# Large-Scale Aircraft Pose Estimation System Based on Depth Cameras
## 2 Measurement Principles
### Registration
Thereafter, all local histograms are combined to form a SHOT descriptor with a dimension of \(b\times 32\). The main goal of point cloud registration is to find the optimal transformation matrix between two different point clouds. Point cloud registration can be divided into coarse  
Figure 7: Model point cloud using the ISS key point extraction algorithm. point cloud registration and fine point cloud registration. The function of coarse point cloud registration is to roughly align two frames of point clouds that are far apart with the aim of providing a good initial estimate for subsequent fine point cloud registration. Since noise in the model point cloud and other factors may cause mismatches in feature matching, the RANSAC algorithm [24] is required to remove these mismatches. The core principle of the RANSAC algorithm is to iteratively find valid intra-office points from a dataset containing out-of-office points. In the application of mismatch elimination, intra-office points are the correctly matched feature point pairs, whereas out-of-office points are the mismatched feature point pairs. More intra-office points can be obtained by iteratively updating the transformation matrix. The steps are as follows:  
1. Randomly select \(n\geq 3\) groups of corresponding points from the feature-matching sets of two point clouds \(P\) and \(Q\). 2. Calculate the transformation matrix according to the selected corresponding points (\(p\), \(q\)): \[ \begin{bmatrix}x_{q}\\ y_{q}\\ z_{q}\\ 1\end{bmatrix} = \begin{bmatrix}r_{11}&r_{12}&r_{13}&t_{x}\\ r_{21}&r_{22}&r_{23}&t_{y}\\ r_{31}&r_{32}&r_{33}&t_{z}\\ 0&0&0&1\end{bmatrix}\begin{bmatrix}x_{p}\\ y_{p}\\ z_{p}\\ 1\end{bmatrix} =H \begin{bmatrix}x_{p}\\ y_{p}\\ z_{p}\\ 1\end{bmatrix} .\] (14)
3. Use \(H\) to rotate and translate point cloud \(P\) to obtain \(P^{\prime}\). 4. The variance of the Euclidean distance of the point cloud is used to construct the evaluation function, and the evaluation scores are calculated according to \(P^{\prime}\) and \(Q\). The pairs of feature points whose scores are smaller than the threshold value are included in the intra-office points, while the rest are excluded as out-of-office points. 5. Set the number of iterations, perform the above steps, and select the iteration result with the largest number of intra-office points as the correct matching feature point pairs that eliminate mismatching. The initial registration results are obtained, and the coarse point cloud registration is completed. The ICP algorithm [25] is the main algorithm for point cloud precision registration and is based on optimal matching based on the least squares method. Two frames of aircraft point clouds \(P\) and \(Q\) are taken as the source point set and target point set for registration. In the target point set \(Q_{i}\), the corresponding point with the shortest Euclidean distance from point \(P_{i}\) in the source point set is determined. The rotation matrix \(R\) and translation vector \(t\) are solved, and the process is iterated to minimize the sum of the squares of the Euclidean distances of the corresponding points until convergence or a preset threshold condition is reached. The error function is as follows:  
\[E(R,t)=\frac{1}{n}{\sum_{i=1}^{n}}{||Q_{i}-(RP_{i}+t)||}^{2}. \tag{15}\]  
The centroid coordinates \(C_{p}\) and \(C_{q}\) of the aircraft point clouds \(P_{i}\) and \(Q_{i}\) are calculated. The covariance matrix \(M\) is obtained as follows:  
\[M=\frac{1}{n}{\sum_{i=1}^{n}}{\big{[}(P_{i}-C_{P})\big{(}Q_{i}-C_{Q}\big{)} \big{]}}. \tag{16}\]  
Singular value decomposition is performed on the covariance matrix \(M\), and the rotation matrix \(R\) and translation vector \(t\) are then calculated. The transformation relationship between point clouds \(P\) and \(Q\) can be described using the following formula:  
\[P=\big{[}(RP+t),Q\big{]}. \tag{17}\]  
The G-ICP algorithm [26] optimizes the traditional ICP algorithm.