# Large-Scale Aircraft Pose Estimation System Based on Depth Cameras
## 2 Measurement Principles
### Preprocessing  
Point cloud filtering is the first step in point cloud data preprocessing. Noise points, holes, and outliers inevitably appear in the collected point cloud data, due to the measurement accuracy of the depth camera, multi-path interference, and the diffraction characteristics of electromagnetic waves. These outliers interfere with the accuracy of subsequent point cloud feature recognition and point cloud registration algorithms. Therefore, we use three filtering algorithms to improve the quality of the point cloud and reduce the amount of point cloud data. The three filtering algorithms used are pass-through filtering, radius outlier removal, and down-sampling. The point cloud filtering process is presented in Figure 2.  
Pass-through filtering is used to remove irrelevant point clouds outside of the target. Given the spatial scope of the model, the maximum and minimum values of the point cloud on the \(x\), \(y\), and \(z\) axes are set, and points whose values are not within the range are deleted. This achieves rapid elimination of irrelevant data points. The principle of radius outlier removal is to set the radius of a sphere, creating a sphere neighborhood, and to determine each point in the model point cloud. If the number of points in the sphere neighborhood of the point is greater than or equal to the set number of points, the point is preserved. If it is less than the set number of points, the point is removed. Radius outlier removal aims to remove noise, outliers, and sparse points in the model point cloud. The voxel grid filter is used to down-sample the model point cloud. This filter computes the cube convex hull based on the input point cloud. Setting the resolution splits the cube into smaller cubes, also known as voxels. Subsequently, all points in each voxel are approximated by the barycenter points in that voxel. The voxel grid filter deletes redundant points on the premise of preserving the geometric features of the point cloud surface, and keeps the point clouds at the same distance. For preprocessing before point cloud registration, the voxel grid filter compresses the point cloud data and improves the computing speed of point cloud registration. The original point cloud collected by the depth camera is presented in Figure 3a; Figure 3b-d shows the aircraft model point cloud through pass-through filtering, radius outlier removal, and down-sampling. The parameters of each filtering method used and the size of point cloud have been given in Table 1.  
Figure 1: Overview of the proposed large-scale aircraft pose estimation system. Figure 2: Process of point cloud filtering. An unaligned coordinate system between the model and depth camera results in angle coupling of the rotation angle obtained by the solution. In addition, point cloud registration error also leads to rotation angle error. Therefore, PCA [21] is used to establish the target coordinate system in order to achieve normalization of the model point cloud. The principle of PCA is to find a new basis for the input dataset, namely the principal component. The data in the principal component acquire the maximum degree of dispersion, leading to improved data representation. The steps to normalize the model with PCA are described below. The model point cloud is set as \(P=\left\{p_{i}\big{|}p_{i}\in R^{3},i=1,2,\ldots,m_{1}\right\}\), and the centroid of the point cloud is calculated. Thereafter, the centroid removal operation is performed:  
\[C_{P}=\frac{1}{n}\sum_{i=1}^{n}p_{i}, \tag{1}\]