# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
## 3 Experimental Results Analysis
### Reference Station AR  
The accurate resolution of the integer ambiguity of a reference station has been the main challenge in network RTK positioning, and it is crucial to realize the comprehensive undifferenced error correction via converting double-difference ambiguity into undifferenced ambiguity. Therefore, before the ambiguity was fixed, it was necessary to obtain an accurate ambiguity float solution in order to achieve rapid and accurate AR. Figures 7 and 8 show the convergence process of B1C/B2a and GPS double-difference ambiguity float solutions into the baseline solution of reference station network 1 (\(A,B,C\)), respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Combined Model** & **Rover Station** & **Maximum Value** & **Minimum Value** & **Mean Value** \\ \hline B1I/B1C/B2a/B3I & \(U_{1}\) & 1.616 & 0.794 & 1.093 \\  & \(U_{2}\) & 1.725 & 0.847 & 1.191 \\ B1C/B2a & \(U_{1}\) & 1.616 & 0.787 & 1.102 \\  & \(U_{2}\) & 1.761 & 0.847 & 1.209 \\  & \(U_{1}\) & 1.605 & 0.778 & 1.102 \\ B1I/B3I & \(U_{2}\) & 1.760 & 0.848 & 1.196 \\  & \(U_{1}\) & 1.658 & 0.783 & 1.030 \\ GPS & \(U_{2}\) & 1.958 & 0.841 & 1.158 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The PDOP statistical results. Figure 6: (**a**) The PDOP values of rover station \(U_{1}\) and (**b**) the PDOP values of rover station \(U_{2}\). Figure 7: The convergence process of B1C/B2a partial satellite float ambiguity. Due to the estimation of the residual atmospheric delay error, for the convergence process of the double-difference ambiguity float solution of each satellite, the ambiguity float solution was rapidly stabilized near the accurate integer ambiguity. In addition, the double-difference ambiguity of the three baselines of the same satellite basically satisfied the closed condition that the sum was zero. When the LAMBDA was used to search for fixed solutions, the calculated value was small, and the fixation success rate was higher. The ratio values of rover stations \(U_{1}\) and \(U_{2}\) are shown in Figure 9, where it can be seen that the ratio values of B1I/BIC/B2a/B3I, BIC/B2a/B3I, and B1I/B2a/B3I were high, and their trends were basically the same. The ratio value of B1I/B3I in dual-frequency mode was the smallest among all combinations, and the GPS performed better than B1C/B2a and B1I/B3I in most time periods. The ratio values in some of the epochs increased because of the emergence of new satellites or the disappearance of individual satellites. When the reference satellite changed, for the satellite whose ambiguity was fixed, the reference satellite transformation could be performed on the current arc observation value, continuing to use the fixed ambiguity, and the double-difference phase integer AR in subsequent epochs was obtained. The sum of double-difference ambiguity values between closed reference stations was zero, as one of the ambiguity-related constraints, which was added to the observation equation of the AR in order to improve the efficiency and success rate of the ambiguity search. Tables 3-6 show the success rate results for the AR of some of the satellites in the two reference station networks of B1I/B1C/B2a/B3I, B1C/B2a/B3I, B1C/B2a, and GPS. As shown in Tables 3-6, the AR success rates of the two reference station networks were high, and reference station network 1 performed better than reference station network 2. Figure 8: The convergence process of GPS partial satellite float ambiguity. Figure 9: (**a**) Ratio values of rover station \(U_{1}\) and (**b**) ratio values of rover station \(U_{2}\). The B1I/B1C/B2a/B3I and B1C/B2a/B3I had better AR rates than did the dual-frequency data, and they were almost all above 99%. The B1C/B2a had the same AR rates as the GPS, most of which were nearly 98%. Thus, compared to the dual-frequency data, the multi-frequency data had more advantages in their AR success rate. This could be due to the fact that multi-frequency data could provide more accurate ambiguity alternatives when the LAMBDA ambiguity search was fixed.