## 3 Results
### Performance of Four-System Integrated SPP with a Priori ISB Constraints  
In this section, the performance of four-system integrated SPP with a priori ISB constraints is rigorously evaluated. For comparison, eight different situations are employed for the four-system SPP processing. In the first case, the a priori ISB constraint is not considered (i.e., traditional four-system SPP processing). For the following seven cases, the a priori ISBs are obtained by prediction with the daily ISB estimates of the last 1-7 days. In addition, as the developed SPP model is mainly for the data processing under the constrained visibility environments, the elevation mask angle is set from 20\({}^{\circ}\) to 50\({}^{\circ}\) in steps of 10\({}^{\circ}\) to simply simulate the real harsh environments. For completeness, the four-system SPP processing at a cutoff elevation of 10\({}^{\circ}\) is also conducted. The data sets collected at all the 120 stations (except for the two stations encountering a replacement of receiver types) \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Time Span of** \\ **Prediction** \\ \end{tabular} } & \multicolumn{4}{c}{**Accuracy of Predicted ISBs (ns)**} \\ \cline{2-5}  & **GPS-GLONASS** & **GPS-Galileo** & **GPS-BDS-2** & **GPS-BDS-3** \\ \hline
2 days & 1.377 & 1.054 & 1.856 & 1.444 \\
3 days & 1.691 & 1.368 & 2.297 & 1.878 \\
4 days & 1.759 & 1.605 & 2.522 & 2.156 \\
5 days & 1.859 & 1.758 & 2.667 & 2.322 \\
6 days & 1.819 & 1.867 & 2.831 & 2.471 \\
7 days & 1.767 & 1.954 & 2.982 & 2.580 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction accuracy of daily ISBs with a time span of prediction of 2–7 days. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Time Span of** \\ **Prediction** \\ \end{tabular} } & \multicolumn{4}{c}{**Correction Rate of Predicted ISBs**} \\ \cline{2-5}  & **GPS-GLONASS** & **GPS-Galileo** & **GPS-BDS-2** & **GPS-BDS-3** \\ \hline
1 day & 96.6\% & 78.0\% & 97.1\% & 97.9\% \\
2 days & 95.6\% & 63.8\% & 95.6\% & 96.4\% \\
3 days & 94.6\% & 53.0\% & 94.6\% & 95.3\% \\
4 days & 94.4\% & 44.8\% & 94.0\% & 94.6\% \\
5 days & 94.1\% & 39.5\% & 93.7\% & 94.2\% \\
6 days & 94.2\% & 35.8\% & 93.3\% & 93.8\% \\
7 days & 94.3\% & 32.8\% & 93.0\% & 93.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correction rate of predicted daily ISBs with a time span of prediction from a day to seven days. spanning a week from DOY 48 to 54 of 2020 are used for the performance analysis of the four-system SPP. Figure 11 illustrates the epochwise positioning errors of four-system integrated SPP with and without a priori ISB constraints under a cutoff elevation of 50\({}^{\circ}\) at station ABMF on DOY 48 of 2020. For clarity, only the results of the two cases with a time span of ISB prediction of a day and seven days for the four-system SPP considering a priori ISB constraints are presented in Figure 11. As we can see, the SPP solutions without a priori ISB constraints at station ABMF are unavailable for a lot of epochs under extremely harsh environments, even though the observations from GPS, GLONASS, Galileo, BDS-2, and BDS-3 are jointly used. In addition, the epochwise position errors show many spikes, and can be over 20, 20, and 30 m in the east, north, and up directions, respectively. By contrast, after taking the a priori ISB constraints into consideration, both the availability and the positioning accuracy of four-system SPP solutions are significantly improved. About 80% of the position solutions become available with an epochwise positioning error usually varying within 10, 10, and 30 m in the three directions, respectively, even when the time span of ISB prediction is set to as long as a week. For further analysis, Table 4 lists the position accuracy in (m) of four-system integrated SPP with and without a priori ISB constraints under different elevation masks.