## 2 Materials and Methods
### Potential Modifications of the ASG-EUPOS's APPS
the coordinates of point P are calculated as simple arithmetic means of the values from Equation (1):  
\[X_{P}=\frac{\sum_{i=1}^{n}X_{P}^{i}}{n};Y_{P}=\frac{\sum_{i=1}^{n}Y_{P}^{i}}{n};Z _{P}=\frac{\sum_{i=1}^{n}Z_{P}^{i}}{n} \tag{5}\]  
The accuracy of the adjusted coordinates from Equation (5) is determined by the average error of the arithmetic mean according to the propagation of mean error [33]:  
\[m_{X}=\pm\frac{m^{\Delta X}}{\sqrt{n}};m_{Y}=\pm\frac{m^{\Delta Y}}{\sqrt{n}};m _{Z}=\pm\frac{m^{\Delta Z}}{\sqrt{n}} \tag{6}\]  
We calculate the a posteriori observation mean errors in Equation (6) i.e., \(m^{\Delta X}\), \(m^{\Delta Z}\) from the corrections of Equation (3) obtained by substituting adjusted coordinates into Equation (5). \[m^{\Delta X}=\pm\sqrt{\frac{\sum_{i=1}^{n}\left(v_{Pi}^{\Delta X}\right)^{2}}{ n-1}};m^{\Delta Y}=\pm\sqrt{\frac{\sum_{i=1}^{n}\left(v_{Pi}^{\Delta Y} \right)^{2}}{n-1}};m^{\Delta Z}=\pm\sqrt{\frac{\sum_{i=1}^{n}\left(v_{Pi}^{ \Delta Z}\right)^{2}}{n-1}} \tag{7}\]  
The current model for adjusting baseline vectors in the APPS (Equations (1)-(7)) employs a simplification; the post-processing results are, in fact, not equally accurate, because not all requirements for considering them equally accurate are satisfied. Namely, the observations used to determine the vectors in post-processing are recorded using various GNSS antennas and receivers in different observation and environmental conditions. Therefore, we validated a method for determining coordinates based on the adjustment of post-processing results (components of baseline vectors) with the unequally accurate observations method (UAM) with baseline vectors to the six nearest reference stations. The spatial distribution of the points in a network can also affect measurements that employ a network of reference stations. Hence, we wondered whether the quality of solutions is significantly affected if the number of baseline vectors is reduced from six to five for the EAM and UAM. Three-dimensional point coordinates are determined with the UAM using a procedure similar to the EAM, with Equations (4)-(7) replaced with Equations (8)-(12) below. Observation weights \(p_{i}^{\Delta X}\), \(p_{i}^{\Delta Y}\), \(p_{i}^{\Delta Z}\) in Equation (8) are determined using the mean errors of the vector's components (\(m_{Pi}^{\Delta X}\), \(m_{Pi}^{\Delta Y}\), \(m_{Pi}^{\Delta Z}\)) from post-processing. \[p_{i}^{\Delta X}=\frac{1}{\left(m_{Pi}^{\Delta X}\right)^{2}};p_{i}^{\Delta Y} =\frac{1}{\left(m_{Pi}^{\Delta Z}\right)^{2}};p_{i}^{\Delta Z}=\frac{1}{\left( m_{Pi}^{\Delta Z}\right)^{2}} \tag{8}\]  
\[\sum_{i=1}^{n}\biggl{[}p_{i}^{\Delta X}\cdot\left(p_{Pi}^{\Delta X}\right)^{2 }\biggr{]}=\text{min.};\;\sum_{i=1}^{n}\biggl{[}p_{i}^{\Delta Y}\cdot\left(p_ {Pi}^{\Delta Z}\right)^{2}\biggr{]}=\text{min.};\;\sum_{i=1}^{n}\biggl{[}p_{i }^{\Delta Z}\cdot\left(v_{Pi}^{\Delta Z}\right)^{2}\biggr{]}=\text{min.} \tag{9}\]  
In this case, the coordinates of point P are calculated as weighted means as follows (Equation (10)):  
\[X_{P}=\frac{\sum_{i=1}^{n}\bigl{(}p_{i}^{\Delta X}\cdot X_{P}^{i}\bigr{)}}{ \sum_{i=  
Note that, if the observation weights in Equation (8) are equal, the UAM adjustment is identical to the EAM adjustment. Furthermore, in the future, weighting based on the full covariance matrix may also be considered. To assess the spatial distribution of network points, we subdivided the territory of Poland by the mean baseline length and its standard deviation.