## 4 Experimental Results
### Single Flying Height  
First, a sub-optimal configuration is used to evaluate the theoretical bias impact analysis for the estimation of system parameters. In this case, six flight lines at a single flying height of 15 m are used along with the target primitives lying exactly below the flight lines (the sixteen boards and five hut-shaped targets) and with no significant \(x^{\prime}\) and \(z^{\prime}\)-coordinate variation. The initial approximations of these mounting parameters and the final results (along with their standard deviations) from the proposed calibration procedure are listed in Table 2. Here, the lever arm \(\Delta Z\) for the laser unit is fixed during the calibration procedure. One should note that the magnitude of lever-arm components depend on the physical location of the LiDAR unit with respect to the GNSS/INS unit. In this case, the very close positioning of LiDAR and GNSS/INS units results in the small values for lever-arm components. On the other hand, the standard deviation obtained for these parameters after LSA is a function of the geometry of the flight lines (flight/primitive configuration) and the accuracy of the involved hardware components (GNSS/INS unit and laser scanner and ranging unit). Hence the standard deviation should decrease as the configuration of the flight lines is improved (as clear from the results of other forthcoming tests). As stated before, according to the accuracies of the involved hardware components, the LiDAR Error Propagation Calculator [19] suggests an accuracy of 5-6 cm in point positioning for a flying height of 15-25 m. Hence, the standard deviations of the lever-arm and boresight parameters, as expected, are observed to lie within the accuracy expected according to the hardware components, thus proving the feasibility of the proposed strategy. The correlation matrix for the estimated mounting parameters of the laser unit is also listed in Table 3, which indicates that \(\Delta Y\) is highly correlated with \(\Delta\omega\) (0.9905). The average accuracy after calibration can be quantified by the square root of the a-posteriori variance factor \((\vartheta_{o})\), which is 3.12 cm in this case. This is better than the expected accuracy of around 5-6 cm according to the accuracies of the hardware involved and an error propagation calculation. The high correlation between the system parameters (\(\Delta Y\) and \(\Delta\omega\)) renders the calibration results unreliable. So, we incorporate planar features located at a high lateral separation from the flight lines (ground patches, rooftops and building facade) while still considering flight lines at a single flying height of 15 m. The corresponding mounting parameters and correlation matrix are listed in Tables 4 and 5, respectively. The standard deviation of all the estimated parameters can be seen to have reduced as compared to the previous case. Moreover, the correlation matrix indicates a reduction \begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline \multicolumn{4}{c}{**VLP-16 LiDAR Unit Mounting Parameters \(\left(\mathbf{r_{\text{{L}}u^{\prime}}^{\prime}}\right)\) \(\left(\mathbf{R_{\text{{L}}u^{\prime}}^{\prime}}\right)\)**} \\ \hline
**System Parameters** & \(\mathbf{\Delta X}\) **(m)** & \(\mathbf{\Delta Y}\) **(m)** & \(\mathbf{\Delta Z}\) **(m)** & \(\mathbf{\Delta\omega}\) **(\(\mathbf{\
abla}\))** & \(\mathbf{\Delta\phi}\) **(\(\mathbf{\
abla}\))** & \(\mathbf{\Delta\kappa}\) **(\(\mathbf{\lx@notemark{footnote}}\))** \\ \hline Initial & 0 & 0.02 & 0 & 0 & 0 & 0 \\ Final & 0.0084 & \(-\)0.0037 & 0 & 0.1676 & \(-\)0.7666 & \(-\)0.2825 \\ Standard Deviation & 0.0168 & 0.0381 & Fixed & 0.0797 & 0.0323 & 0.0542 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mounting parameters of VLP-16 before and after calibration test 1 (the parameter fixed during calibration is shown in red).