## 4 Results
### Precision of the Navigation Solutions  
The authors evaluated the quality of navigation solutions obtained by the receiver in high-sensitivity mode through two tests. In the first test, the receiver processed Galileo E1b/c signals in high-sensitivity mode along with Galileo E5a and GPS signals in normal-sensitivity mode, all received at nominal power levels. In the second test, the receiver processed weak Galileo E1b/c signals with a \(C/N_{0}\) of approximately 20 dB-Hz. The measurements were conducted using the GESTALT testbed rooftop antenna [46]. The experimental scenario described in Section 4.1 was employed, along with the test setup depicted in Figure 10. The OCXO was used for these tests.  
The quality of the navigation solutions was assessed using standard positioning precision measurements and corresponding static confidence regions. Precision, which indicates how closely a solution aligns with the mean of all obtained solutions, reflects repeatability  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **E1b/c Signals Tracked and** & **TTFF** \\  & **C/N\({}_{0}\) in dB-Hz** & \\ \hline \multirow{6}{*}{Test 1} & E2: 27 dB-Hz & \multirow{6}{*}{1 min 40 s} \\  & E8: 20 dB-Hz & \\  & E10: 20 dB-Hz & \\  & E25: 25 dB-Hz & \\  & E36: 23 dB-Hz & \\ \hline \multirow{6}{*}{Test 2} & E13: 23 dB-Hz & \multirow{6}{*}{53 s} \\  & E15: 28 dB-Hz & \\  & E21: 20 dB-Hz & \\ \cline{1-1}  & E27: 28 dB-Hz & \\ \cline{1-1}  & E30: 26 dB-Hz & \\ \cline{1-1}  & E34: 26 dB-Hz & \\ \hline \multirow{6}{*}{Test 3} & E3: 21 dB-Hz & \multirow{6}{*}{1 min 15 s} \\ \cline{1-1}  & E8: 22 dB-Hz & \\ \cline{1-1}  & E13: 22 dB-Hz & \\ \cline{1-1}  & E15: 21 dB-Hz & \\ \hline \hline \end{tabular}
\end{table}
Table 16: Processing weak Galileo E1b/c signals.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **Signals Tracked** & **TTFF** \\ \hline \multirow{2}{*}{Test 1} & 8 Galileo E1b/c + 8 Galileo E5a + 7 GPS L1 & \multirow{2}{*}{1 min 03 s} \\  & C/A + 5 GPS L5 & \\ \hline \multirow{2}{*}{Test 2} & 8 Galileo E1b/c + 8 Galileo E5a + 6 GPS L1 & \multirow{2}{*}{57 s} \\  & C/A + 4 GPS L5 & \\ \hline \multirow{2}{*}{Test 3} & 8 Galileo E1b/c + 8 Galileo E5a + 7 GPS L1 & \multirow{2}{*}{1 min 12 s} \\  & c/a + 4 GPS L5 & \\ \hline \hline \end{tabular}
\end{table}
Table 15: Processing GNSS signals at nominal power levels.  
or the spread of the measurement. Key confidence measurements include Distance Root Mean Square (DRMS) and Circular Error Probability (CEP) for 2D positioning, as well as Spherical Accuracy Standard (SAS), Mean Radial Spherical Error (MRSE), and Spherical Error Probable (SEP) for 3D positioning. Formulas for 2D and 3D position confidence regions are provided in Tables 17 and 18, respectively, [49,50].  
Similar to the measurements reported in [21], the receiver's latitude, longitude, and height coordinates were converted into a local East-North-Up (ENU) coordinate system, with the WGS-84 reference ellipsoid as the reference. Standard deviations for the East (E), North (N), and Up (U) coordinates were computed. Equation (9) demonstrates the calculation of the standard deviation for East coordinates, denoted as \(E[n]\), using the mean value \(\overline{E}\) of the East coordinates and the number of position fixes, \(L\). The standard deviation calculations for North (N) and Up (U) coordinates follow the same procedure as Equation (9) for East coordinates.  
\[\sigma_{E}^{(precision)}=\sqrt{\frac{1}{L-1}\sum_{l=1}^{L}(E[n]-\overline{E})^{ 2}}\] [m] (9)  
The receiver processed GNSS signals in real time and dumped PVT solutions to a file, configured for single-point positioning mode. Each test was conducted over a period of 10 min.