraints by prediction to improve the performance of multisystem combined SPP (real-time data processing). The prediction performance of daily ISBs is assessed in this section. In view that the epochwise ISB estimates are susceptible to various errors and show stable characteristics over a day (see Figure 2), the daily ISBs rather than the epochwise ISBs are employed. Figure 9 illustrates the prediction residuals of daily ISBs for each station on DOY 41-70 of 2020 when the time span of prediction is set to a day. The two stations encountering the receiver replacement are not included in the analysis here. Different receiver types are identified by different colors and marks. The single-day prediction residuals of daily ISBs between Galileo and GPS and between BDS-3 and GPS usually vary within 2 ns, while the corresponding varying range is expanded to 3 and 4 ns for those between GLONASS and GPS and between BDS-2 and GPS, respectively. In addition, the single-day prediction residuals of daily ISBs within the same group for the stations with various receiver types are comparable to each other, which is further validated by the similar root mean square (RMS) statistics of the corresponding prediction residuals for each receiver type (see Figure 10). The RMS statistics of single-day prediction residuals of daily ISBs over all the employed stations and days are provided in each panel in Figure 9. The single-day prediction accuracy of daily ISBs between GLONASS and GPS, between Galileo and GPS, between BDS-2 and GPS, and between BDS-3 and GPS can be 1.055, 0.640, 1.242, and 0.849 ns, respectively.  
Figure 8: STD statistics of daily ISBs over a month for each station (characterized by the receiver types).  
For further analysis, Table 2 provides the prediction accuracy of daily ISBs based on the data sets of all the employed stations and days when the time span of prediction is lengthened to 2-7 days. As we can see, the prediction accuracy of daily ISBs degrades with the increasing time span of prediction, especially for those between BDS-2 and GPS and GPS-Gallieo.  
Figure 10: RMS statistics of prediction residuals of daily ISBs with a time span of prediction of a day for each receiver type.  
Figure 9: Prediction residuals of daily ISBs with a time span of prediction of a day for each station (characterized by the receiver types).  
between BDS-3 and GPS. When the time span of prediction is set to a week, a prediction accuracy of 1.767, 1.954, 2.982, and 2.580 ns can still be achieved for the daily ISBs between GLONASS and GPS, between Galileo and GPS, between BDS-2 and GPS, and between BDS-3 and GPS, respectively.  
As the numerical values differ among the four groups of daily ISBs (see Figure 7), the correction rate is further taken as an index to evaluate the prediction performance of daily ISBs. The differences between the RMS statistics of ISB estimate series and of ISB prediction residual series are first obtained, and the correction rates are then determined as the ratio between the differences and the RMS statistics of ISB estimate series. The derived results of correction rates are provided in Table 3. Similar to the prediction accuracy of daily ISBs, the correction rates decrease with the increment of the time span of prediction. Despite this, the correction rates of predicted daily ISBs are still larger than 94.0% for those between GLONASS and GPS and larger than 93.0% for those between BDS-2 and GPS and between BDS-3 and GPS, respectively, when the time span of prediction is as long as seven days. Due to the small numerical values of daily ISBs between Galileo and GPS (see Figure 7), the correction rates 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.