## 2 Materials and Methods
### GNSS Double-Differenced  
In carrier-phase observations, a GNSS receiver measures the phase difference between the incoming satellite signal and its internally generated signal. While the fractional component of the phase can be measured with high precision, the total number of full wavelengths (denoted as N) between the satellite and the receiver at the initial epoch (t\({}_{0}\)) remains unknown. This unknown integer is referred to as the carrier phase ambiguity, or integer ambiguity. If no signal interruption occurs, the ambiguity remains constant over time and is referred to as the baseline phase uncertainty (BPU) [13; 29]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Year** & **08** & **09** & **10** & **11** & **12** & **13** & **14** \\ \hline Observation point & 886 & 1407 & 820 & 23 & 2396 & 3382 & 1089 \\ Outlier & 48 & 61 & 208 & 1 & 604 & 554 & 422 \\ Rate & 5.4\% & 4.3\% & 25.3\% & 4.3\% & 25.1\% & 16.4\% & 38.8\% \\ \hline Year & 15 & 16 & 17 & 18 & 19 & 20 & 21 \\ \hline Observation point & 488 & 647 & 1941 & 1770 & 774 & 741 & 668 \\ Outlier & 23 & 188 & 923 & 251 & 370 & 328 & 319 \\ Rate & 29.1\% & 29.1\% & 47.6\% & 14.1\% & 47.8\% & 44.2\% & 47.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Unified control point data quality analysis for RINEX network adjustment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite** & **MP1** & **MP2** & **Comparison** \\ \hline G02 & 0.41(m) & 0.45(m) & passed \\ G03 & 0.31 & 0.41 & passed \\ G04 & 0.26 & 0.40 & passed \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\ G06 & 0.47 & 0.74 & unpassed \\ G07 & 0.40 & 0.49 & passed \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RINEX file QC analysis (multipath). The carrier-phase observation model is expressed as follows:  
\[\Phi=\frac{\lambda}{\mathrm{R}}+\mathrm{N}+\varepsilon \tag{1}\]  
\(\Phi\) is the observed phase (in cycles),  
R is the geometric distance between the satellite and the receiver,  
\(\lambda\) is the carrier wavelength,  
N is the unknown integer ambiguity, \(\varepsilon\) is measurement noise or error. Carrier-phase measurements provide extremely high precision, often exceeding 0.01 cycles, which translates to millimeter-level positional accuracy. When two receivers simultaneously observe the same satellite, their observations are physically correlated due to shared propagation paths. However, in processing, this correlation is typically modeled mathematically using differencing techniques [12]. Assuming that the phase error \(\varepsilon\) follows a normal distribution with a mean of 0 and a variance of \(\sigma^{2}\), and that the observations are linear and uncorrelated, the variance-covariance matrix of the raw phase observations becomes  
\[\mathrm{Q}_{\Phi}=\sigma^{2}\cdot\mathrm{I} \tag{2}\]  
where  
\(\mathrm{Q}_{\Phi}\) is the variance-covariance matrix of phase observations,  
I is the identity matrix. GNSS positioning can be performed using either absolute (geocentric) or relative techniques. Absolute positioning typically achieves meter-level accuracy and is mainly used in navigation. In contrast, relative positioning--where the position of one receiver is computed with respect to another fixed receiver--can achieve centimeter- or millimeter-level accuracy [11]. Consequently, geodetic control networks are generally established using relative coordinate systems. To enhance precision and eliminate common-mode errors, differencing techniques are employed as follows:  
Single difference (SD): difference in signals from the same satellite received by two receivers,  
\[\Delta\Phi=\Phi_{A}^{j}-\Phi_{B}^{j} \tag{3}\]  
Double difference (DD): difference in two SDs, typically from two satellites and two receivers,  
\[\
abla\Delta\Phi=\left(\Phi_{A}^{j}-\Phi_{B}^{j}\right)-\left(\Phi_{A}^{k}- \Phi_{B}^{k}\right) \tag{4}\]  
Triple difference (TD): difference in two DDs over time, often used for cycle-slip detection.