# Estimation of Antenna Pose in the Earth Frame Using Camera and IMU Data from Mobile Phones
## 6 Experimental Results
### Comparison with State-of-the-Art Methods
#### 6.2.2 Visual Pose Estimation Methods  
For a comparison of our visual pose estimation method with PWP3D [35] and D2 CO [32], each method was plugged into our overall pipeline for the estimation of the antenna downtilt and azimuth angles, and the estimation results were then evaluated against the ground truth. The camera-IMU calibration parameters were obtained from the results of our calibration method on BoardL with \(w\) set to 0.1.  
To ensure a fair comparison, we slightly modified the two existing methods. For PWP3D, we used the multi-view version and replaced the foreground/background probabilistic model with a deterministic one based on antenna silhouettes to eliminate errors in its segmentation step; for D2 CO, we trivially extended it to obtain a multi-view version by accumulating the costs from each view, which is the strategy adopted in PWP3D. To initiate each method, we used our approximate poses, whose projections in each view show extensive overlap with the ground truth, as shown in the first column of Figure 12.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **Type** & **Default** & [37] & [50] & [51] & [44] & **Ours\({}^{1}\)** & **Ours\({}^{2}\)** \\ \hline \multirow{2}{*}{_hall_} & **downtilt** & 0.87/0.45 & 0.41/0.28 & 0.62/**0.25** & 0.55/0.36 & 6.57/0.26 & **0.39/0.28** & **0.40/0.28** \\  & **azimuth** & 4.81/3.96 & 5.07/3.84 & 4.91/3.88 & 5.02/3.88 & **4.37/2.21** & 5.09/3.85 & **3.87/2.90** \\ \hline \multirow{2}{*}{_balcony_} & **downtilt** & 0.52/0.27 & 0.36/**0.13** & 0.74/0.27 & **0.35**/0.15 & 3.89/2.23 & **0.36/0.13** & **0.36/0.13** \\  & **azimuth** & 4.39/4.42 & 5.60/4.82 & **4.24/2.35** & 5.29/4.71 & 6.45/5.45 & 5.30/4.53 & **3.52/2.41** \\ \hline \multirow{2}{*}{_BoardF_} & **downtilt** & 0.86/0.44 & **0.41/0.28** & 0.57/**0.25** & 0.55/0.37 & 4.48/2.34 & **0.41/0.28** & **0.42/0.28** \\  & **azimuth** & 5.51/4.44 & 5.52/4.50 & 5.53/**4.43** & **5.50/4.53** & 5.93/4.46 & 5.53/4.54 & **3.51/2.18** \\ \hline \hline \end{tabular}  
**In Ours\({}^{1}\): \(\mathbf{w=0}\); in Ours\({}^{2}\): \(\mathbf{w=0.1}\).**  
\end{table}
Table 2: Comparisons of typical camera-IMU calibration methods in terms of downtilt and azimuth estimation. The values before and after the slash represent the mean error and standard error, respectively. The best results are shown in bold, and the next-to-best results are shown in bold italics.  
In Figure 13, the distributions of the estimation errors are shown as cumulative histograms. We first note that all three methods yield satisfactory results on more than 90% of the data, which demonstrates the success of the initialization using our approximated poses. However, there are several exceptions in which PWP3D and D2 CO fail to find the optimal poses, as shown toward the right end of the X axis ; the results for three of these cases are shown in Figure 12, together with the initial poses and the results of our method.  
Table 3 presents the quantitative results for the three methods, where our method shows the lowest mean, standard and maximum errors.  
Figure 12: Examples from three groups of data (a single viewpoint for each) for which Pixel-Wise Posteriors for 3D tracking and segmentation (PWP3D) and direct directional chamfer optimization (D2 CO) both yield unsatisfactory estimates (images are cropped because of space limitations). The white parts are antenna silhouettes in images, and the red curves are contours of antenna projections in estimated poses.  
Figure 13: Error distributions for downtilt (left) and azimuth (right) estimation using the three methods.