# Kinematic In Situ Self-Calibration of a Backpack-Based Multi-Beam LiDAR System
## 4 Experiment Description and Result Analysis
### Simulation Experiments  
Since the zero-order design problem--the datum problem--has been addressed by fixing the EOPs of the reference scan as aforementioned, the first-order design problem--the configuration problem--is our interest. Several network configuration conditions were considered to determine the minimum network configuration for plane-based self-calibration of the backpack-based MBL system. These include: (1) the number and configuration of scans; (2) the size, the number, and the configuration of incorporated planes; (3) the minimum number of points lying on the planar surface. In order to determine the minimum network configuration suitable for the backpack-based MBL system in situ self-calibration, simulation experiments were designed with respect to those two significant conditions. Simulation environments were designed by changing the size of the test site and sensor configurations using our own developed simulator program. All the simulated datasets have 0.2\({}^{\circ}\) horizontal angle increments, and the same systematic errors. The given systematic errors for the simulation data are shown in Table 6. Random noises were set to 0.003 m, and 0.01\({}^{\circ}\) for range and angle observations, respectively.  
The first experiment (Calibration I) was conducted by reducing the number of scans successively to determine the optimal configuration and the minimum number of scans required. As shown in Figure 7a,c, the size of the test site was firstly set to 15 m \(\times\) 15 m \(\times\) 3 m, and four scans were located at the corner, two scans were located near the corner, and one was located at the center. This full network configuration, including seven scans and six planes, was constructed based on [45]. Each scan was slightly tilted along the X axes (omega in orientation parameters) for better estimation of the adjustment [42]. Figure 7b,d show the point cloud generated for Calibration I.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**AP** & **Values** \\ \hline \(\Delta\rho(\text{m})\) & 0.03 \\ \(\Delta\alpha(^{\circ})\) & 0.1 \\ \(\Delta\theta(^{\circ})\) & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Given systematic error level for simulation experiments.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Formula** \\ \hline Conditions & \(m=i\) \\ Unknowns & \(u=6\times(j-1)+(3n-2)+4k\) \\ Observations & \(l=2i\) \\ Constraints & \(c=k\) \\ Degree of Freedom & \(r=m-u+c\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Summary of least squares solution.  
For the second experiment (Calibration II), as described in Figure 7e,g, the dataset was firstly generated in a 15 m \(\times\) 5 m \(\times\) 3 m corridor-shape environment, and the length of the corridor was shortened by 1 m successively until it reached 7 m \(\times\) 5 m \(\times\) 3 m in order to investigate the effective dimensions of the room for the self-calibration. After the investigation, the number of incorporated planes also reduces to determine the minimum  
Figure 7: Simulated environment and their corresponding point clouds: (**a,c**) network configuration for Calibration I; (**b,d**) point cloud generated for Calibration I; (**e,g**) network configuration for Calibration II; (**f,h**) point cloud generated for Calibration II. Color coded by height.  
number of planes required. Figure 7f,h show the point cloud generated for Calibration II. Figure 8 describes the assigned number for each plane.  
For the third experiment (Calibration III), the number of points used in the adjustment reduces to identify the minimum requirement of the redundancy for the adjustment.