## 4 Experimental Results
### Multiple Flying Heights  
Finally, all the flight lines of this experiment (six at a height of 15 m and six at a height of 25 m) are used with all the target primitives described previously. As suggested by the theoretical analysis, this is the most optimal configuration for calibration. The mounting parameters obtained in this case and the corresponding correlation matrix are given in Tables 6 and 7, respectively. The average accuracy after calibration as quantified by the square root of the a-posteriori variance factor (\(\hat{\sigma}_{o}\)) is 2.24 cm in this case, which is 0.2 mm worse than the second case (where \(\hat{\sigma}_{o}\) was 2.22 cm). This perceived deterioration is a result of the higher error propagation in the case of points captured using flight lines at an altitude of 25 m (as compared to 15 m in the second case). The qualitative analysis of some of the target primitives (a checkerboard target, a hut-shaped target, a building facade and a ground patch) is shown in Figure 11, which indicates a major improvement in the alignment for each of the calibration targets. The number of LiDAR points along each feature and the RMSE of normal distance of points from best-fitting plane/line for all the extracted features before calibration and after each of the three cases of calibration are listed in Table 8, which indicates a significant improvement of point clouds after calibration and also that the best results are yielded in the third case, which consists of an optimal target primitive and flight line configuration where there are multiple flight lines at different flying heights and planar/linear features oriented in different directions with sufficient variation in lateral distance from the flight lines. Note that for the Velodyne scanners, the highly reflective traffic signs result in false objects (or, ghosting) but they are found to lie well within the noise level of the data. So, this effect is visible in the qualitative evaluation (Figure 11e) but not necessarily manifested in the quantitative evaluation (Table 8) for the experimental results reported in this study. However, recent advances in our work with systems consisting of higher end laser scanner and GNSS/INS units providing a higher measurement accuracy indicate a negative impact of using such highly reflective boards for calibration since the ghosting effect exceeds the noise level of the data. In such cases, \begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline \multicolumn{3}{c}{**VLP-16 LiDAR Unit**} & \multicolumn{1}{c}{**Mounting Parameters**} & \multicolumn{1}{c}{\(\left(\mathbf{r_{lux}^{\prime}}\right)\)} & \multicolumn{1}{c}{\(\left(\mathbf{R_{lux}^{\prime}}\right)\)} \\ \hline
**System Parameters** & \(\mathbf{\Delta X}\) **(m)** & \(\mathbf{\Delta Y}\) **(m)** & \(\mathbf{\Delta Z}\) **(m)** & \(\mathbf{\Delta\omega}\) **(°)** & \(\mathbf{\Delta\phi}\) **(°)** & \(\mathbf{\Delta\kappa}\) **(°)** \\ \hline Initial & 0 & 0.02 & 0 & 0 & 0 & 0 \\ Final & 0.0180 & \(-\)0.0067 & 0 & 0.1598 & \(-\)0.6942 & \(-\)0.2538 \\ Standard Deviation & 0.0118 & 0.0181 & Fixed & 0.0361 & 0.0139 & 0.0438 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mounting parameters of VLP-16 before and after calibration test 2 (the parameter fixed during calibration is shown in red).