# A Lidar-Inertial Navigation System for UAVs in GNSS-Denied Environment with Spatial Grid Structures
## 3 Experiment
### Experiments and Data Analysis
#### 3.2.2 Analysis of Localization  
During the experiment, we manually controlled the UAV to fly a complex trajectory in the coal shed until it finally returned to the vicinity of the take-off point. The flight trajectory solved by the proposed navigation system is shown in Figure 9.  
Figure 8: The features extracted by the proposed algorithm and LOAM algorithm. (**a**,**b**) are the features extracted by the proposed algorithm for the low-altitude take-off and landing stage of the UAV operations. (**c**,**d**) are the features extracted by the proposed algorithm for the high-altitude cruise stage of the UAV operations. In (**a**–**d**), we marked the shell feature in pink and the grid feature in green. (**e**,**f**) are the features extracted by the LOAM algorithm for the low-altitude take-off and landing stage of the UAV operations. (**g**,**h**) are the features extracted by the LOAM algorithm for the high-altitude cruise stage of the UAV operations. In (**e**–**h**), we marked plane features in pink and line features in green.  
The x-axis, y-axis, and z-axis variation curves of the UAV flight trajectory in the coal shed calculated by LOAM, F-LOAM, LIO-SAM, DJI, and the proposed navigation system with time are shown in Figure 10. The UAV flight trajectory and the mapping described in the following subsection are in the navigation frame. We aligned the trajectories computed by the navigation system above. The navigation frame takes the take-off point as its origin. The z-axis is opposite to the direction of gravity and points upwards. The x-axis and the y-axis point to the front and left of the body frame when it is taking off, respectively. In an analysis, we set the local map resolution to remain the same for all navigation systems except DJI. DJI is the positioning system that comes with the drone platform. While working, it fuses data from the IMU, VO, ultrasonic rangefinder, magnetometer, and the barometer. Since DJI does not use lidar, it is only used as an example of the inability of traditional sensor fusion to complete navigation in GNSS-denied environments with spatial grid structures.  
Figure 10: _Cont._  
Figure 9: The flight trajectory solved by the proposed navigation system.  
It can be seen from Figure 10 that the proposed navigation system has higher initial stability than LIO-SAM in the stationary stage before the take-off of the UAV. Except for the height direction, DJI is very different from other systems in other directions. Since the experiment was performed in a GNSS-denied environment, the true value of the UAV pose could not be obtained. Therefore, we compared the error of the UAV landing point solved by each system. In an analysis in this section, we use the offline ICP algorithm to obtain the relative pose between take-off and landing points by matching the point cloud scanned by the lidar during take-off and landing. We take the landing point of the offline solution as the true value and compare the landing point error of each algorithm, as shown in Table 2. It can be seen that the accuracy of the landing point position calculated by the proposed navigation system is significantly better than for the other navigation systems in the x-axis and y-axis directions. It is also close to the best-performing system in the z-axis direction. It should be noted that LIO-SAM uses loop closure detection based on the ICP method in the backend, which is why it has an advantage in the z-direction. The proposed navigation system only acts as a lidar-inertial odometry.  
Figure 10: The x-axis, y-axis, and z-axis variation curves of the UAV’s flight trajectory. (**a–c**) are x-axis, y-axis, and z-axis variation curves with time, respectively.  
The processing time of a single-scan lidar point cloud of each algorithm is shown in Figure 11. The proposed navigation system converges faster than other algorithms due to the use of better environmental structural constraints in the computation. The average processing time of the proposed system for a single-scan lidar point cloud is under 50 ms.