# Kinematic In Situ Self-Calibration of a Backpack-Based Multi-Beam LiDAR System
## 4 Experiment Description and Result Analysis
### Analysis of Simulation Experiment Results  
In the first experiment (Calibration I), the number of scans was reduced successively. Table 7 provides a summary of the first experiment. Also, please refer to Figures 7a-d and 8. The RMSE between estimated and given AP values are plotted in Figure 9. As can be seen, all the tests show high similarity. The asymmetry network configuration of Calibration I-2 might have affected the accuracy of the adjustment. For Calibration I-5, the scan location was too close to the corner, leading to a high incidence angle to the planes. High incidence angle observation tends to deteriorate the overall accuracy of the adjustment [25]. The results from the first experiments indicate that there is no significant change of accuracy when using only two scans compared with the full network, which uses seven scans. For the rest of the experiments, therefore, only two scans (not too close to the corner) were used for self-calibration. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Used Scans** & **Used Planes** & **Total Points** & **Used Points** & **Redundancy** \\ \hline I-1 & 1, 2, 3, 4, 5, 6, and 7 & & 202,608 & 2048 & 1948 \\ I-2 & 1, 3, 4, 5, 6, and 7 & & 173,664 & 2048 & 1954 \\ I-3 & 1, 3, 5, 6, and 7 & & 144,720 & 2048 & 1960 \\ I-4 & 1, 3, 6, and 7 & & 115,776 & 2048 & 1966 \\ I-5 & 1 and 3 & & 57,888 & 2048 & 1978 \\ I-6 & 6 and 7 & & 57,888 & 2048 & 1978 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of Calibration I (reducing the number of scans). Figure 8: Plane number settings: (**a**) ceiling and floor; (**b**) front and rear walls; (**c**) left and right walls. Following the result from Calibration I, the second experiment (Calibration II) used only two scans for self-calibration by decreasing the dimensions of the room and the number of incorporated planes. Also, please refer to Figures 7e-h and 8. Table 8 summarizes the information on Calibration II. The length of the test site decreased until 7 m. The scan locations were about 3 m apart from the wall and 1 m from each other. Except for Calibration II-13 and II-14, the remaining twelve experiments have calibration solutions. The RMSEs of the estimated APs for the twelve experiments are provided in Figure 10. The range offset showed consistent RMSE values for all experiments, while the two angular offsets showed a slight variance. Even the reduced dimension of the test site (i.e., 7 m \(\times\) 5 m \(\times\) 3 m) with three planes (i.e., ceiling and two orthogonal walls) provided a low level of RMSE values as seen in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Dimensions (m)** & **Used Planes** & **Total Points** & **Used Points** & **Redundancy** & **Convergence** \\ \hline II-1 & \(15\times 5\times 3\) & & & & & O \\ II-2 & \(14\times 5\times 3\) & & & & & O \\ II-3 & \(13\times 5\times 3\) & & & & & O \\ II-4 & \(12\times 5\times 3\) & 1, 2, 3, 4, 5, and & & & & O \\ II-5 & \(11\times 5\times 3\) & 6 & 57,888 & 2048 & 1978 & O \\ II-6 & \(10\times 5\times 3\) & & & & & O \\ II-7 & \(9\times 5\times 3\) & & & & & O \\ II-8 & \(8\times 5\times 3\) & & & & & O \\ \hline II-9 & \(7\times 5\times 3\) & 2, 3, 4, 5, and 6 & 48,407 & 2046 & 1979 & O \\ II-10 & \(7\times 5\times 3\) & 2, 3, 5, and 6 & 35,446 & 2048 & 1984 & O \\ II-11 & \(7\times 5\times 3\) & 2, 3, 4, and 5 & 38,683 & 2046 & 1982 & O \\ II-12 & \(7\times 5\times 3\) & 2, 3, and 5 & 22,550 & 2048 & 1987 & O \\ II-13 & \(7\times 5\times 3\) & 2 and 6 & 14,194 & 2048 & 1990 & X \\ II-14 & \(7\times 5\times 3\) & 2 and 3 & 11,040 & 2048 & 1990 & X \\ \hline \end{tabular}
\end{table} 
Table 8: Summary of Calibration II (reducing the length of the corridor and the number of planes). Figure 9: RMSE of estimated additional parameters (APs) for Calibration I. Following the result from Calibration II-12, the third experiment (Calibration III) was conducted by reducing the number of points in the adjustment. In Table 9, the summary of Calibration III is presented.