## 4 Discussion and Applications
- the minimum observation window lasted 10 min,
11. - the maximum observation window lasted 5 h 00 min,
12. - the average length of the observation window was 1 h 11 min,  
The second stage of the research involved determination of the convergence time for the given accuracy (\(\leq\)0.05 m) using Galileo satellites only. As it was shown in Table 8, 46% of the performed initializations did not exceed 10 s, while for over 63% it was shorter than one minute. Only in one of the thirty analyzed cases, the convergence time was longer than 10 min. One of the reasons in this case may be the high PDOP value. However, if we take into account the fact that the constellation of Galileo satellites was not complete during the test measurements and only 14 satellites could be used, this result should be considered positive and very promising in the future. Because the Galileo constellation is scheduled to reach the target number of operational satellites over the next 3 years, and then continuity of measurements will be assured 24 h a day. Moreover, during the tests, a higher power of observed Galileo signals in comparison to GPS signals was found. The third stage included a detailed analysis of the accuracy of the RTK measurements. For this purpose, 36 independent RTK measurements series were made 10 s interval, at the cut horizontal angle of 10\({}^{\circ}\). The duration of the series ranged from 30-60 min. In individual series, 160 to 360 measurements were registered. The absolute (true) errors of time series of coordinates of the same control point were determined in the first place. Then, on their basis, the systematic errors of measurements were determined empirically (formula (1)) together with the length of confidence intervals (d/2) at a confidence level of 0.95 for each measurement series and individual coordinates (Table 9). It was shown that systematic errors are contained in the intervals: \(\delta_{x}^{j}\in[-0.0171;0.0238]\) m, \(\delta_{y}^{j}\in[0.0059;0.0306]\) m, \(\delta_{h}^{j}\in[-0.0068;0.0330]\) m.  
Next, average errors of a single measurement were determined (Table 11) in two variants (Formulas (2) and (3)), the first one did not take into account the reduction of absolute errors with the value of systematic errors, while the second one eliminated systematic errors from the observations. It was shown that the elimination of systematic errors significantly improves the accuracy of the average errors of a single measurement. The systematic errors depend on the quality of the constellation of satellites (PDOP) and from a specific set of satellites that is involved in the determination of the position. It was shown (Table 12) that the average errors of a single RTK measurement based on a Galileo navigation system only are, respectively: for the northern coordinate (\(x\)): \(m_{\Delta x}=\pm 0.0151\)\(m\), for the eastern coordinate (\(y\)): \(m_{\Delta y}=\pm 0.0291\)\(m\), for the height (\(h\)): \(m_{\Delta h}=\pm 0.0294\)\(m\). The elimination of systematic errors improves the accuracy of the average error of a single RTK measurement for the northern coordinate (\(x\))--of about 9%, for the eastern coordinate (\(y\))--of about 68% and for the height (\(h\))--of about 23%. Due to the well-known features and advantages of global navigation systems, the results presented above can be considered as the reliable for a wider area of Poland and even for Central and Eastern Europe. In order to confirm and increase their credibility, this type of research is needed elsewhere in Europe and in the world. However, it depends not only on the availability of Galileo satellites, but also on the ground infrastructure enabling corrections to RTK measurements.