# Assessment of Quad-Frequency Long-Baseline Positioning with BeiDou-3 and Galileo Observations
## 3 Results
### Performance of EWL AR for BDS-3 and Galileo  
We analyzed the data of the entire observation span and plotted the single-epoch ambiguity decimal fraction of the \"true\" ambiguities and float ambiguities of the EWL of BDS-3 and Galileo satellite pairs. According to Table 5, the EWL signals of combination schemes No. 1, No. 2, and No. 4 are the same in BDS-3, of which the wavelength is 20.93 m. The EWL signal wavelength of combination scheme No. 3 is 3.26 m. In Galileo, the EWL signals of combination schemes No. 1 and No. 2 are the same, of which the wavelength is 9.77 m. The EWL signal wavelength of combination scheme No. 3 is 2.93 m, and that of combination scheme No. 4 is 4.19 m. The EWL ambiguity fractions of the BDS-3 and Galileo satellite pairs for all epochs are shown in Figures 2 and 3, and different colors represent different satellite pairs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Models** \\ \hline Satellites & BDS-3 and Galileo \\ Observations & Carrier phase and observations \\ Frequency selection & BDS-3: B1C/B11/B3I/B2a; Galileo \\  & E1/E5a/E5b/E6 \\ Cutoff elevation & 10\({}^{\circ}\) \\ Sampling rate & 10s \\  & Elevation-dependent weighting \\ Observation weighting & Relative weighting of code and phase \\  & observations: 1:100 \\ Satellite orbit & Broadcast ephemeris \\ Satellite clock & DD eliminated or weakening \\ Receiver clock & DD eliminated or weakening \\ Ionospheric delay & Estimated as parameters \\ Tropospheric delay & Corrected by GPT2w model [30] \\ Phase ambiguities & LAMBDA \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Long-baseline data process strategy settings. Figure 2: EWL ambiguity fractions of combination schemes No. 1, No. 2, No. 4 (top), and No. 3 (bottom) for BDS\(-\)3: (a) experiment 1; (b) experiment 2. Each color denotes one satellite pair. It can be seen that the ambiguity fractions of EWL have a strong correlation with their wavelengths: the longer the wavelength, the smaller ambiguity fractions. The ambiguity fractions of EWL between BDS-3 and Galileo satellite pairs are mostly less than 0.25 cycles; especially BDS-3 (1,\(-\)1,0,0) and Galileo (0,\(-\)1,1,0) are less than 0.1 cycles, which are consistent with the description of Tables 2 and 3 in Section 2.4. Table 7 counts the mean and STD values of the EWL ambiguity fractions. It can be found that the mean and STD values of the five EWL ambiguity fractions are less than 0.01 and 0.07 cycles, of which BDS-3 (1,\(-\)1,0,0) is only 0.002 and 0.021 cycles and Galileo (0,\(-\)1,0,1) is \(-\)0.001 and 0.030 cycles, respectively. This indicates that the EWL ambiguities of BDS-3 and Galileo can be fixed instantaneously. Therefore, the application of EWL AR for large scales and complex environments has great potential. Compared with Tables 2-4, it can be found that the EWL ambiguity fraction STD values of the experimental results are smaller than the theoretical values. The reason for this is that the actual pseudo-range and carrier phase precision are higher than our preset [31; 32; 33]. of combination scheme No. 2 are obviously more scattered than the other three schemes. Figures 6 and 7 show the WL ambiguity fractions of BDS-3 and Galileo correspond to experiment 2, respectively. It can be seen that the WL ambiguity fractions of experiment 2 are more scattered compared to that of experiment 1 and have a great relationship with the worst observation data. Figure 4: Experiment 1: WL ambiguity fractions and the corresponding histograms of combination schemes No. 1, No. 2, No. 3, and No. 4 (from top to bottom) for BDS\(-\)3: (**a**) WL ambiguity fractions, each color denotes one satellite pair; (**b**) WL ambiguity fraction statistics histograms. Figure 5: Experiment 1: WL ambiguity fractions and the corresponding histograms of combination schemes No. 1, No. 2, No. 3, and No. 4 (from top to bottom) for Galileo: (**a**) WL ambiguity fractions, each color denotes one satellite pair; (**b**) WL ambiguity fraction statistics histograms.