# GPS/BDS Medium/Long-Range RTK Constrained with Topospheric Delay Parameters from NWP Model
## 3 Results
### Gps/BDS RTK Results
Figures 7 and 8 show the time needed to fix the ambiguities using the data processing algorithms mentioned above. Table 3 presents the mean times for AR and the improvement of NWP-constrained RTK, with respect to the standard RTK for both GPS/BDS and GPS alone solutions. For the baseline of 80 km, it is noted that about 40% of ambiguities are fixed in 20 min with standard GPS RTK, while over 77% of initialization can be achieved in 20 min with standard GPS/BDS RTK. The mean time needed is reduced by 31.0% when BDS is involved. GPS RTK constrained with NWP ZTD only need a mean time of 13.3 min for initialization and this can be improved by 41.2%, compared with the standard GPS RTK. Over 90% of ambiguities can be fixed in 15 min by using the process scheme of GPS/BDS RTK constrained with NWP ZTD. The mean time needed (8.8 min) is also improved by 43.6% comparing with the standard GPS/BDS RTK. For the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **C01** & **C02** & **C03** & **C04** & **C05** \\ \hline MP1 & 0.200 & 0.210 & 0.231 & 0.277 & 0.263 \\ \hline MP2 & 0.223 & 0.232 & 0.244 & 0.309 & 0.301 \\ \hline  & C06 & C07 & C08 & C09 & C10 \\ \hline MP1 & 0.433 & 0.411 & 0.306 & 0.316 & 0.278 \\ \hline MP2 & 0.381 & 0.392 & 0.371 & 0.382 &baseline of 260 km, the initialization required time is about twice as much as that of the baseline of 80 km. The mean time of 49.7 min is needed for obtaining the fixed solution with standard GPS RTK. In comparison, it takes about 20 min (mean time) for the AR with the GPS RTK constrained with NWP ZTD, shortening the solution initialization time by 58.8%. Similarly, a significant reduction of 62.7% is revealed by the GPS/BDS RTK constrained with NWP ZTD compared with the standard GPS/BDS RTK. The mean time needed is only 12.9 min. In addition, an improvement 30% or more can be found in the initialization time when BDS is involved in RTK for both the standard and NWP-constrained mode solutions. As a result, firstly, the initialization speed can be remarkably improved with the GPS/BDS solutions, compared with that of the GPS RTK for both medium- and long-range baselines. Secondly, the NWP-constrained RTK reveals significant contribution to improving the initialization speed of both GPS and GPS/BDS solutions. Another important index to measure the performance of the RTK is the positioning precision. Figures 9 and 10 illustrate the positioning error compared to the precise position. Since the experimental stations are continuously operating reference stations, the precise position of them are known. Table 4 shows the positioning precision (the standard deviation of the positioning error) of the baseline of 80 and 260 km in terms of the North, East and Up direction. Since the positioning precision of GPS/BDS RTK constrained with NWP is very similar to that of the other three RTK schemes mentioned above after the ambiguities are fixed successfully, we only display of the results of the NWP-constrained GPS/BDS RTK. From these figures and table, we can see the positioning precision is better than 3 cm in the horizontal direction and better than 5 cm in the vertical direction, which satisfies the requirement of the precise positioning service. The positioning error of the medium-range baseline (80 km) in the North and East direction floats between \(-\)0.02 m and +0.02 m, which increases to \(\pm\)0.04 m for the long-range baseline (260 km)