# Kinematic In Situ Self-Calibration of a Backpack-Based Multi-Beam LiDAR System
## 4 Experiment Description and Result Analysis
### Analysis of Kinematic Self-Calibration Results  
Experiments using the real dataset were conducted to implement the minimum network configuration for the kinematic self-calibration found on the above analysis. Two experiments were conducted to investigate the accuracy when the full and minimum network configurations were used. First, Calibration IV-1 was conducted including all eight planes and 8140 points. Calibration IV-2 was also performed for comparison with Calibration IV-1. Three planes (ceiling and two orthogonal walls) and 2308 points were used for the self-calibration. A summary of the two experiments is presented in Table 10.  
For accuracy evaluation of the kinematic self-calibration, planar misclosure vectors were examined to confirm that the self-calibration had effectively modeled the sensor. For planar misclosure calculations, parameters other than APs were held to the same values in order to compare the results from self-calibration. The planar misclosure results before and after adjustment are given in Figure 15.  
As can be seen, in both cases, the systematic errors were not completely removed after the adjustment. Nevertheless, the results of both cases showed improvements of planar misclosure RMSE by 35.7 and 53.3% after the adjustment. The RMSE of Calibration \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Used Planes** & **Total Points** & **Used Points** & **Redundancy** \\ \hline IV-1 & 1, 2, 3, 4, 5, 6, 7, and 8 & 54,867 & 8140 & 8067 \\ IV-2 & 1, 3, and 5 & 41,259 & 2308 & 2247 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Summary of Calibration IV. Figure 15: Planar misclosure before and after the adjustment: (**a**) before Calibration IV-1; (**b**) after Calibration IV-1; (**c**) before Calibration IV-2; (**d**) after Calibration IV-2. IV-2 was even lower than that of Calibration IV-1. This is reasonable, as more outliers were included in the Calibration IV-1 dataset. A summary of the results regarding planar misclosure can be found in Table 11.  
In order to further investigate the existence of systematic trends, observation residuals from the adjustment were also examined. Figures 16 and 17 describe two observation residuals (a range and a horizontal angle) versus vertical angle, horizontal angle, and range for Calibration IV-1 and IV-2, respectively. For both cases, similar unmodelled systematic errors still existed in the observation residual. Residuals versus vertical angle showed no trends of systematic effects, as the mean residual values with respect to laser elevation angle had zero values (refer to Figure 16a,b and Figure 17a,b). On the other hand, residuals versus horizontal angle showed large variations at 90\({}^{\circ}\) and 270\({}^{\circ}\), which are the directions of high incidence angles to the walls (refer to Figure 16c,d and Figure 17c,d). This was expected from simulation tests and previous studies in the literature. For the final analysis for residuals, residuals versus range were plotted (refer to Figure 16e,f and Figure 17e,f). As can be seen, outliers increased as range increased, in both the range and horizontal angle observations. Figure 16: Measurement residuals of Calibration IV-1: (**a**,**c**,**e**) range residuals; (**b**,**d**,**f**) horizontal angle residuals; red line and blue line in (**a**,**b**) mean average and RMSE of residuals, respectively. Figure 17: _Cont_. Furthermore, the reliability of the estimated parameter could be presumed by examining the correlation coefficients between the estimated parameters. The correlation coefficients between the APs and EOPs are presented in Tables 12 and 13. The correlations between the EOPs and APs were averaged over all of the lasers with one EOP, and the correlations between APs were averaged over all lasers with the same laser. In general, correlations between the EOPs were higher than the correlations between the EOPs and the APs.