# A Comprehensive Signal Quality Assessment for BDS/Galileo/GPS Satellites and Signals
## 2 Data and Methods
### Carrier-to-Noise Density Ratio Evaluation Model  
The carrier-to-noise density ratio (_C/N0_) values are usually used to indicate the signal quality of GNSS observed data. In the experiment, the _C/N0_ values of all epochs corresponding to a certain satellite \(s\) at the frequency \(j\) were first extracted, and then the corresponding satellite elevation \(EL\) on each epoch was calculated.  
\[EL=\arcsin\ (e_{u}) \tag{1}\]  
where \(e_{u}\) is the transformation coordinate value between the earth-centered fixed coordinate system and the topocentric coordinate system.  
Two models with regard to \(C/N0\) were established in the contribution so as to evaluate the power of different signals in different GNSS systems.  
The first model was for comparing the signal power between different satellite types at the same frequency. In the model, the satellite elevations were used as the basis for grouping the \(C/N0\) values, and the \(C/N0\) values of a certain satellite at a certain frequency  
\begin{table}
\begin{tabular}{c c c c} \hline
**Receiver Type** & **Firmware Version** & **Observation Signal** & **Selection of Stations** \\ \hline \multirow{4}{*}{JAVAD} & \multirow{4}{*}{TRE\_3 3.7.6} & G: L1, L2, L5 & POTS, SGOC, SUTM, \\  & & E: E1, E5a, E5b, E5 & ULAB, URUM, WIND, \\  & & C: B1, B2I, B3I, B2a & WUH2 \\ \cline{2-4}  & \multirow{4}{*}{Others} & G: L1, L2, L5 & 9 measuring stations, \\  & & E: E1, E5a, E5b, E5 & such as BSHM, KOKV \\  & & C: B1, B2I, B3I & 25 measuring stations, \\ \hline \multirow{2}{*}{LEICA} & \multirow{2}{*}{GR10, GR25, GR30, GR50} & G: L1, L2, L5 & 25 measuring stations, \\  & & E: E1, E5a, E5b, E5 & such as ALIC, EBRE \\  & & C: B1I, B2I & \\ \hline \multirow{2}{*}{TRIMBLE} & \multirow{2}{*}{NETR9} & G: L1, L2, L5 & 48 measuring stations, \\  & & E: E1, E5a, E5b, E5 & such as BOR1, CUT0 \\  & & C: B1I, B2I, B3I, & 40 measuring stations, \\ \hline \multirow{2}{*}{SEPT} & \multirow{2}{*}{POLARX5} & G: L1, L2, L5 & 40 measuring stations, \\  & & E: E1, E5a, E5b, E5, E6 & \\  & & C: B1I, B2I, B3I & \\ \hline \end{tabular}
\end{table}
Table 2: Classifications of different receiver types in MGEX stations (G: GPS; E: Galileo; C: BDS).  
point were divided into groups every 10 degrees. Afterward, an average value of \(C/N0\) was calculated within each group. The formula is as follows.  
\[C/N0^{s}_{j,ave}(k)=\frac{\sum_{i=1}^{n}C/N0^{s}_{j}(i)_{[k\cdot 10^{\circ},(k+1) \cdot 10^{\circ}]}}{n} \tag{2}\]  
where \(k=0\sim 8\) denotes the \(k_{th}\) elevation group, and \(n\) is the number of epochs within the elevation group of \(\left[k\cdot 10^{\circ},\ (k+1)\cdot 10^{\circ}\right]\). \(C/N0^{s}_{j,ave}(k)\) is the average \(C/N0\) value of satellite \(s\) at the frequency \(j\) within the \(k_{th}\) elevation interval.  
The second model was for comparing the signal power at different signals. Different from the first model, the \(C/N0\) values over the same type of satellites at the same frequency were grouped according to their elevations. Then, \(C/N0\) values in each elevation interval of 10 degrees were averaged, and STDs of \(C/N0\) were calculated to estimate uncertainties.  
\[C/N0_{j,ave}(k)=\frac{\sum_{s=1}^{m}\sum_{i=1}^{n}C/N0^{s}_{j}(i)_{[k\cdot 10^{ \circ},(k+1)\cdot 10^{\circ}]}}{n} \tag{3}\]  
where \(m\) is the number of satellites that are the same type, and \(C/N0^{s}_{j,ave}(k)\) is the average \(C/N0\) value over a certain type of satellite at the frequency \(j\) within the \(k_{th}\) elevation interval. STDs can be expressed as:  
\[C/N0_{j,\text{STD}}(k)=\sqrt{\frac{\sum_{s=1}^{m}\sum_{i=1}^{n}(C/N0^{s}_{j}(i )_{[k\cdot 10^{\circ},(k+1)\cdot 10^{\circ}]}-C/N0_{j,ave}(k))^{2}}{n}} \tag{4}\]