## 4 Results
### Comparison with Formal Calibration
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Mean Error** & **Std Deviation Error** & **Maximum Error** \\ \hline Soft calibration & 0.241\({}^{\circ}\) & 0.202\({}^{\circ}\) & 0.646\({}^{\circ}\) \\ Formal calibration & 0.157\({}^{\circ}\) & 0.146\({}^{\circ}\) & 0.440\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Errors in the calculation of the rotation angle using emitters 1 and 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Error Using Calculated Height**} & \multicolumn{3}{c}{**Error Using Known Height**} \\ \hline
**Indexes of the Emitters** & **Mean** & **Std** & **Max** & **Mean** & **Std** & **Max** \\ \hline
2–4 & 20.2 mm & 7.9 mm & 42.4 mm & 13.7 mm & 7.5 mm & 34.1 mm \\
3–4 & 24.9 mm & 11.6 mm & 54.1 mm & 8.6 mm & 6.5 mm & 26.9 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Positioning errors using two emitters obtained by a weak calibration procedure. Figure 8: Receiver positioning errors shown graphically by calculating the height. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Error Using Calculated Height**} & \multicolumn{3}{c}{**Error Using Known Height**} \\ \hline
**Indexes of the Emitters** & **Mean** & **Std** & **Max** & **Mean** & **Std** & **Max** \\ \hline
2–4 & 15.1 mm & 6.3 mm & 31.3 mm & 8.9 mm & 5.8 mm & 27.1 mm \\
3–4 & 11.8 mm & 6.3 mm & 27.7 mm & 9.2 mm & 5.2 mm & 25.1 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Positioning errors using two emitters obtained by formal calibration. Up to this point, the results shown have been those obtained after a single run. Since a random error was introduced in the receiver position, the results are particular to that particular execution. To avoid this situation, the results shown are for 100 runs. Table 5 shows the average and SD values for the 100 runs with the average positioning error of the 44 receiver positions for the two combinations of emitters, for calculated or known height. Similarly, in Table 6, the same data are shown for the standard deviations of the positioning error of the 44 positions. In addition, three cases are shows in detail:  
* Case 1. Same case as shown above. The error in the positioning of the receiver is a random error with a standard deviation of 5 mm and the error in the positioning of the emitters is limited to \(\pm\)2 cm. * Case 2. The error in the positioning of the receiver is a random error with a standard deviation of 10 mm, and the error in the positioning of the emitter is limited to \(\pm\)3 cm. * Case 3. The error in the positioning of the receiver is a random error with a standard deviation of 20 mm, and the error in the positioning of the emitter is limited to \(\pm\)4 cm. It can be seen how the results shown are higher than those shown in the Table 2, because the calibration was performed with lower error values (random errors). Even so, the average errors were below 33 mm when the height was calculated and below 16 mm when the height was known. It can be seen that even when emulating a very bad receiver position measurement, case 3, the errors were below 45 mm and below 24 mm for calculated and known height, respectively. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Error Using Calculated Height (mm)**} & \multicolumn{6}{c}{**Error Using Known Height (mm)**} \\ \cline{2-13} \multirow{2}{*}{**Indexes of the Emitters**} & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 3**} & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 3**} \\ \cline{2-13}  & **Mean** & **std** & **Mean** & **std** & **Mean** & **std** & **Mean** & **std** & **Mean** & **std** & **Mean** & **std** \\ \hline
2–4 & 18.8 & 9.9 & 18.2 & 8.2 & 20.3 & 10.9 & 7.4 & 1.6 & 8.6 & 2.3 & 11.1 & 3.6 \\
3–4 & 17.4 & 6 & 18.7 & 5.7 & 19.1 & 6.8 & 10.2 & 2.5 & 11.1 & 3.7 & 12.6 & 4.8 \\ \hline \hline \end{tabular}
\end{table}