# A Survey of Low-Cost 3D Laser Scanning Technology
## 2 Overview of Principles
Next, point \(\mathbf{p}_{L}\) in coordinate frame \(L\) is converted to the corresponding point \(\mathbf{p}_{W}\) in coordinate frame \(W\)  
\[\mathbf{p}_{W}=R_{L}^{W}\mathbf{p}_{L}+T_{L}^{W} \tag{2}\]  
where \(R_{L}^{W}\) and \(T_{L}^{W}\) are the rotation matrix and the translation vector from coordinate frame \(L\) to coordinate frame \(W\), respectively. In this way, the 3D coordinates of the sampling point \(p\) relative to the world coordinate frame \(W\) can be calculated. For the sampling points of the 2D LiDAR at different positions, methods similar to (1) and (2) can be used to calculate their 3D coordinates, relative to the world coordinate frame \(W\)--that is, the first step is to calculate the coordinates of the sampling points relative to the 2D LiDAR coordinate frame, according to the raw data of a 2D LiDAR. The second step is to calculate the coordinates of the sampling points relative to the world coordinate frame by space rigid body transformations. According to the above principle, in order to ensure the accuracy of the 3D point cloud built by a moving 2D LiDAR, first, the raw data of the 2D LiDAR should be accurate (this depends on the accuracy of the 2D LiDAR), so that the coordinates of the sampling points relative to the 2D LiDAR coordinate frame can be accurately calculated by Equation (1). Second, the parameters of the space rigid body transformation between the 2D LiDAR coordinate frame and the world coordinate frame need to be accurately known, so that the coordinates of the sampling point relative to the world coordinate frame can be accurately calculated by Equation (2). If the space rigid body transformation parameters are not accurate, the 3D point cloud will be distorted. The research on this issue is important for the improvement of the accuracy of the 3D point cloud built by a moving 2D LiDAR. We will discuss it more in the following sections. From the above, we can see that there are two factors that determine the accuracy of a moving 2D LiDAR. First, the accuracy of the 2D LiDAR used. Second, the accuracy of the estimation of the movement of the 2D LiDAR. At present, there is no method to significantly improve the accuracy of 2D LiDAR for researchers--this is the job of the manufacturers. Therefore, to improve the accuracy of a moving 2D LiDAR, we seek to improve the accuracy of the estimation of the movement of 2D LiDAR as much as possible. In the following, some specific topics that need to be studied in order to accurately estimate the movement of 2D LiDAR will be listed and discussed. We believe that the ideal situation is that the measurement accuracy of a moving 2D LiDAR is consistent with the accuracy of the used 2D LiDAR, because the movement estimation of the 2D LiDAR is accurate enough so that the measurement accuracy of a moving 2D LiDAR will not be affected by it. According to Table 11, the accuracy level of most 2D LiDARs is centimeter-level. In our opinion, for a moving 2D LiDAR (especially for a rotating 2D LiDAR or a pitching 2D LiDAR, for them, the estimation of the movement of the 2D LiDAR is relatively simple and mature), it is feasible to control the systematic error within \(\pm\)50 mm, which is slightly larger than the systematic errors of most 2D LiDARs in Table 1.