# GPS + BDS Network Real-Time Differential Positioning Using a Position Domain Estimation Method
## 4 Discussion  
GPS + BDS network real-time differential positioning using a position domain estimation method was studied in this paper. Beneficial results were obtained to show the superiority of GPS + BDS solution and PD. This contribution will enrich the application of network real-time differential positioning in the meter and sub-meter level's navigation. Furthermore, in the scenarios where gross errors often happen or ambiguity cannot be correctly fixed, the network real-time differential positioning can also provide a potential solution [42]. The results of the experiments show that the performance of network real-time differential positioning using PD is better than that using RD. PD performs consistently even when observed satellites change frequently, as it is immune to the smoothing window and only depends on the number of available satellites. Further, it is demonstrated that PD is less affected by the satellite constellation, since the improvements of PD over RD are more obvious in GPS-only solution, and the improvements of GPS + BDS solution with respect to GPS-only solution are greater in RD, as shown in Tables 1, 2, 4 and 6. To verify this feature more intuitively, Table 8 gives the increases of the RMS errors and STD values of PD and RD when using GPS-only solution instead of GPS + BDS solution. The degrees of accuracy and precision decreases of PD are significantly smaller than those of RD, which confirms the previous inference. The possible reasons why PD is less affected by the satellite constellation than RD would be: (1) the calculated position variation is accurate enough using GPS-only solution and will not be improved much more if replaced by GPS + BDS solution. Thus, the difference between GPS + BDS and GPS-only solutions when using PD is mainly attributed to the different number of available satellites; (2) the positioning performance of RD is mainly due to the number of carrier-phase-smoothed pseudorange observations. GPS + BDS solution can provide more carrier-phase-smoothed pseudorange observations, as well as more available satellites, and thus can achieve more significant improvement. \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{3-10}  & & **\(\pm\)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 + BDS} & RD & 89.2 & 98.7 & 100.0 & 88.0 & 97.8 & 99.8 & 77.4 & 91.7 \\  & PD & 93.7 & 99.1 & 100.0 & 94.2 & 99.1 & 99.8 & 77.6 & 95.6 \\  & Improvement & 5.0 & 0.4 & 0.0 & 7.1 & 1.3 & 0.0 & 0.3 & 4.3 \\ \hline \multirow{3}{*}{GPS + BDS} & RD & 95.2 & 97.4 & 99.9 & 91.6 & 99.2 & 100.0 & 78.6 & 95.5 \\  & PD & 96.2 & 97.8 & 99.9 & 96.3 & 99.4 & 100.0 & 79.8 & 95.7 \\ \cline{1-1}  & Improvement & 1.0 & 0.4 & 0.0 & 5.1 & 0.2 & 0.0 & 1.5 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Percentages of the position errors of the network real-time differential positioning in predefined thresholds for the dynamic user station. (Unit: %) \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**RMS**} & \multicolumn{3}{c}{**STD**} \\ \cline{3-8}  & & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline \multirow{3}{*}{Static} & RD & 113.3 & 74.2 & 70.2 & 126.1 & 80.5 & 71.7 \\  & PD & 71.9 & 40.0 & 51.1 & 76.4 & 41.5 & 59.0 \\ \hline \multirow{2}{*}{Dynamic} & RD & 23.2 & 16.0 & 35.5 & 28.2 & 23.6 & 47.1 \\  & PD & 10.8 & 2.6 & 11.1 & 14.4 & 14.9 & 18.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Increases of RMS errors and STD values of GPS-only solution compared with GPS + BDS solution. (Unit: %)By comparing the outside and inside user stations, one can see that the positioning accuracy variation does not only depend on whether the user is inside or outside the network, but also on the position relation between the user and network.