# GPS + BDS Network Real-Time Differential Positioning Using a Position Domain Estimation Method
## 3 Results
### Static Experiment
#### 3.1.1 Data Set I
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**GPS**} & \multicolumn{3}{c}{**GPS + BDS**} \\ \cline{3-8}  & & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline \multirow{3}{*}{Inside} & RD (m) & 0.748 & 0.458 & 1.278 & 0.275 & 0.259 & 0.619 \\  & PD (m) & 0.401 & 0.297 & 0.721 & 0.193 & 0.223 & 0.432 \\  & Improvement (\%) & 46.3 & 35.1 & 43.6 & 29.6 & 13.7 & 30.2 \\  & RD (m) & 0.714 & 0.473 & 1.228 & 0.264 & 0.243 & 0.867 \\ \multirow{3}{*}{Outside} & PD (m) & 0.395 & 0.281 & 0.801 & 0.187 & 0.153 & 0.537 \\  & Improvement (\%) & 44.7 & 40.6 & 34.8 & 29.0 & 37.0 & 38.1 \\ \multirow{3}{*}{All} & RD (m) & 0.731 & 0.466 & 1.253 & 0.269 & 0.251 & 0.753 \\  & PD (m) & 0.398 & 0.289 & 0.762 & 0.190 & 0.191 & 0.487 \\ \cline{1-1}  & Improvement (\%) & 45.5 & 37.9 & 39.2 & 29.3 & 23.8 & 35.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RMS errors of the network real-time differential positioning for the inside, the outside and all user stations. Figure 4: Root mean square (RMS) errors of the network real-time differential positioning for each user station in the north (N, **top**), east (E, **middle**) and up (U, **bottom**) components, respectively. Left panels: GPS-only; right panels: GPS + BDS. The percentages on each bar are the improvements of PD over RD. solution. In particular, the improvements of RMS errors when replacing RD with PD are 13.7%-38.1% in GPS + BDS solution, while the corresponding improvements in GPS-only solution increase. It is also indicated that PD is less affected by the satellite constellation. The RMS errors for the inside and outside user stations have little difference. Since the outside user stations HUAD and HMSC are very close to the reference stations SSGT and HELI, respectively, their correction accuracy is comparable to that of the inside user stations. The STD values of the network real-time differential positioning for each user station are shown in Figure 5. An obvious decrease of STD values occurred when replacing RD with PD. The maximum improvement of PD with respect to RD can reach up to 63.3%. Similar to Figure 4, for both PD and RD, remarkable improvements can also be found when using GPS + BDS solution instead of GPS-only solution. The STD values of GPS + BDS solution are smaller than 0.3 m, 0.3 m and 0.9 m in the N, E and U components, respectively. Table 2 gives the STD values for the inside, the outside and all user stations. The STD values of PD are much smaller than those of RD. For all user stations, the improvements are about 37.7%, 30.9% and 40.9% in the N, E and U components, respectively. For both PD and RD, a significant decrease can be found when replacing GPS-only solution with GPS + BDS solution. The STD values of GPS + BDS solution are 0.265 m, 0.242 m and 0.745 m for RD in the N, E and U components, and 0.188 m, 0.187 m and 0.437 m for PD. Improvements of GPS + BDS solution with respect to GPS-only solution are about 20%-50% for PD, and about 30%-66% for RD. Specifically, the improvements of PD over RD are 39.1%-48.6% in GPS-only solution, which are larger than those in GPS + BDS solution. This is consistent with the results in Table 1, and further shows that PD is less affected by the satellite constellation. In addition, the STD values for the outside user stations are similar with those for the inside ones, which also attributes to the close position relation between the outside user station and network. The percentages of the position errors falling within predefined thresholds are given in Table 3 according to the types of user stations. From the table, one can see that the percentages of the position errors of PD are larger than those of RD in almost all thresholds. Figure 5: Standard deviation (STD) values of the network real-time differential positioning for each user station in the N (top), E (middle) and U (bottom) components, respectively. Left panels: GPS-only; right panels: GPS + BDS. The percentages on each bar are the improvements of PD over RD.