## 3 Results
### Results of Static Surveys Using a Single Receiver from Smart Station Set  
In the case of static surveys using a single receiver from a smart station set, the differences between reference coordinates from model static GNSS occupation and the results from single receiver were considered. The calculated differences from the model static GNSS coordinates and the results of the post-processing from the single receiver static survey are present below in Figure 3a-i. Figure 3: _Cont._  
Figure 3: Differences of coordinates between reference coordinates from model static GNSS occupation and rapid static surveys (in subfigures **a**–**i** are presented differences in meters with commas as decimal signs). Additionally, Dilutions of Precision (DOP) parameters and root mean square (RMS) errors of analyzed scenarios of measurements were considered. In accordance with the literature [37] in science and engineering, the probability density curve is often of a particular shape known as a normal distribution (the Gaussian law of errors). To quantify such a distribution or dispersion of possible errors with a single number, we use the standard deviation (\(\sigma\)). We can determine \(\sigma\) experimentally by using a large number of observations and calculating the square root of the sum of the squares of the errors in the observations divided by one less than the number of observations (n). It is a method of computing \(\sigma\) as the RMS error with a probability of 68.3% [37], for example, in the case of X coordinate, \(\sigma_{X}=\sqrt{\sum D_{X}^{2}/(n-1)}\). When researching a three-dimensional position (using \(X\), \(Y\), and \(Z\) coordinates), \(RMS=\sqrt{\sigma_{X}^{2}+\sigma_{Y}^{2}+\sigma_{Z}^{2}}\). Generally, satellite positioning accuracy is measured using the combined effect of the unmodeled measurement errors of pseudo-range (\(\sigma\)) and the effect of satellite geometry (DOP). The Dilutions of Precision can be measured using a single non-dimensional coefficient, where a low DOP coefficient represents a better positional precision due to the wider angular reparative between the satellites used to calculate a user's position. So, the lower the value of this coefficient, the better the geometric strength and vice versa [30]. The various DOP forms are used [38]; the Geometric Dilution of Precision (GDOP) coefficient determines the multiplication factor of the estimation of total position and time errors. The Horizontal Dilution of Precision (HDOP represent the contribution to the 2D positioning accuracy) \(HDOP=\sqrt{\sigma_{X}^{2}+\sigma_{Y}^{2}}/\sigma\), the Vertical Dilution of Precision (VDOP represent the contribution to the altitude accuracy) \(VDOP=\sqrt{\sigma_{Z}^{2}}/\sigma\), and the Position Dilution of Precision (PDOP represents the contribution of the satellite geometry to the 3D positioning accuracy) \(PDOP=\sqrt{\sigma_{X}^{2}+\sigma_{Y}^{2}+\sigma_{Z}^{2}}/\sigma\). The extreme value of the DOP and RMS for realized scenarios of measurements were stated and the results are presented in Table 1.  
Today's surveyors are more interested in the concept of the maximum error, which varies from 95% to the 99% probability limits [39]. For the post-processing accuracy estimation of fast static GNSS surveying, in accordance with technical characteristics of the typical satellite receivers [40]: \(\pm 3\) mm + 0.5 ppm \(\times\) D for horizontal (Hz) component and \(\pm 5\) mm + 0.5 ppm \(\times\) D for vertical (V) component, where D is the distance to the nearest reference station were used. In analyses considering standard uncertainty, both horizontal and vertical components are accounted for together (about 68% probability) \(U_{68}(3D)=\sqrt{[u^{2}(Hz)+u^{2}(V)]}\). Multiply by a coverage factor (k) an use the fairly standard coverage factor of 3 too, which provides a coverage probability (confidence level) of approximately 99%.