## 3 Results and Discussion  
### Results  
#### 3.1.1 Step 1  
The results in Tables 2 and 3 show that: (a) method \(A\) was the only method with fixed integer ambiguities in all elevation angle conditions; (b) All differential methods (\(A\)-\(D\)) had fixed ambiguities in the 10\({}^{\circ}\) condition; and (c) the number of trajectories with fixed ambiguities was substantially reduced for methods \(D\) in the 30\({}^{\circ}\) and methods \(B\)-\(D\) in the 40\({}^{\circ}\) condition. Table 3 shows that method \(A\) had float ambiguities (real number ambiguities) for 8% of the time but as the only lacked time periods without solution (NaN). In the 40\({}^{\circ}\) condition methods \(B\)-\(E\) had substantial periods of time without solutions (NaN). Comparing method \(B\) and \(C\) in the 40\({}^{\circ}\) condition, method \(B\) managed to compute float (real number ambiguities) for a larger period of time, reducing the periods with no solution substantially compared to method \(C\). Table 4 shows the he system's overall performance, the combination of fixed and float solutions for the differential methods \(A\)-\(D\), hence the position differences between \(\mathbf{A}\)-\(\mathbf{E}\) and \(\mathbf{P_{REF}}\) (mean, median, \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{2}{c}{**\# of Trajectories with Fixed Solutions**} \\
**Elev. Angle** & \(\mathbf{10}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{40}^{\circ}\) \\ \hline Method \(A\) & 12 & 12 & 12 \\ Method \(B\) & 12 & 11 & 2 \\ Method \(C\) & 12 & 10 & 3 \\ Method \(D\) & 12 & 5 & - \\ Method \(E\) & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of trajectories with fixed positioning solutions when passing through the reference area. The total number of trajectories was 12.  
maximum and SD). Examining the mean and median of the position differences in Table 4 reveals that: (a) the position differences generally increased with increasing elevation angle; (b) the position differences (mean and median) and SD were larger in the Z dimension than in the XY dimension; (c) method \(E\) had the largest position difference mean, median, SD and maximal difference of all methods in all conditions; (d) in the conditions 10\({}^{\circ}\) and 30\({}^{\circ}\) the position differences (mean and median) were smallest for method \(A\), followed by \(C\), \(B\), \(D\) and \(E\); (e) the differences (mean and median) in the condition 40\({}^{\circ}\) were smallest for method \(A\), followed by \(C\), \(B\) and \(E\), while method \(D\) was unable to compute a differential solution; (f) method \(A\) was the only method with mean and median XYZ differences smaller than 7 cm in all elevation angle conditions; (g) in the 10\({}^{\circ}\) condition methods _A_-_C_ had mean and median XYZ differences smaller than 2 cm and SDs smaller than 4 cm. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Mean XYZ [m]**} & \multicolumn{3}{c}{**Mean XY [m]**} & \multicolumn{3}{c}{**Mean Z [m]**} \\ \cline{2-10}
**Elev. Angle** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** \\ \hline Method \(A\) & 0.00 & 0.02 & 0.30 & 0.00 & 0.01 & 0.09 & 0.00 & 0.01 & 0.28 \\ Method \(B\) & 0.01 & 1.02 & 4.28 & 0.00 & 0.48 & 1.27 & 0.00 & 0.90 & 3.99 \\ Method \(C\) & 0.01 & 0.47 & 0.82 & 0.00 & 0.34 & 0.27 & 0.00 & 0.33 & 0.76 \\ Method \(D\) & 0.95 & 1.35 & NaN & 0.48 & 0.44 & NaN & 0.78 & 1.18 & NaN \\ Method \(E\) & 1.88 & 3.60 & 12.22 & 1.09 & 1.92 & 3.17 & 1.32 & 2.74 & 11.72 \\ \hline  & \multicolumn{3}{c}{**Median XYZ [m]**} & \multicolumn{3}{c}{**Median XY [m]**} & \multicolumn{3}{c}{**Median Z [m]**} \\ \cline{2-10}
**Elev.