## 5 Experiment Design and Test Results
### Positioning Solution
The elevation model was characterized by the lowest efficiency of integer ambiguity estimation and validation compared to other experiments, and the efficiency increased along with including additional correlation parameters in the stochastic model. A dozen or so times higher number of incorrectly fixed ambiguities than in the single-system GPS solution proves that adopting the same stochastic parameters for all systems is erroneous and disrupts the solution reliability for Multi-GNSS positioning. The use of the empirical model ensures 100% effectiveness of AR and gives the lowest maximum errors (15.2 mm) among all tested scenarios. \begin{table}
\begin{tabular}{l l c c c c c c c} \hline
**GNSS** & \multicolumn{3}{c}{**Stochastic Model**} & \multicolumn{3}{c}{**Ambiguity Resolution**} & \multicolumn{3}{c}{**Positioning Accuracy [mm]**} \\
**System** & **Model** & **Cross** & **Time** & **P succ. [\%]** & **FA/FR** & **RMS (ne)** & **RMS (u)** & **Err. \(<5\)** & **Max (err.)** \\ \hline G-(5Q)E(-5Q) & Elev. & – & – & 99.8 (128) & 33/0 & 2.5 & 7.6 & 14.3\% & 18.7 \\ G-(5Q)E(-5Q) & C/N\({}_{0}\) & – & – & 100 (0) & 0/0 & 2.0 & 6.3 & 33.8\% & 17.2 \\ \hline G-(5Q)E(-5Q) & Elev. & ✓ & – & 99.9 (124) & 36/0 & 2.4 & 7.2 & 19.2\% & 18.7 \\ G-(5Q)E(-5Q) & C/N\({}_{0}\) & ✓ & – & 99.9 (1) & 1/0 & 1.9 & 5.5 & 48.1\% & 16.6 \\ \hline G-(5Q)E(-5Q) & Elev. & ✓ & ✓ & 99.9 (100) & 30/13 & 2.3 & 6.9 & 25.6\% & 18.8 \\ G-(5Q)E(-5Q) & C/N\({}_{0}\) & ✓ & ✓ & 100 (0) & 0/0 & 1.9 & 5.7 & 46.8\% & 17.0 \\ G-(5Q)E(-5Q) & C/N\({}_{0}\)(b) & ✓ & ✓ & 100 (0) & 0/0 & 1.9 & 5.6 & 48.1\% & 16.9 \\ \hline \end{tabular}
\end{table} 
Table 6: Positioning model solution results for GPS + Galileo. \begin{table}
\begin{tabular}{l l c c c c c c c} \hline
**GNSS** & \multicolumn{3}{c}{**Stochastic Model**} & \multicolumn{3}{c}{**Ambiguity Resolution**} & \multicolumn{3}{c}{**Positioning Accuracy [mm]**} \\
**System** & **Model** & **Cross** & **Time** & **P succ. [\%]** & **FA/FR** & **RMS (ne)** & **RMS (u)** & **Err. \(<5\)** & **Max (err.)** \\ \hline G & Elev. & – & – & 99.7 (258) & 127/4 & 4.7 & 8.9 & 27.1\% & 58.1 \\ R & C/N\({}_{0}\) & – & – & 99.8 (218) & 218/0 & 4.4 & 7.3 & 31.5\% & 35.7 \\ \hline R & Elev. & ✓ & – & 99.6 (330) & 214/4 & 4.7 & 8.8 & 27.2\% & 58.9 \\ R & C/N\({}_{0}\) & ✓ & – & 99.9 (50) & 50/0 & 4.5 & 7.4 & 30.8\% & 36.0 \\ \hline R & Elev. & ✓ & ✓ & 99.6 (218) & 129/5 & 4.5 & 8.6 & 29.5\% & 58.1 \\ R & C/N\({}_{0}\) & ✓ & ✓ & 100 (0) & 0/0 & 4.4 & 7.2 & 32.6\% & 37.3 \\ R & C/N\({}_{0}\)(b) & ✓ & ✓ & 100 (0) & 0/0 & 4.4 & 7.2 & 33.0\% & 37.1 \\ \hline \end{tabular}
\end{table} 
Table 5: Positioning model solution results for GLONAS. Figure 24 shows a summary of position errors for all tested scenarios for three stochastic approaches: the elevation-dependent model, the elevation model including the time- and cross-correlation (denoted as \"Elev.+C.\") and individual for satellite blocks empirical model including correlation parameters (denoted as \"C/N\({}_{0}\)(b)+C.\"). The 3D position error statistics are shown in the form of a box plot, where a central mark of the box indicates the median, the top and bottom edges of the box mark the 75 th and 25 th percentiles of errors, and the whiskers are extended to the most extreme values of errors not considered outliers for a confidence level of approximately 99%. A red dot marks the maximum position error for each scenario. These statistics confirm that the positioning accuracy is increasing when considering the empirical stochastic parameters of measurement properties. The greatest accuracy characterizes the GPS and GPS + BeiDou solutions (with median 3.9 mm and 3.7 mm, respectively), while for the GPS + Galileo solution very low maximum errors were obtained (16.9 mm). The optimal compromise is the Multi-GNSS solution, where high accuracy (with median 4.3 mm) and the lowest maximum error (15.2 mm) are achieved.