## 6 Conclusions  
We comparatively analysed the quality of multi-frequency GNSS observations in the Xiaomi Mi 8 smartphone. The analysis results allowed us to use improved algorithms including a stochastic model and ambiguity resolution for short-baseline RTK positioning. The ambiguity fixing rate, positioning performance, and convergence time using only the embedded smartphone GNSS antenna were then determined. The feasibility of using a smartphone for dynamic deformation monitoring was also verified. The cycle slips in the smartphone were severe, especially when C/N0 was below 30 dB-Hz. In addition, C/N0 of band L5/E5a was lower than that of band L1/E1, and its cycle-slip ratio was higher than that of band L1/E1, limiting the use of the second frequency in smartphones. In future work, we will explore the effective use of the second frequency for GNSS observations. Using an improved C/N0 stochastic model and partial ambiguity resolution combined with other solving strategies can improve the positioning accuracy and ambiguity fixing  
Figure 18: Results of RTK segmented positioning in choke-coil experiment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Segment**} & \multirow{2}{*}{
\begin{tabular}{c} **Convergence** \\ **Time (min)** \\ \end{tabular} } & \multicolumn{2}{c}{**RMS Error of Fixed Solution**} & \multicolumn{2}{c}{**Mean Number of**} & \multicolumn{1}{c}{**Cycle-Slip**} & \multicolumn{1}{c}{**Pseudo-Range**} \\  & & **East (m)** & **North (m)** & **Up (m)** & **Candidate Ambiguities** & **Rate (\%)** & **RMS Residual (m)** \\ \hline
1 & 5.0 & 0.021 & 0.004 & 0.023 & 6.0 & 0.0 & 2.15 \\
2 & 3.9 & 0.008 & 0.004 & 0.011 & 7.6 & 0.0 & 2.10 \\
3 & 3.2 & 0.004 & 0.004 & 0.012 & 7.4 & 0.0 & 2.26 \\
4 & 1.5 & 0.003 & 0.004 & 0.007 & 8.9 & 0.0 & 2.12 \\ \hline \end{tabular}
\end{table} 
Table 10: Statistical results of RTK segmented positioning in choke-coil experiment. rate. The ambiguity fixing rate varies greatly with different combinations of observations, and it is mainly affected by the number of satellites and cycle slips. It can reach 80-90% or above. The solution using GPS + Galileo + BDS single-frequency combination while keeping the BDS float ambiguity is the best, and its ambiguity fixing rate can reach approximately 90% in 3 h observations. However, it still takes a long time (usually 10-30 min) for a fixed solution to converge within 0.1 m. The accuracy of the fixed solutions for different band combinations can reach 1 and 2 cm along the horizontal and vertical directions, respectively. By simulating dynamic deformation monitoring, the smartphone can recognise 2 cm deformation trends, being insufficient for actual monitoring applications. Nevertheless, a smartphone may be applied for high-precision measurements in applications such as vibration monitoring. After using a choke coil around the smartphone, the fixing rate, convergence speed, and positioning accuracy improve, demonstrating the importance of antenna design on the positioning performance. With the advancement of hardware development, improved GNSS modules may lead to fast centimetre- or millimetre-level positioning accuracy in smartphones. Conceptualization, S.Z. and C.K. ; methodology, S.Z. and W.Y. ; software, S.Z. and W.Y. ; validation, S.Z. and C.K. ; formal analysis, S.Z. ; investigation, S.Z. ; resources, S.Z. ; data curation, S.Z. ; writing--original draft preparation, S.Z. and W.Y. ; writing--review and editing, S.Z. and C.K. ; visualization, S.Z. ; supervision, C.K. ; project administration, C.K. ; funding acquisition, C.K. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China, grant number 41774040, National Key Research and Development Program of China, grant number 2016 YFB0501800, and Fundamental Research Funds for the Central Universities of Central South University, grant number 2021 zzts0843. Not applicable. Raw GNSS measurements used in the study are available from the Science Data Bank.