## 2 Materials and Methods
### Network Adjustment Process  
Geodetic network adjustment is a fundamental process in geodesy, designed to determine the most probable coordinates of network points by minimizing observational errors. This adjustment ensures that geospatial data maintain high levels of accuracy and reliability, which are essential for applications such as topographic mapping, infrastructure design, and satellite-based navigation systems. The process typically involves constructing mathematical models that relate observations to unknown parameters, and then applying statistical estimation techniques--such as least squares adjustment--to solve and validate these parameters [28; 32]. In GNSS-based geodetic networks, the process begins with the establishment of a functional model, A\(\cdot\)x = L, and a corresponding stochastic model, \(\Sigma=\mathrm{a}^{2}\cdot\)Q. The functional model relates the observation equations to unknowns, while the stochastic model describes the expected behavior of observation errors. Together, these models form the basis for least squares estimation [11; 33]. A minimally constrained adjustment is typically applied at the initial stage. This yields preliminary station coordinates (X), variance-covariance matrices (Q\(\chi\), Q\(\chi\)), and observation residuals (V), providing an internal check on the network geometry and data quality [34]. If anomalies or gross errors are found, the adjustment process is refined iteratively. This iterative refinement does not alter the overall network structure but aims to improve internal consistency by re-evaluating residual patterns and verifying redundancy within the observations. The variance-covariance matrices serve as diagnostic tools, allowing the analyst to assess the relative strength and geometry of the network. In particular, the off-diagonal elements of these matrices offer insight into correlations between parameters, which can indicate potential instability in poorly constrained regions. As illustrated in Figure 2, residuals are also examined not only for magnitude but for systematic trends, as these may point to modeling errors or inconsistencies in observational conditions. Through this process, the adjustment achieves statistical rigor without compromising the spatial integrity of the original network design. The role of variance-covariance matrices in evaluating network strength and parameter interdependence has been extensively discussed in the adjustment literature [35; 36; 37]. Figure 2: Workflow of GNSS network adjustment process. Following model definition, a minimally constrained adjustment is performed to derive initial estimates for station coordinates (X), along with their associated variance-covariance matrices (Q\({}_{X}\), Q\({}_{Y}\)) and observation residuals (V). Subsequent GNSS quality control (QC) procedures ensure that input observations satisfy predefined accuracy and stability thresholds [38]. Subsequent GNSS quality control (QC) procedures are essential to ensure that observations meet predefined accuracy and stability standards. These include multipath filtering, cycle-slip detection, and statistical outlier analysis using chi-square and F-ratio tests [39; 40]. When required, baseline vectors or observations may be excluded, reweighted, or recomputed. Empirical statistics such as the unit weight variance (a\({}_{\text{u}}\)\({}^{2}\)) and iterative factor variance (a\({}_{\text{i}}\)\({}^{2}\)) are used to validate the adequacy of the model. If the assumed unit weight variance a\({}^{2}\) is consistent with the empirical values (i.e., a\({}^{2}\)\(\approx\) a\({}_{\text{u}}\)\({}^{2}\) and a\({}^{2}\)\(\approx\) a\({}_{\text{i}}\)\({}^{2}\)), the stochastic model is considered accurate, and the network solution can be finalized. Otherwise, the adjustment process is repeated with updated variance assumptions, where a\({}^{2}\) is typically updated using a\({}_{\text{u}}\)\({}^{2}\), as it is derived directly from the residuals.