## 3 Results
### ISB Estimates Derived from Smartphones
The accuracy improvement is the most obvious at an elevation mask of 50\({}^{\circ}\), which can be 42%, 45%, 7%, and 13% and 34%, 39%, 13%, and 16% for Xiaomi Mi8 (1) and Xiaomi Mi8 (2) in the east, north, up, and 3D directions, respectively. Figure 17: Epochwise positioning errors of four-system integrated SPP for two smartphones with and without a priori ISB constraints under a cutoff elevation of 40\({}^{\circ}\) on DOY 320 of 2020. Table 10 provides the availability, average satellite number, and average PDOP value of four-system integrated SPP for two smartphones with and without a priori ISB constraints under different elevation masks. Similar to the availability results with the geodetic receivers (see Table 6), the availability for the four-system integrated SPP with smartphones ignoring a priori ISBs also starts to slightly decrease at an elevation mask of 40\({}^{\circ}\). Under a cutoff elevation of 50\({}^{\circ}\), the corresponding availability declines to only 62.7% and 69.9% for Xiaomi Mi8 (1) and Xiaomi Mi8 (2), respectively. After introducing the a priori ISB constraints, the availability still keeps 100.0% at an elevation mask of 40\({}^{\circ}\) and is improved to 82.9% and 93.0% at an elevation mask of 50\({}^{\circ}\) for the two smartphones, respectively. In view that many unsolvable epochs become solvable after considering the a priori ISB constraints under a cutoff elevation of 50\({}^{\circ}\), the average satellite number is reduced from 8.7 and 9.5 to 8.2 and 8.8 for the two smartphones, respectively, while the corresponding average PDOP value is increased from 8.4 and 7.2 to 9.0 and 7.4, respectively. The average satellite number for the smartphone-based four-system integrated SPP is 20.0 and 22.4 for the two Xiaomi Mi8 smartphones at an elevation mask of 10\({}^{\circ}\), respectively, which is significantly less than that derived from the geodetic-type receivers with a statistic of 30.7 (see Table 6), indicating that the capability of tracking GNSS signals needs to be enhanced for the smartphones. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Devices**} & \multirow{2}{*}{**Strategy**} & \multirow{2}{*}{**Directions**} & \multicolumn{6}{c}{**Elevation Mask Angles**} \\ \cline{4-9}  & & & \(\mathbf{10}^{\circ}\) & \(\mathbf{20}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{40}^{\circ}\) & \(\mathbf{50}^{\circ}\) \\ \hline \multirow{6}{*}{Xiaomi} & Without & East (m) & 2.528 & 2.673 & 2.998 & 3.862 & 9.073 \\  & Without & North (m) & 2.632 & 2.879 & 3.236 & 3.883 & 8.850 \\  & A Priori & \begin{tabular}{c} UB (m) \\ 3D (m) \\ \end{tabular} & 6.044 & 8.064 & 10.264 & 12.650 & 25.571 \\  & \begin{tabular}{c} 3D (m) \\ \end{tabular} & 7.060 & 8.970 & 11.172 & 13.784 & 28.540 \\ \cline{2-9}  & With A & East (m) & 2.437 & 2.586 & 2.886 & 3.454 & 5.237 \\  & Priori & North (m) & 2.348 & 2.455 & 2.650 & 2.903 & 4.908 \\  & ISB (1 & Up (m) & 5.018 & 6.892 & 9.399 & 11.971 & 23.724 \\  & day) & \begin{tabular}{c} 3D (m) \\ \end{tabular} & 6.052 & 7.760 & 10.183 & 12.793 & 24.786 \\ \hline \multirow{6}{*}{Xiaomi} & Without & East (m) & 2.614 & 2.791 & 3.120 & 4.074 & 8.679 \\  & A Priori & North (m) & 2.790 & 2.961 & 3.104 & 3.799 & 6.423 \\  & ISB & Up (m) & 6.866 & 8.328 & 10.369 & 14.994 & 28.309 \\  & ISB & \
\begin{tabular}{c} 3D (m) \\ \end{tabular} & 7.859 & 9.269 & 11.264 & 15.995 & 30.299 \\ \cline{2-9}  & With A & East (m) & 2.477 & 2.645 & 2.855 & 3.579 & 5.763 \\ \cline{2-9}  & Priori & North (m) & 2.499 & 2.565 & 2.599 & 3.019 & 3.925 \\ \cline{2-9}  & ISB (1 & Up (m) & 5.858 & 7.237 & 9.403 & 13.721 & 24.587 \\ \cline{2-9}  & day) &
\begin{tabular}{c} 3D (m) \\ \end{tabular} & 6.834 & 8.121 & 10.165 & 14.498 & 25.556 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Positioning accuracy in (m) of four-system integrated SPP for two smartphones with and without a priori ISB constraints under different elevation masks. \begin{table}
\begin{tabular}{c} 3D (\%) \\ \end{tabular} & 13 & 12 & 10 & 9 & 16 \\ \hline \hline \end{tabular}
\end{table}