## 4 Experimental Results
### Multiple Flying Heights
\begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline
**System Parameters** & \(\mathbf{\Delta X}\) & \(\mathbf{\Delta Y}\) & \(\mathbf{\Delta Z}\) & \(\mathbf{\Delta\omega}\) & \(\mathbf{\Delta\phi}\) & \(\mathbf{\Delta\kappa}\) \\ \hline \(\mathbf{\Delta X}\) & 1.0000 & 0.0240 & 0.0000 & 0.0141 & **0.1025** & 0.0298 \\ \(\mathbf{\Delta Y}\) & 0.0240 & 1.0000 & 0.0000 & **0.9032** & 0.1390 & 0.0171 \\ \(\mathbf{\Delta Z}\) & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \(\mathbf{\Delta\omega}\) & 0.0141 & **0.9032** & 0.0000 & 1.0000 & 0.1775 & 0.0221 \\ \(\mathbf{\Delta\phi}\) & **0.1025** & 0.1390 & 0.0000 & 0.1775 & 1.0000 & 0.2456 \\ \(\mathbf{\Delta\kappa}\) & 0.0298 & 0.0171 & 0.0000 & 0.0221 & 0.2456 & 1.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation matrix of mounting parameter estimates from calibration test 2 (the potential high correlation values are shown in red). the highly reflective boards can be used as calibration targets to obtain precise initial estimates of mounting parameters (especially when the initial estimates are highly inaccurate) since these boards are easier to extract using just the intensity data. However, with relatively good initial approximations of the parameters, the target boards that result in ghosting can be excluded during calibration. \begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline \multicolumn{2}{c}{**VLP-16 LiDAR Unit**} & \multicolumn{2}{c}{**Mounting Parameters**} & \multicolumn{2}{c}{\(\left(\begin{array}{c}\mathbf{r}_{\mathbf{L}^{\prime}}^{\mathbf{\prime}}\\ \mathbf{\prime}\end{array}\right)\)} & \multicolumn{2}{c}{\(\left(\begin{array}{c}\mathbf{R}_{\mathbf{L}^{\prime}}^{\mathbf{\prime}}\\ \mathbf{\prime}\end{array}\right)\)} & \multicolumn{2}{c}{\(\left(\begin{array}{c}\mathbf{\sigma}\\ \mathbf{\sigma}\end{array}\right)\)} & \multicolumn{2}{c}{\(\left(\begin{array}{c}\mathbf{\sigma}\\ \mathbf{\sigma}\end{array}\right)\)} & \multicolumn{2}{c}{\(\left(\begin{array}{c}\mathbf{\sigma}\\ \mathbf{\sigma}\end{array}\right)\)} \\ \hline \hline
**System Parameters** & \(\Delta\mathbf{X}\) **(m)** & \(\Delta\mathbf{Y}\) **(m)** & \(\Delta\mathbf{Z}\) **(m)** & \(\Delta\mathbf{\omega}\) **(\({}^{\circ}\))** & \(\Delta\mathbf{\phi}\) **(\({}^{\circ}\))** & \(\Delta\mathbf{\kappa}\) **(\({}^{\circ}\))** \\ \hline Initial & 0 & 0.02 & 0 & 0 & 0 & 0 \\ Final & 0.0189 & 0.0086 & 0 & 0.0427 & -0.7051 & -0.3381 \\ Standard Deviation & 0.0103 & 0.0145 & Fixed & 0.0263 & 0.0118 & 0.0377 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mounting parameters of VLP-16 before and after calibration test 3 (the parameter fixed during calibration is shown in red). Figure 11: Qualitative evaluation of calibration targets before and after calibration: (**a**) Checkerboard target; (**b**) hut-shaped target; (**c**) building facade; (**d**) ground patch; and (**e**) highly reflective sign board. \begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline
**System Parameters** & \(\Delta\mathbf{X}\) & \(\Delta\mathbf{Y}\) & \(\Delta\mathbf{Z}\) & \(\Delta\mathbf{\omega}\) & \(\Delta\mathbf{\phi}\) & \(\Delta\mathbf{\kappa}\) \\ \hline \(\Delta\mathbf{X}\) & 1.0000 & 0.0215 & 0.0000 & 0.0187 & **0.0908** & 0.0778 \\ \(\Delta\mathbf{Y}\) & 0.0215 & 1.0000 & 0.0000 & **0.8438** & 0.0794 & 0.0022 \\ \(\Delta\mathbf{Z}\) & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \(\Delta\mathbf{\omega}\) & 0.0187 & **0.8438** & 0.0000 & 1.0000 & 0.1414 & 0.0133 \\ \(\Delta\mathbf{\phi}\) & **0.0908** & 0.0794 & 0.0000 & 0.1414 & 1.0000 & 0.2458 \\ \(\Delta\mathbf{\kappa}\) & 0.0778 & 0.0022 & 0.0000 & 0.0133 & 0.2458 & 1.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Correlation matrix of mounting parameter estimates from calibration test 3 (the potential high correlation values are shown in red).