## 3 Results
### Structure of the PS-NETM Software  
PS-NETM is a software product whose main purpose is the statistical analysis of time series of permanent GNSS station coordinates based on the use of mathematical methods of statistics and NETM. Structurally, the PS-NETM software product consists of several modules. Figure 1 shows a brief description of each of them. \begin{table}
\begin{tabular}{l l} \hline \hline
**Result** & **Diagnosis by Result** \\ \hline Confirmation of hypotheses: & There is no need to apply NETM. \\ (\(H_{0}\colon\, A=0\)), (\(H_{0}\colon\,\varepsilon=0\)) & There is no need to apply NETM. \\ \hline Confirmation of hypotheses: & There is an effect of weak systematic errors that were not excluded when processing GNSS observations. An evaluation by NETM \\ (\(H_{0}\colon\, A=0\)), (\(H_{0}\colon\,0<\varepsilon<1.2\)) & \\ (\(H_{0}\colon\, A=0\)), (\(H_{0}\colon\,\varepsilon<0\)) & methods is required. \\ \hline Confirmation of hypotheses: & \\ (\(H_{0}\colon\, A<0\)) i (\(H_{0}\colon\,\varepsilon=0\)) & \\ (\(H_{0}\colon\, A>0\)) i (\(H_{0}\colon\,\varepsilon=0\)) & Significant data pathology. Evaluation is \\ (\(H_{0}\colon\, A<0\)) i (\(H_{0}\colon\,\varepsilon<0\)) & not possible. \\ (\(H_{0}\colon\, A<0\)) i (\(H_{0}\colon\,\varepsilon>0\)) & \\ (\(H_{0}\colon\, A>0\)) i (\(H_{0}\colon\,\varepsilon<0\)) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diagnostics of mathematical modeling by residual errors. The first five modules (see Figure 1) are aimed at the preliminary processing of input data. 1. Reading data from a specified file (if the time series has already been generated) or a folder with pos-files (PS-NETM_readcoords module);
2. Converting from a geocentric to topocentric coordinate system if necessary (PS-NETM_XYZ_to_NEU module);
3. Removing random outliers from the time series using the modified Z-score method (PS-NETM_filters module);
4. Resampling the time series and interpolating missing data using the linear interpolation method. (PS-NETM_readcoords module);
5. Removing the constant component (trend) by fitting linear regression of the first degree. Once all five procedures have been performed, preprocessing is considered complete. The next step is to filter the time series. PS-NETM supports the following two filtering methods: EMD (Empirical Mode Decomposition) filter and Wavelet analysis. The EMD method is a signal decomposition method that was first proposed in [24]. It is a data-driven method that can decompose a nonlinear and nonstationary signal into a finite number of components called intrinsic mode functions (IMFs). EMD can adapt to the characteristics of the signal and reveal its underlying structure without any prior assumptions. EMD is a widely used method for reducing noise influence on GNSS time series; its main feature is that the filtering process is completely \"unbiased\", meaning that no prior assumptions are made about its signal structure. For our software, we incorporated Ensemble EMD (EEMD), which is an improved version of EMD. It is more computationally expensive but mitigates the main drawback of a regular EMD, mode mixing, by adding white noise to the original signal before applying EMD. Wavelet transformation is a mathematical tool that decomposes a signal into different frequency components and then studies each component with a resolution matched to its scale. Wavelet transformations are classified into two different types as follows: discrete wavelet transform (DWT), which uses a set of orthogonal wavelet basis functions (so-called \"mother wavelets\"), and continuous wavelet transform (CWT) which uses a continuous wavelet transform (CWT). Wavelet transform is a wavelet transform (CWT) which uses a continuous wavelet transform (CWT) which uses a  
family of wavelet functions. In PS-NETM, two discrete wavelets are available as denoising options-Symlet4 and Coiflet5. Both of these wavelets are modifications of Daubechies wavelets, although they possess slightly different characteristics.