## 3 Precision Analysis of GNSS-Derived elevations
### Precision Analysis
As mentioned above, this maximum difference likely occurred due to the station's long baseline. Other stations in region five (UMS76, UMS88, and UMS99) use a different region name to UHA89, indicating that they are located in a different region. Thus, the incomplete  
Figure 3: Elevation differences between GNSS-derived height determination and spirit leveling for target precisions of 3 and 5 cm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**unit: m**} & **Unknown** & \multicolumn{2}{c}{**GNSS-Derived Elevation (A)**} & \multicolumn{2}{c}{**Elevation Difference (C = A \(-\) B)**} \\ \cline{3-6}  & **Stations** & **3 cm** & **5 cm** & & **3 cm** & **5 cm** \\ \hline \multirow{3}{*}{Region 1} & US04 & 6.0192 & 6.0283 & 6.0103 & 0.0089 & 0.018 \\  & US13 & 4.4073 & 4.4266 & 4.4114 & \(-\)0.0041 & 0.0152 \\  & US04B & 4.183 & 4.1995 & 4.1729 & 0.0101 & 0.0266 \\  & US13B & 4.4914 & 4.5133 & 4.4885 & 0.0029 & 0.0248 \\ \hline \multirow{3}{*}{Region 2} & UDB05 & 12.1599 & 12.1448 & 12.156 & 0.0039 & \(-\)0.0112 \\  & UDB26 & 8.1791 & 8.1622 & 8.1654 & 0.0137 & \(-\)0.0032 \\  & UDB58 & 6.3785 & 6.391 & 6.3627 & 0.0158 & 0.0283 \\ \hline \multirow{3}{*}{Region 3} & USA03 & 43.3425 & 43.3506 & 43.3313 & 0.0112 & 0.0193 \\  & USA01 & 3.617 & 3.625 & 3.6184 & \(-\)0.0014 & 0.0066 \\  & U1168 & 8.7048 & 8.7171 & 8.686 & 0.0188 & 0.0311 \\  & U1167 & 57.3538 & 57.3554 & 57.3403 & 0.0135 & 0.0151 \\ \hline \multirow{3}{*}{Region 4} & U0531 & 8.7046 & 8.7044 & 8.7003 & 0.0043 & 0.0041 \\  & UGN58 & 6.1594 & 6.1653 & 6.1688 & \(-\)0.0094 & \(-\)0.0035 \\  & TBM1 & 6.4718 & 6.4729 & 6.4767 & \(-\)0.0049 & \(-\)0.0038 \\  & TBM2 & 20.8838 & 20.8877 & 20.8871 & \(-\)0.0033 & 0.0006 \\ \hline \multirow{3}{*}{Region 5} & UMS76 & 2.8706 & 2.873 & 2.8567 & 0.0139 & 0.0163 \\  & UMS88 & 27.3836 & 27.3993 & 27.3977 & \(-\)0.0141 & 0.0016 \\  & UMS99 & 80.7112 & 80.7201 & 80.7027 & 0.0085 & 0.0174 \\  & UHA89 & 3.1589 & 3.1498 & 3.1886 & \(-\)0.0297 & \(-\)0.0388 \\ \hline \multicolumn{6}{c}{} & Min & 0.0014 & 0.0006 \\ \multicolumn{6}{c}{} & Max & 0.0297 & 0.0388 \\ \multicolumn{6}{c}{} & Mean & 0.0101 & 0.015 \\ \multicolumn{6}{c}{} & STD & 0.0069 & 0.0112 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Elevation differences between GNSS-derived height determination and spirit leveling. removal of local bias from the geoid model may also have led to this larger discrepancy. Despite the relatively large difference, however, it still did not exceed the target precision of 5 cm. It was found that elevations with precisions smaller than 3 cm or 5 cm could be determined through GNSS-derived height determination, despite being fixed to only two inland stations. Of course, well-conducted GNSS surveying and precise geoid model were mainly used to complement the weaknesses of traditional geometry. In addition, the gentle changes in topography in coastal areas and islands could also have helped to contribute to the observed stability. For reference, the unknown stations in this study are located in the coastal area or islands, so variations in the terrain are quite small. Most elevations of unknown points were smaller than 50 m and the maximum did not exceed 100 m; thus, the geoidal heights in the same test region changed within a 30 cm level. Thus, it is expected that precision will be improved in scenarios where unknown stations are surrounded by fixed stations, for example, during inland surveying.