# Large-Scale Aircraft Pose Estimation System Based on Depth Cameras
## 2 Measurement Principles
### Preprocessing
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Filtering Method** & **Point Cloud Size** & **Filtering Parameter** \\ \hline Original point cloud & 256,796 & / \\ \hline \multirow{3}{*}{Pass-through filtering} & \multirow{3}{*}{16,899} & X Limits (\(-\)800, 300) \\  & & Y Limits (\(-\)400, 500) \\  & & Z Limits (1700, 2400) \\ \hline \multirow{3}{*}{Radius outlier removal} & \multirow{3}{*}{15,764} & Take the close points of the average = 3.0 \\  & & Threshold for the number of adjacent points = 1 \\ \hline Down-sampling & 4321 & Grid size = 10 mm \(\times\) 10 mm \(\times\) 10 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Filtering parameters and point cloud scale of each filtering stage. Figure 3: (**a**) Original point cloud captured by the depth camera; (**b**) model point cloud after pass-through filtering; (**c**) model point cloud after radius outlier removal; (**d**) model point cloud after down-sampling. \[p_{i}^{\prime}=p_{i}-c_{p}. \tag{2}\]  
The covariance matrix \(Cov\) of the cloud data of centroid point removal is calculated:  
\[Cov=\frac{1}{N}\sum_{i=1}^{N}p_{i}^{\prime}p_{i}^{\prime T}. \tag{3}\]  
After eigenvalue decomposition of \(Cov\), three eigenvalues, from large to small, and their corresponding eigenvectors are obtained: \(v_{1p}\), \(v_{2p}\), and \(v_{3p}\). The model point cloud takes the camera coordinate system as the basis, and the three feature vectors of the aircraft model are calculated and arranged from largest to smallest as \(e_{x}\), \(e_{y}\), and \(e_{z}\). The target coordinate system is constructed according to the following formulas:  
\[e_{x}=\frac{v_{1}}{\|v_{1}\|}, \tag{4}\]  
\[e_{y}=\frac{v_{2}}{\|v_{2}\|}, \tag{5}\]  
\[e_{z}=e_{x}\times e_{y}. \tag{6}\]  
The basis vector of the model coordinate system and depth camera coordinate system is used. The following formula is employed:  
\[R= \begin{bmatrix}v_{1p}^{T}v_{1q}&v_{1p}^{T}v_{2q}&v_{1p}^{T}v_{3q}\\ v_{2p}^{T}v_{1q}&v_{2p}^{T}v_{2q}&v_{2p}^{T}v_{3q}\\ v_{3p}^{T}v_{1q}&v_{3p}^{T}v_{2q}&v_{3p}^{T}v_{3q}\\ \end{bmatrix} , \tag{7}\]  
\[t=c_{p}-Rc_{q}. \tag{8}\]  
The transformation matrix of the target coordinate system and camera coordinate system is calculated. The CAD model of an aircraft is used for PCA principal direction correction, as illustrated in Figure 4. The \(XYZ\) axis direction is given, and the red point cloud represents the original point cloud, while the blue point cloud represents the point cloud after PCA normalization. Due to the limitations of the shape and scanning angle of the aircraft model, the point cloud of the aircraft model scanned by a single-depth camera is incomplete and morphologically inconsistent, which affects the accuracy of subsequent point cloud registration. Therefore, we use several depth cameras to scan the aircraft model at different positions, and fuse the collected point clouds. As illustrated in Figure 5, 16 depth cameras scan the calibration plate in four directions. Figure 4: Original point cloud and point cloud after PCA principal direction correction. The ICP algorithm is used to register the point cloud of the calibration plate, and the coordinate transformation matrix between the two depth cameras is obtained. The calibration plate is rotated, and the process is repeated until the exact position and pose of all ToF cameras are obtained. In Figure 6, the point clouds of the calibration plate scanned by the depth camera in different directions are indicated by different colors.