# GPS + BDS Network Real-Time Differential Positioning Using a Position Domain Estimation Method
## 3 Results
### Dynamic Experiment  
A dynamic experiment was conducted in the Jiangsu Province of China. The data were collected from 2:53:47 to 3:59:59 (UTC) on day of year 112, 2019 (22 April 2019). The sampling interval was set as 1 s, and the cut-off angle was set at 10\({}^{\circ}\). The locations of three reference stations Ref1, Ref2 and Ref3 are shown in Figure 9, as well as the trajectory of the dynamic user station. The GAMIT/GLOBK 10.6 software [39; 40] was used to obtain precise coordinates for the three reference stations. The centimeter-level accuracy reference coordinates of the dynamic user station were computed by the GPS real-time kinematic positioning (RTK) using forward and backward filters. It should be pointed out that only the GPS RTK solutions with fixed integer ambiguities were adopted as the reference true values. The network real-time differential positioning results were used to evaluate the performance of PD and RD. The performances of GPS + BDS and GPS-only solutions were compared as well. The same statistical analysis methods used in the static experiment were applied. \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}{*}{RMS} & RD (m) & 0.340 & 0.289 & 0.619 & 0.219 & 0.177 & 0.356 \\  & PD (m) & 0.293 & 0.205 & 0.481 & 0.217 & 0.159 & 0.330 \\  & Improvement (\%) & 13.9 & 28.9 & 22.3 & 0.7 & 10.1 & 7.1 \\ \hline \multirow{3}{*}{STD} & RD (m) & 0.316 & 0.283 & 0.617 & 0.178 & 0.167 & 0.346 \\  & PD (m) & 0.251 & 0.206 & 0.479 & 0.173 & 0.155 & 0.319 \\ \cline{1-1}  & Improvement (\%) & 20.6 & 27.3 & 22.2 & 2.9 & 6.9 & 7.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMS errors and STD values of the network real-time differential positioning for all user stations. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**N**} & \multicolumn{3}{c}{**E**} & \multicolumn{3}{c}{**U**} \\ \cline{3-8}  & & \(\pm\)**0.25 m** & \(\pm\)**0.5 m** & \(\pm\)**1 m** & \(\pm\)**0.25 m** & \(\pm\)**0.5 m** & \(\pm\)**1 m** & \(\pm\)**0.5 m** & \(\pm\)**1 m** \\ \hline \multirow{3}{*}{GPS} & RD & 72.9 & 93.3 & 99.1 & 81.0 & 96.4 & 99.2 & 75.1 & 95.0 \\  & PD & 73.7 & 93.4 & 99.2 & 82.8 & 97.7 & 99.7 & 78.9 & 96.1 \\  & Improvement & 1.0 & 0.1 & 0.1 & 2.3 & 1.4 & 0.6 & 5.0 & 1.2 \\ \hline \multirow{3}{*}{GPS + BDS} & RD & 79.0 & 95.7 & 99.8 & 87.2 & 99.2 & 99.8 & 86.7 & 98.7 \\  & PD & 81.0 & 95.7 & 99.9 & 90.4 & 99.5 & 99.8 & 89.2 & 99.3 \\ \cline{1-1}  & Improvement & 2.5 & 0.0 & 0.1 & 3.7 & 0.3 & 0.0 & 2.9 & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percentages of the position errors of the network real-time differential positioning in predefined thresholds for all user stations. (Unit: %)Figure 10 shows the position errors of the network real-time differential positioning and the number of observed satellites for the dynamic user station. The position errors of PD fluctuate less than those of RD. Further, for both PD and RD, the position errors of GPS + BDS solution are smaller than those of GPS-only solution. Most of the position errors of GPS + BDS solution are within 0.5 m in the N and E components, and 1.5 m in the U component. The breaks in this figure are due to the discontinuous reference coordinates. In this experiment, only the GPS RTK solutions with fixed integer ambiguities participate in the results analysis, and the epochs with unfixed GPS RTK solutions are excluded, which leads to the interruption of the position errors. The statistic results of the network real-time differential positioning for the dynamic user are given in Table 6. Significant improvements can be seen when using PD instead of RD. The overall improvements are about 14.4%, 18.5% and 13.8% in the N, E and U components, respectively. For both PD and RD, the RMS errors and STD values of GPS + BDS solution are smaller than those of GPS-only solution.