## 2 Materials and Methods
### Displacement Analysis: Relative Positioning
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **RTKLIB** \\ \hline Observations & L1, L2 \\ Duration & 1 h \\ Constellations & GPS, GLONASS, Galileo \\ Ambiguity & Fix and hold (LAMBDA) \\ Elevation mask & 15\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used in the data processing. \[x_{i}^{T}x_{i}=min\text{ and }\hat{x}_{i}=x_{0i}+x_{i} \tag{2}\]  
where \(v_{i}\) is the residual vector for the \(i\)-th session, \(P_{i}\) is the weight matrix for the \(i\)-th session, \(x_{0i}\) is the vector of approximate coordinates for the \(i\)-th session, \(x_{i}\) is the parameter correction vector for the \(i\)-th session, and \(\hat{x}_{i}\) is the vector of adjusted coordinates for the \(i\)-th session. The data screening method (\(\tau\)-test) with a significance level of 5% was used afterward for outlier detection. To analyze whether statistical equality of network precision was achieved between the corresponding sessions, the following hypothesis was established:  
\[H_{0}=E\left(\hat{\sigma}_{i}^{2}\right)=E\left(\hat{\sigma}_{j}^{2}\right)\]  
\[H_{a}=E\left(\hat{\sigma}_{i}^{2}\right)\
eq E\left(\hat{\sigma}_{j}^{2}\right)\]  
where \(\hat{\sigma}_{i}^{2}\) is a posteriori variance from the \(i\)-th session, and \(\hat{\sigma}_{j}^{2}\) is a posteriori variance from the \(j\)-th session. To determine whether the null hypothesis could be rejected, the \(F\) test was performed, defined as follows [34]:  
\[F=\frac{\hat{\sigma}_{i}^{2}}{\hat{\sigma}_{j}^{2}}\leq F_{1-\alpha,f_{1},f_{ 2}} \tag{3}\]  
\[f_{1}=n_{1}-u_{1}+d \tag{4}\]  
\[f_{2}=n_{2}-u_{2}+d \tag{5}\]  
where \(f_{i}\) is degrees of freedom for a certain session, \(n_{i}\) is the number of observations for a certain session, \(u_{i}\) is the number of unknowns for a certain session, \(d\) is the geodetic network datum defect, and \(\alpha\) is the significance level. To determine the size of the detected 1D, 2D, and 3D displacements, statistical tests were used to test the hypothesis [33; 34; 35; 36]. Displacements were analyzed by defining the following hypothesis:  
\(\mathbf{H_{0}}\)**. \(d=0\); _Point did not move between two sessions_;  
\(\mathbf{H_{A}}\)**. \(d\
eq 0\); _Point moved between two sessions_. To determine whether the null hypothesis could be rejected, the following statistical test was performed [35]:  
\[T=\frac{d}{\sigma_{d}} \tag{6}\]  
The estimated value of the statistical test (\(T\)) was compared with its corresponding critical value from the normal (\(N\), in the case of 1D displacements) and chi-squared (\(\chi^{2}\), in the case of 2D and 3D displacements) distributions. The critical values are defined based on the displacement dimension: the critical values are 1.96, 2.45, and 2.80 for 1D, 2D, and 3D displacements, respectively, for a significance level of 5% (\(\alpha\) = 0.05). The imposed 1D, 2D, and 3D movements were estimated as follows:  
\[d_{1D}=h_{i}-h_{j} \tag{7}\]  
\[d_{2D}=\sqrt{\left(e_{i}-e_{j}\right)^{2}+\left(n_{i}-n_{j}\right)^{2}} \tag{8}\]  
\[x_{i}^{T}x_{i}=min\text{ and }\hat{x}_{i}=x_{0i}+x_{i} \tag{2}\]0  
where \(e_{i},n_{i},h_{i}\) are FGG1 coordinates from the \(i\)-th session in the topocentric coordinate system, and \(e_{j},n_{j},h_{j}\) are FGG1 coordinates from the \(j\)-th session in the topocentric coordinate system. The network adjustment was performed in a global coordinate system, and the variance-covariance matrix for the point FGG1 was transformed to its topocentric coordinate system as follows [37]:  
\[x_{i}^{T}x_{i}=min\text{ and }\hat{x}_{i}=x_{0i}+x_{i} \tag{2}\]1  
\[R=\left[ \begin{array}{ccc}-sin\lambda_{i}&cos\lambda_{i}&0\\ -sin\varphi_{i}cos\lambda_{i}&-sin\varphi_{i}sin\lambda_{i}&cos\varphi_{i}\\ cos\varphi_{i}cos\lambda_{i}&cos\varphi_{i}sin\lambda_{i}&sin\varphi_{i}\\ \end{array}