## 2 Methods
### Unordered Point Cloud Normal Vector Estimation  
Current 3D sensing technology utilizes laser emissions to measure the time it takes for the emitted light to reflect from a target surface to the sensor, enabling the determination of point locations on the surface. However, the resulting point cloud data are often disordered and contain varying levels of noise, both of which can directly impact the accuracy of estimating normal vectors for the point cloud. Normal vectors are crucial as they describe the orientation of an object's surface in three-dimensional space, providing essential information for understanding the object's geometry. These normal vectors play a key role in localized surface information for spatial target position estimation, aiding in tasks such as surface fitting, feature extraction, and model matching. When dealing with disordered point cloud data and unknown actual normal vectors, it is typical to assess the consistency between the estimated normal vectors of a point and those of its neighboring points. It is desirable for neighboring points to exhibit similar normal orientations in regions that are geometrically similar. The angular difference in the estimated normal vectors of neighboring points \(\Delta\theta_{ij}\) can be calculated as Equation (1). \[\Delta\theta_{ij}=\cos^{-1}\left(\frac{n_{i}\cdot n_{j}}{\parallel n_{i} \parallel\parallel n_{j}\parallel}\right) \tag{1}\]  
If the distribution of normal angle differences in the input point cloud is concentrated, it suggests that the normal of the point cloud closely aligns with those of its neighboring points. This indicates that the local surface of the point cloud experiences minimal directional changes, resulting in accurate and consistent normal estimation within that region. Conversely, a significant difference in normal directions signifies inaccurate normal estimation. Fitting Micro-Planar Projections Using Moving Least Squares Process Based on Moving Least Squares Method  
In order to enhance the registration accuracy of point cloud data, it is crucial to address the challenges posed by uneven sampling and the presence of noisy redundant points affecting normal vector estimation. Preprocessing the input point cloud set is essential not only to alleviate computational burden on the on-board computer but also to enhance alignment efficiency and accuracy by eliminating unnecessary details. While existing downsampling techniques like random, distance, and uniform methods exist, they primarily rely on a simplistic global selection approach that overlooks the local geometric characteristics of the point cloud. Building upon previous research by [PERSON] et al. (2019), we introduce a microplanar projection-based moving least squares (mpp-MLS) downsampling method for selecting projected points. This method aims to enhance alignment accuracy and  
Figure 1: Flowchart of the pose estimation. efficiency by fitting a microplane to a local region of the target point cloud and effectively removing redundant points through projection. First, from a piece of the point cloud with measurement noise, select the local region point set \(P_{i}\in\mathbb{R}^{3},\ i\in\{1,\ \dots,N\}\) centered on the index point \(r\). We estimate a local plane by fitting these points with a cubic polynomial \(H=\left\{x|<n,x>-D=0,x\in\mathbb{R}^{3}\right\}\), \(n\in\mathbb{R}^{3},\ ||n||=1\). The goal of the fit is to minimize the points \(P_{i}\) to the plane \(H\) by reducing the sum of the weighted distances from the \(P_{i}\) to the center point \(r\) of the plane, with the weight determined by the distance to the center point.