## 2 Materials and Methods
### Analysis of \(\Delta\)N/\(\Delta\)E and Regional Statistics  
We focus on the horizontal components (N, E), since these define the planar position; ellipsoidal or orthometric heights are not analyzed in this comparison. For each station, the difference in northing (\(\Delta\)N) and easting (\(\Delta\)E) is computed as  
\[\Delta\text{N}=\text{N}_{\text{official}}-\text{N}_{\text{software}},\,\Delta \text{E}=\text{E}_{\text{official}}-\text{E}_{\text{software}} \tag{1}\]  
A positive \(\Delta\)N or \(\Delta\)E indicates that the official KGD2002 coordinate lies to the north or east of the software-derived coordinate, respectively (i.e., the software solution is displaced slightly south or west of the official position), and vice versa for negative values. These differences reflect how closely the GAMIT or Bernese solutions reproduce the official KGD2002 coordinates for each location. In the ideal case of perfect alignment, both \(\Delta\)N and \(\Delta\)E would be zero. In practice, residual differences on the order of a few millimeters to centimeters are expected due to random observational errors, baseline processing differences, and slight systematic offsets in the network adjustment procedures.  
We evaluated the coordinate differences using several statistical metrics applied separately to the northing (\(\Delta\)N) and easting (\(\Delta\)E) components. These metrics are as follows:  
* Mean difference (MD): The average of \(\Delta\)N or \(\Delta\)E across all stations, representing the overall bias or systematic offset of the solution relative to the official KGD2002 coordinates [21].
* Standard deviation (SD): The dispersion of the differences around the mean, indicating the typical magnitude of random error in the coordinate estimates [22].  
* Root mean square error (RMSE): A combined measure of bias and scatter, calculated as RMSE = \(\surd\)(Mean\({}^{2}\) + SD\({}^{2}\)). This metric represents the overall positional accuracy of the software-derived coordinates relative to the official KGD2002 values [23].
* Mean absolute deviation (MAD): The mean of the absolute values of \(\Delta\)N or \(\Delta\)E, providing a robust measure of typical error magnitude that is less affected by outliers than SD or RMSE [24].
* 95% confidence interval: The range between the 2.5 th and 97.5 th percentiles of the difference distribution, indicating the interval within which approximately 95% of the coordinate differences fall. Given that the distributions are generally centered near zero, this interval is approximately equivalent to \(\pm\)1.96 standard deviations under the assumption of normality [25].  
These metrics are computed separately for the GAMIT/GLOBK vs. KGD2002 differences and for the Bernese vs. KGD2002 differences, and separately for northings and eastings. We also performed a regional analysis by grouping stations by province or major city. For each region, we computed the mean and RMSE of \(\Delta\)N and \(\Delta\)E to see if certain areas have larger or systematic offsets. This can reveal any network distortions or regional biases in the adjustments (for example, poorer network fit in the peripheries vs. the center). We present both national-level statistics and region-by-region results, including tables and a figure for visualization.  
In addition to quantifying coordinate differences, this study also considers the broader implications of using a national reference frame that is now over two decades old. Based on the comparative results obtained from GAMIT/GLOBK and Bernese processing, we assess whether the existing KGD2002 framework still provides a reliable foundation for high-precision GNSS applications. Furthermore, we discuss the potential need for adopting a more modern reference frame--such as ITRF2020--given the evolving demands of geodetic infrastructure, positioning services, and international compatibility.