# Characterization of GNSS Signals Tracked by the iGMAS Network Considering Recent BDS-3 Satellites
## 3 Methodology and Results
### Pseudo-range Noise and Multipath  
In order to analyze the pseudo-range noise and multipath errors, the multipath (MP) combination is computed as follows [15; 16]:  
\[ \begin{array}{c}MP_{i}=P_{i}-(a+1)\cdot L_{i}+a\cdot L_{j}+B\\ \text{with }a=2\cdot f_{j}^{2}/\left(f_{i}^{2}-f_{j}^{2}\right)\end{array}  \tag{1}\]  
where the subscripts \(i\) and \(j\) indicate the carrier phase frequencies, \(MP_{i}\) is the code multipath of the signal \(i\), \(P_{i}\) is the pseudo-range observation of signal \(i\), \(L_{i}\) and \(L_{j}\) are carrier phase observations (in meters), and \(B\) is a bias that can be considered a constant if no cycle slip occurs on phase observations. The corresponding frequencies are \(f_{i}\) and \(f_{j}\). This combination eliminates all errors except for receiver noise, multipath errors and bias variations in the pseudo-range observation. Results of the MP combination for all available GPS, Galileo, BDS-2, and BDS-3 signals at HMNS, PETH, and LHA1 stations equipped with different receivers are illustrated in Figure 4. The root mean square (RMS) of the MP combinations by satellite elevation is plotted. The used satellites and test period are the same as for the aforementioned C/N\({}_{0}\) analysis. For GPS and Galileo signals in the top panels of Figure 4, we can see that signals observed at low elevation angles are affected more severely by multipath conditions. At the station HMNS, the GPS L5 and Galileo E5a/E5b signals exhibit smaller noise and multipath errors, which are less than 0.3 m over the entire elevation range. This superior performance could be explained by the fact that the L5/E5a/E5b signals have higher chip rates of 10.23 Mbps and are therefore less susceptible to multipath errors. For PETH and LHA1 stations, only the Galileo E1 signal has obviously larger noise and multipath errors, and GPS L1 and L2 signals do not exhibit this phenomenon, which could be due to the receiver firmware. It should be noted, however, that multipath errors are largely affected by the specific choice of bandwidth, which may differ among receivers and tracked signals. For BDS-2 and BDS-3 signals in the bottom panels of Figure 4, we can see that the variations of noise and multipath errors for BDS-2 B1I/B3I signals are obviously different from the GPS and Galileo signals when the elevation angles are higher than about 50\({}^{\circ}\), especially for the B1I signal. This is due to BDS-2 satellite-induced code biases, which are discussed in the next section. For the same signals of B1I and B3I, BDS-3 shows a better performance compared with BDS-2 for all stations. For all signals of BDS-3, as expected, the B1C signal exhibits the largest noise and multipath errors for both stations due to a lower chipping rate of 1.023 Mcps. For the station HMNS, the errors of BDS-3 B1I/B3I/B2a/B2b  
Figure 3: Mean C/N\({}_{0}\) values as a function of elevation for the signals with overlapping frequencies of BDS-3, GPS, and Galileo at ABJA station. The signals include BIC/L1/E1 (**a**); B2a/L5/E5a (**b**); and B2b/E5b (**c**). signals are less than 0.3 m at low elevation angles and about 0.05 m at zenith, while for PETH and LHA1 stations, the B2a signal shows an abnormal performance with larger errors. Figure 5 shows the RMS of receiver noise and multipath errors of BDS-3, GPS, and Galileo signals with overlapping frequencies, which are B1C/L1/E1, B2a/L5/E5a, and B2b/E5b. It can be seen that the differences of the RMS values are insignificant for each group of signals, and the pseudo-range errors of BDS-3 signals are comparable to those of GPS and Galileo. For B1C/L1/E1, the RMS values of the receiver noise and multipath errors are 0.1-0.2 m close to the zenith and increase to 0.4-0.6 m at low elevation angles, while for B2a/L5/E5a and B2b/E5b, the RMS values are less than 0.3 m over the entire elevation range, and less than 0.1 m at high elevation angles.