## 3 Data Collection and Observation Quality Assessment
### Multipath Errors  
Multipath error is one of the major errors affecting the quality of GNSS observations. For the dual-frequency GNSS observations, usually, a combination of pseudo-range and carrier phase can be used to extract multipath errors. In this study, mainly single-frequency GNSS observations were available; therefore, we used the pseudo-range minus the carrier phase (CMC) to evaluate the multipath error, which can be expressed as [32,36]  
\[CMC=P-\lambda\Phi=2I-\lambda N_{\Phi}+M_{P}+\varepsilon_{P}+M_{\Phi}+ \varepsilon_{\Phi} \tag{31}\]  
where \(M_{P}\) and \(M_{\Phi}\) denote multipath errors in pseudo-range and carrier phase, respectively. Due to the observation noise of the pseudo-range being much larger than the observation noise and multipath error of the carrier phase, Equation (34) can be approximately simplified as [36]  
\[CMC\approx 2I-\lambda N+M_{P}+\varepsilon_{P} \tag{32}\]  
Since the ionosphere delay changes slowly over a short time, this characteristic ensures that it can be regarded as a constant. In addition, the ambiguity is a constant when there is no cycle slip. Therefore, removing the average value of the CMC in Equation (32) can eliminate the influence of the ionosphere delay and ambiguity, and the residual value (CMCR) of the CMC can be used to reflect the multipath error and measuring noise of the pseudo-range.  
\[CMCR=CMC-\overline{CMC}=M_{P}+\varepsilon_{P} \tag{33}\]  
Figure 4: Variation in Mß’s C/N0 for visible GPS/BDS satellites in the static experiment (**left**) and dynamic experiment (**right**).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Static (dB-Hz)**} & \multicolumn{3}{c}{**Dynamic (dB-Hz)**} \\ \cline{2-7}  & **MIN** & **MAX** & **AVG** & **MIN** & **MAX** & **AVG** \\ \hline GPS & 9.55 & 47.76 & 36.50 & 24.97 & 47.38 & 40.46 \\ BDS & 9.02 & 46.91 & 32.74 & 9.20 & 49.12 & 34.27 \\ \hline \hline \end{tabular}
\end{table}
Table 3: C/N0 values of these visible GPS L1 and BDS B1 satellites in the Mß smartphone.  
As is known, the multipath error on a pseudo-range is larger than the measuring noise. Therefore, the CMCR can be used to characterize multipath errors. Shown in Figures 5 and 6 are the statistics RMS values of multipath errors for these observed GPS and BDS satellites in both the static and dynamic experiments. Accordingly, in the static experiment, the RMS values of multipath error for these observed satellites are within 3.95 m \(\sim\) 10.71 m, except G30, which has a higher RMS value of 15.95 m. In the dynamic experiment, the RMS values of the multipath error for GPS satellites are distributed between 1.95 m and 4.30 m, while these values for BDS satellites range from 1.95 m to 4.30 m. In general, the multipath error strength of BDS satellites is larger than that of GPS satellites.  
Figure 5: RMS of multipath error for GPS and BDS satellites in the static experiment.  
Figure 6: RMS of multipath error for GPS and BDS satellites in the dynamic experiment.  
To present the relationship between the multipath error, satellite elevation angle, and C/N\({}_{0}\), the corresponding results of G22 (GPS) and C35 (BDS) in the static experiment and that of G15 (GPS) and C19 (BDS) in the dynamic experiment are shown in Figures 7 and 8, respectively, as examples. Obviously, there is an anti-correlation between the multipath errors and C/N\({}_{0}\) values, and similar relations between multipath errors and elevation angles can also be found. However, the correlation of C/N\({}_{0}\) and multipath error is much stronger than that of elevation angle and multipath error. Usually, lower elevations could lead to smaller C/N\({}_{0}\) values and greater multipath errors.