## 3 Data Processing and Analysis for Smartphone Real-Time Kinematic (RTK) Positioning
### Evaluation of Ambiguity Resolution for Different Observation Combinations  
Next, we evaluated the actual fixing rate and fixed-solution accuracy of different observation combinations to improve observation selection. The positioning parameters are as listed in Table 2. The solutions for single-frequency observations are listed in Table 6.  
Table 6 shows that when using single-constellation and single-frequency observations, the mean number of satellites is approximately six, and thus the fixing rates are low and cannot converge. When using the G/C combination, which nearly doubles the number of satellites, the fixing rate increases to 55.6%, but it remains low and has a slow convergence. On the other hand, the fixing rate of the G/E combination can reach 90.8% and converges after 25.1 min, indicating substantial improvement in both the fixing rate and convergence time. When using combinations G/E/C and G/R/E/C, the number of satellites greatly increases, but the fixing rate decreases drastically, possibly due to anomalies in the BDS and GLONASS observations acquired by the smartphone. After analysis, we found that for combination G/C or G/E/C, after excluding the BDS GEO and GLONASS satellite \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **Observation** & **Mean Number** & **Fixing Rate** & **Error-Fixing Rate (\%)** & \multicolumn{2}{c}{**Convergence**} & \multicolumn{2}{c}{**RMS Error after Convergence**} \\ \cline{4-9}  & **Combination** & **of Satellites** & **(\%)** & **Rate (\%)** & **Time (min)** & **East (m)** & **North (m)** & **Up (m)** \\ \hline G & 6.6 & 28.3 & 28.3 & Non-convergent & – & – & – \\ C & 6.5 & 3.3 & 3.2 & Non-convergent & – & – & – \\ G/C & 13.1 & 55.6 & 5.9 & 71.7 & 0.011 & 0.015 & 0.021 \\ G/E & 10.0 & 90.8 & 5.3 & 25.1 & 0.012 & 0.011 & 0.025 \\ G/E/C & 16.5 & 60.7 & 12.4 & 58.3 & 0.012 & 0.009 & 0.019 \\ G/R/E/C & 21.2 & 49.7 & 0.8 & 36.3 & 0.023 & 0.009 & 0.022 \\ G/C (no GEO) & 11.2 & 80.3 & 0 & 23.0 & 0.013 & 0.016 & 0.026 \\ G/E/C (no GEO) & 14.6 & 85.7 & 0 & 32.5 & 0.013 & 0.012 & 0.017 \\ G/E/C (no GEO/float C) & 14.6 & 88.5 & 2.9 & 25.0 & 0.012 & 0.010 & 0.022 \\ \hline \hline \end{tabular}  
No GEO, exclude BDS GEO satellites; float C, BDS satellites do not participate in ambiguity resolution; non-convergent, positioning accuracy remained above 0.1 m.  
\end{table} 
Table 6: Solutions for single-frequency observation combinations (G, GPS; R, GLONASS; E, Galileo; C, BDS). Figure 10: Fixed ambiguity solutions using fix-and-hold mode for GPS L1 + Galileo E1 observations. observations, the fixing rate increases to 80.3% and 85.7%, respectively, and the convergence speed also increases. This is mainly attributable to the GEO satellite observations in smartphones, which have a half-cycle jump, and the GEO satellite itself has a very poor orbit accuracy [30]. Figure 11 shows that in the observations from the two BDS GEO satellites, C01 and C03, the carrier-phase residuals of the float solutions in many epochs are close to 0.5, likely corresponding to half-cycle jumps. However, the half-cycle jumps are very difficult to detect. Such jumps should be identified by the loss-of-lock indicator in the RINEX file or in field AccumulatedDeltaRangeState [4] of the GNSS raw measurements. In addition, in the combination of G/E/C, when excluding the BDS GEO satellite observations and not fixing the BDS ambiguities, the fixing rate increases again to 88.5%. The main reason is that the cycle slips of BDS are more frequent than those of other constellations (Figure 5). As frequent cycle slips severely undermine positioning, it is better not to fix the BDS ambiguity. In contrast, although GLONASS observations have fewer cycle slips, the fixing rate of combination G/R/E/C is also lower than that of combination G/E/C, mainly because the noise of GLONASS observations in smartphones is higher than that of observations from other constellations [6].