## 4 Experiment
### Outdoor Experiment  
The outdoor experiment was carried out on a city street. This scene has rich feature points, so the drift of lidar odometry grows very slowly. The localization accuracy of LeGO-LOAM, LIO-SAM, and HSDLIO have very little difference, but the mapping of HSDLIO can provide finer structural details. Figure 11: (**a**) Stairs scene for experiment 2. (**b**) Mapping results of LeGO-LOAM in the stairs scene, with LeGO-LOAM’s mapping result having failed. (**c**) Mapping results of LIO-SAM in the stairs scene, with LIGO-SAM’s mapping results lacking height information. (**d**) Mapping results of HSDLIO in the stairs scene, with the mapping of HSDLIO the most complete and accurate. Figure 12: Comparison of LeGO-LOAM, LIO-SAM, and HSDLIO trajectories. The red line is the trajectory of HSDLIO, the blue line is the trajectory of LIO-SAM, and the black line is the trajectory of LeGO-LOAM. While LeGO-LOAM’s trajectory drifted and LIO-SAM’s trajectory produced cumulative errors in the \(z\) direction, the trajectory of HSDLIO approximated the real trajectory. The trajectories obtained by LeGO-LOAM, LIGO-SAM, and HSDLIO are shown in Figure 14. Because there is more feature information outdoors, the drift of lidar odometry grows very slowly. LeGO-LOAM can obtain relatively accurate localization only through horizontal lidar. In LIO-SAM and HSDLIO, GPS measurement is introduced by loosely coupling with IMU through UKF, which can provide relatively accurate initial positioning. The localization accuracy of HSDLIO and LIO-SAM is higher than LeGO-LOAM. The available data in Table 3 further supports the performance of the HSDLIO algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **LeGO-LOAM** & **LIO-SAM** & **HSDLIO** \\ \hline \(\mathbf{x_{o}}\) & Fail & 0.033 & 0.011 \\ \hline \(\mathbf{y_{o}}\) & Fail & 0.036 & 0.024 \\ \hline \(\mathbf{z_{o}}\) & Fail & 0.062 & 0.004 \\ \hline RTE & Fail & 0.078 & 0.026 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relative translational error when the backpack returns to the starting point (meters). Figure 14: Comparison of LeGO-LOAM, LIO-SAM, and HSDLIO trajectories. The red dashed line is the trajectory of HSDLIO, the blue dashed line is the trajectory of LIO-SAM, and the black dashed line is the trajectory of LeGO-LOAM. Figure 13: Comparison of the height information of LIO-SAM and HSDLIO in the \(\mathbf{z}\) direction. The trajectory of HSDLIO provides height information from going up and down four floors of stairs, while LIO-SAM failed to position in the \(\mathbf{z}\) direction. The 3D city street scene is shown in Figure 15a. In Figure 15a-d, the marks in the white circle represent trees and the marks in the yellow circle represent the building structure. Figure 15b-d shows the overall mapping of LeGO-LOAM, LIO-SAM, and HSDLIO algorithms in the city street scene, with the white points being their localization trajectories. Figure 15b,c shows that the overall effect of the mapping lacks building height information, while the structure of buildings and trees is blurred. The mapping details are analyzed at the marker, compared with the mapping results of LeGO-LOAM and LIO-SAM (Figure 15b,c), while the HSDLIO mapping result is shown in Figure 15d. It can be seen in Figure 15d that the structure of the trees and buildings is complete and has finer details. To further demonstrate the advantages of HSDLIO mapping, the mapping details of the building are shown in Figure 16, with the mapping results of LeGO-LOAM and LIO-SAM lacking the structural details and height information of the building. However, the mapping result of HSDLIO show finer structural details and more height information of the building. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **LeGO-LOAM** & **LIO-SAM** & **HSDLIO** \\ \hline RTE & 0.082 & 0.036 & 0.031 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative translational error when the backpack returns to the starting point (meters).