## 3 Results
### Test and Results  
To conduct the experiment, data were selected from four permanent GNSS stations that are simultaneously part of the IGS and EPN (EUREF Permanent GNSS Network) networks, namely, WTZR, HELG, PTBB, and WROC. This choice was made because the SOPAC [18] or CDDIS [26] databases contain the time series of these stations for the entire period of their operation, and the EPN website [27] provides information on their classification. The classification proposed there is aimed at identifying \"stable\" and \"reliable\" permanent stations and is based on the use of traditional mathematical apparatus. The time series were formed with a daily frequency for the period from 1 January 2018, to 31 December 2019, so the final number of series was 730 days. At all stations, identical LEIAR25.R4/R3 antennas were installed, although the receivers were from different manufacturers. Table 3 shows some technical characteristics of the selected stations. The data preparation procedure was the same for all stations: trend removal, the interpolation of missing data, and filtering. For filtering, the Symlet 4 Wavelet analysis of the first order was used. This filtering method reduced the amount of white noise and, at  
Figure 4: Histograms of the residual error distribution for north (**a**), east (**b**) and up (**c**) coordinate components. the same time, preserved the main properties of the signal. The results of the PS-NETM software are shown in Table 4.  
As can be seen from Table 3, the confidence intervals of the asymmetry for all coordinate components (N, E, U) at each station cover zero, except for HELG. The results of the statistical evaluation can be seen more clearly in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Station**} & \multicolumn{2}{c}{**RMSE, mm**} & \begin{tabular}{c} **Asymmetry and Its** \\ **Deviations** \\ \end{tabular} & \begin{tabular}{c} **Confidence** \\ **Interval for A** \\ \end{tabular} & \
\begin{tabular}{c} **Kurtosis and** \\ **Its Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Confidence** \\ **Interval for E** \\ \end{tabular} \\ \hline \multirow{3}{*}{WTZR} & N & 1.06 & 0.06 \(\pm\) 0.14 & \(-\)0.17, 0.29 & \(-\)0.02 \(\pm\) 0.19 & \(-\)0.33, 0.29 \\ \cline{2-7}  & E & 1.15 & 0.2 \(\pm\) 0.13 & \(-\)0.01, 0.41 & \(-\)0.15 \(\pm\) 0.17 & \(-\)0.43, 0.13 \\ \cline{2-7}  & U & 4.25 & \(-\)0.05 \(\pm\) 0.13 & \(-\)0.26, 0.16 & \(-\)0.35 \(\pm\) 0.1 & \(-\)0.51, \(-\)0.19 \\ \hline \multirow{3}{*}{HELG} & N & 1.18 & \(-\)0.46 \(\pm\) 0.15 & \(-\)0.71, \(-\)0.21 & 0.61 \(\pm\) 0.41 & \(-\)0.06, 1.28 \\ \cline{2-7}  & E & 1.3 & 0.19 \(\pm\) 0.15 & \(-\)0.06, 0.44 & 0.09 \(\pm\) 0.26 & \(-\)0.34, 0.52 \\ \cline{2-7}  & U & 4.23 & 0.11 \(\pm\) 0.13 & \(-\)0.1, 0.32 & \(-\)0.36 \(\pm\) 0.11 & \(-\)0.54, \(-\)0.18 \\ \hline \multirow{3}{*}{PTBB} & N & 1.46 & \(-\)0.03 \(\pm\) 0.13 & \(-\)0.24, 0.18 & \(-\)0.49 \(\pm\) 0.1 & \(-\)0.65, \(-\)0.33 \\ \cline{2-7}  & E & 1.2 & 0.07 \(\pm\) 0.13 & \(-\)0.14, 0.28 & \(-\)0.34 \(\pm\) 0.13 & \(-\)0.55, \(-\)0.13 \\ \cline{2-7}  & U & 4.38 & \(-\)0.11 \(\pm\) 0.13 & \(-\)0.32, 0.1 & \(-\)0.36 \(\pm\) 0.1 & \(-\)0.52, \(-\)0.2 \\ \hline \multirow{3}{*}{WROC} & N & 1.24 & \(-\)0.17 \(\pm\) 0.14 & \(-\)0.4, 0.06 & 0.16 \(\pm\) 0.18 & \(-\)0.14, 0.46 \\ \cline{2-7}  & E & 1.19 & \(-\)0.04 \(\pm\) 0.14 & \(-\)0.27, 0.19 & 0.01 \(\pm\) 0.2 & \(-\)0.32, 0.34 \\ \cline{2-7}  & U & 4.89 & \(-\)0.02 \(\pm\) 0.12 & \(-\)0.22, 0.18 & \(-\)0.56 \(\pm\) 0.08 & \(-\)0.69, \(-\)0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time series statistics for each of the selected stations.