# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
## 3 Experimental Results Analysis
### Positioning Accuracy  
The undifferenced error correction values were substituted into the observation equation of the rover station, and the accurate position of the current station was obtained after fixing the integer ambiguity. Before analyzing the positioning results, the first convergence time in each combined positioning process is presented in Table 7, where it can be seen that the convergence times of each combination of rover stations \(U_{1}\) and \(U_{2}\) differed slightly. The convergence times of B1I/B1C/B2a/B3I, B1C/B2a/B3I, B1I/B2a/B3I, and B1C/B2a were 2-3 min, while the convergence times of B1I/B3I and GPS were obviously longer, about 6 min, which was twice the former value. Thus, the convergence time of multi-frequency data was shorter, the convergence time of B1C/B2a was better than that of B1I/B3I, and the convergence time of B1I/B3I was slightly worse than that of the GPS. The positioning result deviations of observation data corresponding to various combination modes of rover station \(U_{1}\) are provided in Figure 14. Considering the number of satellites, although B1I/B3I had the largest number of satellites, its positioning result was not the best. This is mainly due to the improved modulation of the new B1C/B2a frequency, which has better signal quality compared to B1I/B3I [26; 27]. However, the positioning results of B1I/B3I here are significantly better than other combinations in the U direction, which is related to the observation environment and the quality of the observation data. This is a special case and will not be discussed in this paper. The positioning result of multi-frequency data was obviously better than that of dual-frequency data, particularly in the elevation direction. The increase in frequency improved not only the success rate of the AR and convergence time, but also the stability of positioning results, and the deviations in the results of multi-frequency data were slighter. The positioning result deviations in the observation data of various combination modes of rover station \(U_{2}\) are shown in Figure 15. With the increase in the distance between reference stations, the accuracy of network RTK data decreased, but the overall trend was the same as that of rover station \(U_{1}\); the only difference was that the accuracy of B1I/B3I decreased significantly. With the increase in the distance between stations, the correlation of errors, such as atmospheric delay, was weakened. The satellite observation data of low elevation angle had a great influence on the AR, which affected the final positioning result. The RMS statistical results of the positioning deviations of each combination mode are presented in Table 8. Based on the time series and statistical results of the positioning error, the systematic errors of the BDS-3 and GPS observations were basically eliminated. In the dual-frequency combination, the positioning result of B1C/B2a was better than that of B1I/B3I in the horizontal direction, and the results in the elevation direction were different due to the influence of the distance between the reference stations; namely, B1C/B2a performed better than GPS, and B1I/B3I achieved a result equivalent to that of the GPS. Compared to the GPS, B1C/B2a showed average increases of 10.96%, 40.77%, and 13.73% in the E, N, and U directions, respectively, and performed the same as B1I/B2a/B3I. For the multi-frequency combination, the positioning results of B1C/B2a/B3I and B1I/B2a/B3I were better than those of the dual-frequency combination. Compared to BIC/B2a and B1I/B3I, B1C/B2a/B3I and B1I/B2a/B3I had average increases of 24.69%, 20.41%, and 12.58% in the E, N, and U directions, respectively. Further, compared to the GPS, B1C/B2a/B3I and B1I/B2a/B3I had average increases of 16.16%, 42.73%, and 28.44% in E, N, and U directions,