# Large-Scale Aircraft Pose Estimation System Based on Depth Cameras
## 3 Experiments and Results
They can be calculated via the following formula:  
\[R=\sqrt{\frac{\sum\limits_{i=1}^{n}(\theta_{i}-\theta^{\prime})}{n-1}}, \tag{20}\]  
where \(\theta\) represents the angle measurement error and \(\theta^{\prime}\) represents the average value of the angle measurement error. The standard deviations of the measurement errors of the yaw angle, pitch angle, and roll angle of the model were \(0.0507^{\circ}\), \(0.0583^{\circ}\), and \(0.0628^{\circ}\), respectively. The experiment thus verifies the feasibility of our proposed pose measurement system. For the three aircraft model point clouds, we use several different registration methods for comparison with our proposed method. The accuracy registration results were classified and averaged, and are listed in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Time (ms)** & **Score** \\ \hline ISS + SHOT & 28.712 & 1.066 \\ ISS + PFH & 41.312 & 1.895 \\ ISS + FPFH & 37.386 & 2.379 \\ NARF + SHOT & 257.903 & 17.570 \\ NARF + FFH & 298.447 & 24.796 \\ NARF + FPFH & 285.421 & 28.633 \\ HARRIS + SHOT & 145.142 & 7.296 \\ HARRIS + PFH & 136.381 & 7.731 \\ HARRIS + FPFH & 177.272 & 5.427 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RANSAC coarse registration results with different feature descriptors and key point extraction methods (average point cloud size: 4321). Figure 11: Aircraft pose measurement scenario. Figure 12: (**a**) Yaw angle measurement error; (**b**) pitch angle measurement error; (**c**) roll angle measurement error. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Time (ms)** & **Mean Angle Error (\({}^{\circ}\))** \\ \hline OURS & 67.591 & 0.068 \\ ICP & 139.640 & 0.863 \\ VG-ICP & 116.673 & 0.173 \\ GO-ICP & 362.842 & 0.223 \\ NDT & 311.973 & 2.380 \\ RPM-Net & 1183.240 & 0.018 \\ FGR & 849.924 & 0.127 \\ LM3D & 2671.333 & 0.012 \\ DEEPVCP & 7893.679 & 0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of registration methods (average point cloud size: 3851). The ISS key point extraction method exhibits good repeatability with regard to the point cloud data of an aircraft model after fusion, and can suitably cooperate with other feature descriptors. The SHOT feature descriptor encodes the geometric attributes of feature points and their neighborhood points via a local reference frame (LRF), which can adequately describe situations in which the wing or other normal directions change greatly in point cloud models of large-sized aircraft. A RANSAC coarse registration algorithm was used to remove the mismatched points and obtain the correctly matched feature points. Good initial pose estimation improves the accuracy and speed of the point cloud precision registration algorithm. The accuracy of the registration results of ICP depends on the accuracy of the coarse registration results. If the coarse registration error is large, the ICP cannot be corrected independently. Therefore, for point cloud registration with large changes, accurate coarse registration results are important. As seen in Table 5, our method has advantages in both speed and accuracy and can maintain a fast calculation speed and high registration accuracy for different models and point cloud densities. Although deep learning algorithms such as RPM-Net [27], LM3D [28], and DeepVCP [29] can achieve better registration accuracy, a single run takes a long time; therefore, these methods are not suitable for application scenarios requiring high-speed measurement.