# GPS/BDS Medium/Long-Range RTK Constrained with Topospheric Delay Parameters from NWP Model
## 3 Results
### Gps/BDS RTK Results  
To investigate the performance of the GPS/BDS RTK constrained with the ZTD derived from the medium-range NWP model, 10 days of GPS/BDS observations from three stations located in the medium-range NWP model covered area were collected. The observation interval was 1 s. The Trimble NetR9 receiver and TRM59800.00 antenna was used on these stations. Dual-frequency code and carrier phase signals of GPS (L1, L2) and BDS (B1, B2) were used in this experiment. In this experimental period, two baselines between the stations were studied and the lengths of the baselines were about 80 and 260 km, respectively. GPS/BDS observation was processed every minute using four schemes following the data processing algorithms presented in Section 2 until the corresponding ambiguity validation conditions were satisfied. The four schemes were the standard GPS RTK, standard GPS/BDS RTK, GPS RTK constrained with NWP ZTD and GPS/BDS RTK constrained with NWP ZTD. In the data processing, we mitigated the ionospheric delay using the medium/long-range baselines ionospheric \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Station** & **BTLU** & **BFYH** & **BTUZ** & **BXTC** & **SDHM** & **ZJHZ** & **SDJM** & **SHBS** \\ \hline
**Mean (mm)** & \(-4.10\) & \(-0.47\) & \(-5.34\) & \(3.17\) & \(5.60\) & \(-3.65\) & \(0.45\) & \(-5.50\) \\ \hline
**RMS (mm)** & 24.02 & 24.08 & 24.47 & 25.08 & 27.63 & 28.10 & 28.22 & 32.62 \\ \hline
**CC** & 0.978 & 0.976 & 0.978 & 0.977 & 0.979 & 0.980 & 0.976 & 0.970 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean residual, RMS and the correlation coefficients (CC) of NWP ZTD. Figure 5: Time series of NWP ZTD (blue line) and GAMIT ZTD (red line) at station SHBS. Figure 6: Tropospheric delay residuals of the experimental stations. delay estimation method we developed [11]. The popular R-ratio [38] was used as the validation method and a threshold value was set to 2.5. For composing the weight matrix, the sigma of carrier phase noise was set to 3 mm for both GPS and BDS. Before setting the sigma of the code measurements of BDS and GPS, we assess the multipath and code noise level using the multipath combination (MPC). The combination is constructed using a single-frequency code measurement and dual-frequency phase measurements, which can be expressed as:  
\[\text{MP1}=P_{1}-\frac{f_{1}^{2}+f_{2}^{2}}{f_{1}^{2}-f_{2}^{2}}\big{[} \big{|}\!\big{|}\!\big{|}_{1}+\frac{2f_{2}^{2}}{f_{1}^{2}-f_{2}^{2}}\big{|}\! \big{|}\!\big{|}_{2} \tag{7}\]  
\[\text{MP2}=P_{2}-\frac{2f_{1}^{2}}{f_{1}^{2}-f_{2}^{2}}\big{[}\big{|}\!\big{|} _{1}+\frac{f_{1}^{2}+f_{2}^{2}}{f_{1}^{2}-f_{2}^{2}}\big{|}\!\big{|}\!\big{|}_{ 2} \tag{8}\]  
where \(P_{i}\) and \(\big{|}\!\big{|}\!\big{|}\!\big{|}\!\big{|}_{1}\) (\(i~{}=~{}1,2\)) are the GNSS code and carrier phase measurements, respectively; and \(f_{i}\) denotes the frequency for carrier phase. One day of GPS/BDS dual-frequency observations from one station located in the medium-range NWP model covered area were collected for this experiment. Table 2 shows the standard deviations of BDS MPCs. The standard deviations vary in a range of 0.200-0.577 m. The average of all standard deviations for B1 MPCs is 0.318 m, which is larger than that of GPS L1 codes (0.243 m). While for B2 MPCs, the average of standard deviations is 0.385 m, which is also larger than that of GPS L2 codes (0.297 m). Experimental results show that the multipath and noise level of BDS code measurements is higher than that of GPS collected using the same receiver. However, it should be mentioned that it is not completely fair to compare MPCs of BDS and GPS satellites as the constellations of two GNSS system are completely different. As the multipath and code noise level of BDS pseudo-range measurements was larger than that of GPS, the sigma of pseudo-range noise was set to 0.5 m for BDS, instead of 0.3 m for GPS [11]. Time required for AR or initialization is an important index to measure the performance of the RTK and the benefit of the NWP ZTD.