# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
## 3 Experimental Results Analysis
### Undifferenced Error Correction Results  
Next, the double-difference integer ambiguities were converted into undifferenced integer ambiguities, and then the undifferenced integer ambiguities were substituted into the observation equation of the reference station in order to obtain the comprehensive undifferenced error correction values corresponding to each reference station. The comprehensive undifferenced error corrections of C25, C39, and G24 satellites in the first frequency continuous visible period of reference stations \(A\), \(B\), \(C\), and \(D\) were calculated, as shown in Figure 10. The results indicated that the comprehensive undifferenced error correction values of each satellite changed linearly, but the changing trends of the same satellite on the four reference stations were similar.  
For a long-range network RTK, the weakening of atmospheric delay error correlation could reduce the accuracy of positioning results. Therefore, in order to ensure the reliability of the undifferenced corrections obtained via the inverse distance weighted interpolation algorithm, the comprehensive undifferenced error corrections were classified. The comprehensive undifferenced error corrections of two frequencies (B1/B2, B1/B3, or L1/L2) of each satellite were selected. The undifferenced ionospheric delay was calculated using the GF model, and the non-dispersion error was calculated using the IF model. Figures 11-13 show the error calculation results of C21, C25 (MEO satellite), C39, and C40 (IGSO satellite) in the BDS-3, and G10 and G24 (MEO satellite) in the GPS at four reference stations. Because different types of satellites were in different orbits, the satellite's visible time also differed among the orbits. As shown in Figures 11-13, the undifferenced ionospheric delay error of each satellite changed slightly between epochs; the variation trends of the undifferenced ionospheric delay error of the four reference stations for the same satellite were basically the same, and they were proportional to the reciprocal of the height-angle-sine function. The non-dispersion error contained most of the errors in the comprehensive undifferenced error correction process, so its changing trend coincided with that of the comprehensive undifferenced error correction performance. The starting time of station \(D\) was different  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & **Reference Station** & **Number of** & **Fixed** & **Unfixed Number** & **Fixed Success** \\  & **Network** & **Observations** & **Number** & **Rate (\%)** \\ \hline \multirow{3}{*}{G06} & 1 & 18,413 & 18,234 & 179 & 99.02 \\  & 2 & 16,675 & 16,299 & 376 & 97.74 \\  & 1 & 15,248 & 15,186 & 62 & 99.59 \\  & 2 & 14,808 & 14,702 & 106 & 99.28 \\  & 1 & 20,926 & 20,877 & 49 & 99.76 \\  & 2 & 19,084 & 18,551 & 533 & 97.20 \\  & 1 & 14,860 & 14,060 & 254 & 98.29 \\  & 2 & 14,860 & 14,534 & 326 & 97.80 \\  & 1 & 24,459 & 24,155 & 304 & 98.75 \\  & 2 & 24,459 & 23,885 & 574 & 97.65 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistical results of the GPS AR success rate.  
Figure 10: (**a**) Comprehensive undifferenced error correction values of the C25 satellite; (**b**) comprehensive undifferenced error correction values of the C39 satellite; and (**c**) comprehensive undifferenced error correction values of the G24 satellite.