## 3 Results and Discussion  
The mathematical model from Chapter 2 was implemented in the Mathcad 15 software, which conducted statistical calculations and analyses using the data from the measurement campaigns mentioned in the previous subchapter. For each of the IHO orders (which are characterized by different allowable position errors), the availability function value was calculated. Figure 6 shows an example of three availability functions: \(A1(t),\ A2(t),\ A3(t)\), determined based on Equation (17), as well as their limit values: \(A1,\ A2,\ A3\), calculated based on Equation (18) for the maximum allowable position errors corresponding to the IHO orders: special (2 m), 1a/1b (5 m), and 2 (20 m). Diagrams of the availability functions for the orders 1a and 1b were combined because of the identical requirements. Analogous calculations were conducted for the measurement results of the DGPS and EGNOS systems, as well as multi-GNSS receivers (installed in Samsung Galaxy smartphones). The summary results are listed in Table 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Statistics of Position Error**} & \multicolumn{6}{c}{**Samsung Galaxy Series**} \\ \cline{2-7}  & **Y** & **S3 Mini** & **S4** & **S5** & **S6** & **S7** \\ \hline Number of measurements & 6,041 & 3,410 & 10,950 & 10,939 & 10,906 & 10,926 \\
2 DRMS (2D) & 9.47 m & 5.23 m & 6.59 m & 6.72 m & 8.32 m & 10.54 m \\ R95 (2D) & 6.84 m & 3.67 m & 5.80 m & 5.77 m & 9.38 m & 9.62 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics for the Samsung Galaxy phones’ predicted position errors over the course of a dynamic measurement campaign [36]. Figure 6: Availability functions: \(A1(t)\), \(A2(t)\), and \(A3(t)\) and their limit values: \(A1\), \(A2\), and \(A3\). These correspond to four IHO orders: special (red colour), 1a/1b (blue colour), and 2 (brown colour). The analysis of the DGPS system testing results for stationary and dynamic measurements clearly demonstrates that the system complied with all the requirements set out for all IHO orders. Hence, it can be applied while carrying out hydrographic surveys, irrespective of the order. The results presented are consistent with results of studies by other authors [39]. Having compared the DGPS and EGNOS solutions, it should be noted that the DGPS system ensured a slightly greater availability than the EGNOS system did in terms of hydrographic survey needs. What needs an additional comment is the result for the availability of the EGNOS system (Table 4), which in the course of stationary measurements, amounted to 89.11% for the IHO special order without reaching the minimum value (95%). In the author's opinion, since the presented multi-annual research results prove that this system permanently improves the positioning characteristics, its use in hydrography will soon be possible for all IHO orders. A significant increase in the EGNOS system's accuracy over recent years has also been noted by other authors [40; 41] and official regulations [42]. Despite this fact, the EGNOS system is still not used in hydrography [43], as one would expect. An unambiguous assessment of the possibility for using multi-GNSS receivers in hydrography requires an alternative form of result presentation due to significant differences in the results of stationary and dynamic tests. Figure 7 presents diagrams of the availability of particular positioning solutions for both stationary and dynamic measurements, dividing them into two orders: special and 1a/1b. The final order, order 2, required no separate analysis as the interpretation of results from Table 4 is clear. While assessing multi-GNSS receivers in the context of the possibility for ensuring the required accuracy for the special order, one should note the significant difference in the results of both stationary and dynamic measurements, particularly for models S4 and S5.