# Estimation of Antenna Pose in the Earth Frame Using Camera and IMU Data from Mobile Phones
## 6 Experimental Results
### Pose Estimation on Antennas
#### 6.3.2 Extrinsic Camera Calibration from Pattern and SfM  
We also evaluated the performance of our method when the camera is extrinsically calibrated using an SfM technique. We substituted the extrinsic camera parameters obtained from the checkerboards in Section 6.2.2 with results obtained from an SfM implementation in OpenMVG [55] while leaving all other details of the configurations unchanged. Figure 14 and Table 5 show the resulting estimation errors. Whereas nine out of 65 (or 13.8%) of the data cases failed to yield an estimate with a downtilt error of no more than 1.5 degrees and an azimuth error of no more than 15 degrees when the SfM technique was used, as seen from Figure 14, the majority of the results (at least 75%) show a precision comparable to that of the results obtained using a calibration pattern, as indicated by the first three quartiles reported in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Downtilt**} & \multicolumn{4}{c}{**Azimuth**} \\ \hline
**Method** & **Default** & [37] & [50] & [51] & **Ours** & **Default** & [37] & [50] & [51] & **Ours** \\ \hline
**Mean** & 0.87 & 0.49 & 0.76 & **0.45** & 0.47 & 7.14 & 7.19 & 7.26 & 7.18 & **5.60** \\
**Std.** & 0.39 & 0.29 & 0.36 & **0.26** & 0.27 & 4.20 & 4.14 & 4.17 & 4.13 & **2.62** \\
**Max** & 2.08 & 1.41 & 2.12 & **1.32** & 1.38 & 17.17 & 17.93 & 18.23 & 17.84 & **12.02** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison with state-of-the-art camera-IMU calibration methods in terms of antenna downtilt and azimuth angles. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Downtilt**} & \multicolumn{4}{c}{**Azimuth**} \\ \cline{2-7}  & **PWP3D** & **D2 CO** & **Ours** & **PWP3D** & **D2 CO** & **Ours** \\ \hline
**Mean** & 0.93 & 0.6 & **0.47** & 6.83 & 5.98 & **5.6** \\
**Std.** & 1.37 & 0.38 & **0.27** & 4.35 & 4.23 & **2.62** \\
**Max** & 10.08 & 1.53 & **1.38** & 23.01 & 19.36 & **12.02** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation errors achieved using PWP3D, D2 CO and our method. The few unsatisfactory estimates are strongly related to the accuracy of the SfM calibrations. To demonstrate this, we first measured the SfM accuracy against the calibration results obtained using the checkerboards by comparing the corresponding camera rotations relative to the first viewpoint for both calibration results for each data group, where the largest rotation angle was treated as the SfM accuracy. The histogram of the rotation angles is shown in Figure 15, in which seven of the nine data groups with the largest errors (larger than 1.5 degrees) also appear among the nine instances of unsatisfactory estimates, demonstrating the strong connection between the estimation error and the SfM accuracy. Moreover, we find that the failures in the SfM experiment can be identified from the results of the coarse visual pose estimation stage: the projection of the center point of the recovered 3D principal axis falls outside of the antenna contour from at least one viewpoint, as demonstrated in Figure 16. This situation arises in all nine of the unsuccessful estimations and can be used to trigger an instruction to the end user to capture more images or to manually select matching features in the SfM procedure to overcome the problem. Figure 14: The estimation errors for each group of data from AntennaS when the camera was extrinsically calibrated using an SfM technique implemented in OpenMVG. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Downtilt**} & \multicolumn{2}{c}{**Azimuth**} \\ \cline{2-5}  & **SfM** & **Pattern** & **SfM** & **Pattern** \\ \hline
**Min** & 0.08 & 0.02 & 0.79 & 1.20 \\
**Q1** & 0.22 & 0.27 & 3.63 & 3.70 \\
**Q2** & 0.36 & 0.43 & 6.74 & 5.59 \\
**Q3** & 0.64 & 0.61 & 9.60 & 6.97 \\
**Mean** & 0.66 & 0.47 & 7.84 & 5.60 \\
**Std.** & 1.03 & 0.27 & 5.45 & 2.62 \\
**Max** & 7.32 & 1.38 & 26.90 & 12.02 \\ \hline \hline \end{tabular}
\end{table}