# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
## 3 Experimental Results Analysis  
In this study, two sets of long baseline observation data were solved using the self-made long-range URTK positioning algorithm program. The experiment included BDS-3 single-system B1C/B2a and B1I/B3I dual-frequency signals, B1C/B2a/B3I and B1I/B2a/B3I triple-frequency signals, B1I/B1C/B2a/B3I four-frequency signals, and GPS single-system L1/L2 dual-frequency six-combination mode signals. The experiment was conducted using the CORS network observation data of a province collected on 20 August 2022. The sampling interval was 1 s, the observation time was 24 h, and the satellite elevation angle was set to 15\({}^{\circ}\). The installation diagram of a data acquisition device in the CORS network is shown in Figure 3, where it can be seen that it is mainly composed of the GNSS receiver and GNSS antenna. The observation data related to four reference stations denoted as \(A\), \(B\), \(C\), and \(D\) and two rover stations denoted as \(U_{1}\) and \(U_{2}\). The distances between stations are given in Table 1, where it can be seen that the lengths of baselines \(A\)-\(B\), \(B\)-\(C\), \(C\)-\(A\), \(A\)-\(D\), and \(D\)-\(C\) were 108 km, 136 km, 151 km, 161 km, and 172 km, respectively, and the distance between the two rover stations was 85 km. In this study, the reference stations were divided into two groups: reference stations of network 1 (\(A\), \(B\), \(C\)) and reference stations of network 2 (\(A\), \(D\), \(C\)). The station azimuth distribution is presented in Figure 4. All experiments were conducted using the same data. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Baseline** & \(A\)**-\(B\)** & \(B\)**-\(C\)** & \(C\)**-\(A\)** & \(A\)**-\(D\)** & \(D\)**-\(C\)** & \(U_{1}\)**-\(U_{2}\)** \\ \hline Length (km) & 108 & 136 & 151 & 161 & 172 & 85 \\ \hline \end{tabular}
\end{table} 
Table 1: Baseline information. Figure 4: Distribution of stations. Figure 3: Data acquisition equipment. The two rover stations were located in the same region, and the satellite visibility at the two stations was similar. The satellite visibility of rover station \(U_{1}\) is presented in Figure 5. The number of B1I/B1C/B2a/B3I, B1C/B2a/B3I, B1I/B2a/B3I, and B1C/B2a observation data satellites of the BDS-3 was approximately eight; the number of B1I/B3I observation data satellites, nine, was the largest; and the number of GPS satellites was seven, which could meet the calculation requirements. The position dilution of precision (PDOP) of each frequency combination was calculated using the observation data and broadcast ephemeris of \(U_{1}\) and \(U_{2}\), as shown in Figure 6. The PDOP indicated the position accuracy, which specifically represents the spatial geometric strength of satellite distribution. The smaller the PDOP value was, the better the satellite distribution was. Generally, a PDOP value of less than three was an ideal state [33]. In Figure 6, it can be clearly seen that the PDOP values of B1I/B1C/B2a/B3I, B1C/B2a/B3I, and B1I/B2a/B3I were basically the same. Although the PDOP values of B1C/B2a, B1I/B3I, and GPS showed different trends, all PDOP values were lower than two. Thus, all combinations met the ideal state required for positioning. In order to compare the PDOP values of several combinations in more detail, the PDOP values were statistically analyzed, and the maximum, minimum, and average PDOP values of B1I/B1C/B2a/B3I, B1C/B2a, B1I/B3I, and GPS were calculated, as shown in Table 2. Also shown in Table 2, the maximum and minimum PDOP values of B1I/B1C/B2a/B3I and B1C/B2a were almost the same, and their average PDOP values differed slightly, which was consistent with the results presented in Figure 6. Although the trends of B1I/B3I and GPS were completely different from the former, the numerical difference was very small. The PDOP values of different combinations ranged from 0.77 to 1.96, with an average value of approximately 1.1.