## 3 Quality Assessment of the BIC/B2a Signals from BDS-3 Operational Satellites
### Differential ISB estimation between BDS-3/GPS/Galileo BIC-L1-E1 and B2a-L5-E5a signals
#### 4.3.2 Test Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Freq.**} & \multirow{2}{*}{**Ratio**} & \multicolumn{3}{c}{**GPS/BDS-3 (Epoch)**} & \multicolumn{3}{c}{**GPS/Galileo/BDS-3 (Epoch)**} \\ \cline{3-8}  & & **LCM** & **TCM** & **Imp.**3 **} & **LCM** & **TCM** & **Imp.** \\ \hline \multirow{3}{*}{SF 1  } & \(\geq\)2.0 & 1941 & 3084 & 58.9\% & 4004 & 4805 & 20.0\% \\  & \(\geq\)3.0 & 1087 & 2114 & 94.5\% & 3108 & 4523 & 45.5\% \\  & \(\geq\)5.0 & 450 & 1133 & 151.8\% & 1782 & 3616 & 102.9\% \\ \hline \multirow{3}{*}{DF 2  } & \(\geq\)2.0 & 3607 & 4387 & 21.6\% & 4922 & 4978 & 1.1\% \\  & \(\geq\)3.0 & 3005 & 4015 & 33.6\% & 4800 & 4888 & 1.8\% \\ \cline{1-1}  & \(\geq\)5.0 & 2088 & 3337 & 59.8\% & 4334 & 4602 & 6.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of ratio values for GPS/BDS-3 and GPS/Galileo/BDS-3 solutions with 10\({}^{\circ}\) elevation cut-off angle. Number of epochs 5041. Figure 11: ADOP for GPS/Galileo/BDS-3 single-frequency (**a**) and dual-frequency (**b**) solutions with 10\({}^{\circ}\) elevation cut-off angle. Figure 12: Ratio values for GPS/BDS-3 (**top panels**) and GPS/Galileo/BDS-3 (**bottom panels**) solutions with 10\({}^{\circ}\) elevation cut-off angle. Table 5 lists the instantaneous empirical ambiguity resolution success rates for GPS/BDS-3 and GPS/Galileo/BDS-3 solutions with different integer ambiguity validation strategies under 10\({}^{\circ}\) and 20\({}^{\circ}\) elevation cut-off angles. It's shown that the observed satellites under 10\({}^{\circ}\) elevation cut-off angle are 9.3 and 13.1 for GPS/BDS-3 and GPS/Galileo/BDS-3, respectively, which is, to some extent, not promising. Therefore, the empirical ambiguity resolution success rates are not very satisfactory (e.g., only 33.2% and 78.4% with single-frequency observations and ratio threshold of 2.0). If TCM is adopted, improved empirical ambiguity resolution success rates are achieved with respect to the LCM whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. For positioning based on GPS/BDS-3 single-frequency observations, the empirical ambiguity resolution success rates of TCM are increased by approximately 25.5%, 21.1%, 29.7%, 14.4% and 23.2%, 19.8%, 19.0%, 5.8% with respect to LCM under 10\({}^{\circ}\) and 20\({}^{\circ}\) elevation cut-off angles, respectively. The improvement become approximately 16.7%, 28.8%, 25.7%, 50.4% and 24.6%, 34.7%, 42.2%, 60.9% if GPS/Galileo/BDS-3 single-frequency observations are adopted. Similar results are also obtained with GPS/BDS-3 dual-frequency observations. Nevertheless, the improvement is marginal (less than 5.0%) for GPS/Galileo/BDS-3 solutions with dual-frequency observations. This is reasonable since under this case, the LCM can already deliver excellent (more than 92.8%) ambiguity resolution success rates due to the relatively good observational geometry and strong model strength. Table 6 lists the empirical STDs of float and correctly-fixed (integer ambiguity validation with ratio threshold of 3.0) single-epoch positioning errors in the North, East, and Up under 10\({}^{\circ}\) and 20\({}^{\circ}\) elevation cut-off angles. We can observe that comparable results are achieved for correctly-fixed solutions whereas obvious improvements are obtained for float solutions if TCM is adopted. For example, in case of GPS/BDS-3 dual-frequency observations with 10\({}^{\circ}\) elevation cut-off angle, the three-dimension STDs are reduced from (54.5, 75.0, 137.6) to (48.3, 65.9, 130.9) cm, while for GPS/Galileo/BDS-3 solutions, they reduced from (39.5, 48.9, 102.9) to (35.6, 45.7, 93.4) cm. Although higher accuracy of the float solutions does not imply higher final positioning accuracy, they have an undeniable impact on the performance of the ambiguity resolution [23]. Figure 13 shows the horizontal and vertical positioning errors of different solutions with only single-frequency observations under 10\({}^{\circ}\) elevation cut-off angle.