## 1 Introduction
### Methodology of UAV-Based Laser Scanning  
For the analysis of the system accuracy, the influencing parameters and the basic principle of UAV-based laser scanning are relevant. The concept is always based on sensors to localize the UAV with position and orientation, as well as sensors to acquire the environment with a laser scanner and an optional camera. The entire processing, starting with the raw data (blue boxes) and ending with the 3D point cloud (green box), is shown in Figure 1 with additional processing steps (orange boxes) and potential error sources, discussed later. For the trajectory estimation with positions and orientations of the system, a combination of GNSS and IMU measurements is used. The GNSS observations from the receiver on the UAV are usually processed in differential mode with the observations from an additional GNSS master station, and then fused with the IMU data using a Kalman filter  
Figure 1: Processing of UAV-based laser scanning data with major error sources. or similar algorithm [9]. The result is the UAV trajectory described by a set of estimated positions and orientations. With subsequent georeferencing of time-synchronized laser scans based on the estimated trajectory and laser scanner measurements, the georeferenced point cloud is created. Additional information needed in this processing chain are the system calibration parameters describing the relative positions and orientations between the sensors on the platform. The calculation of each 3D point \(\left[x_{e},y_{e},z_{e}\right]^{T}\) can further be described with the equation  
\[\left[ \begin{array}{c}x_{e}\\ y_{e}\\ z_{e}\end{array} \right]=\left[ \begin{array}{c}t_{x}\\ t_{y}\\ t_{z}\end{array} \right]+\mathbf{R}_{n}^{e}(L,B)\mathbf{R}_{b}^{n}(\phi,\theta, \psi)\cdot\left(\left[ \begin{array}{c}\Delta x\\ \Delta y\\ \Delta z\end{array} \right]+\mathbf{R}_{s}^{b}(\alpha,\beta,\gamma)\cdot\left[ \begin{array}{c}x_{s}=0\\ y_{s}=d\cdot\sin b\\ z_{s}=d\cdot\cos b\end{array} \right]\right), \tag{1}\]  
including the parameters for the trajectory, sensor calibration and laser scanner measurements, which contribute to the calculation and, thus, the accuracy [10]. The calibration parameters of the system are defined with the lever arm \(\left[\Delta x,\Delta y,\Delta z\right]^{T}\) and the bore-sight angles \(\alpha,\beta\) and \(\gamma\) between the 2D laser scanner and GNSS/IMU unit. The measurements of the 2D laser scanner are introduced with \(\left[0,d\cdot\sin b,d\cdot\cos b\right]^{T}\), with \(d\) the measured distance and \(b\) the scan angle. Further parameters are the orientation angles of the platform with roll \(\phi\), pitch \(\theta\) and yaw \(\psi\) and its position with translation vector \(\left[t_{x},t_{y},t_{z}\right]^{T}\) and ellipsoidal longitude \(L\) and latitude \(B\). Based on these parameters and the additional rotation matrices \(\mathbf{R}\) between the sensor \((s)\), body \((b)\), navigation \((n)\) and earth \((e)\)-frame, the coordinates of each 3D point can be derived. For a detailed description of the included coordinate frames, calibration parameters and the functional model we refer to [1,11]. For system evaluation, the assumed uncertainty of the point cloud, or rather of the single 3D points, is crucial, which, in turn, is a combination of several systematic and random errors that influence the estimation process [7]. As mentioned before, the major error sources influencing the accuracy of the point cloud are the trajectory estimation of the UAV, the system calibration, the accuracy of the laser scanner itself and further miscellaneous errors like the ones coming from sensor time synchronization [12]. A more detailed list of errors can be found in Table 1, which is assigned to the included parameters in Equation (1). Typically, the largest errors of mobile mapping systems as well as UAV-based laser scanning come from the GNSS/IMU-based trajectory estimation and they can be expressed in terms of platform position and orientation errors.