## 3 Results
### Experimental Results in Urban Canyon 2
#### 3.3.2 Positioning Results Comparison  
The effectiveness of the adaptive GNSS-RTK/LIO fusion method for continuous position estimation is further validated on urban-2. The trajectories generated by the adaptive integrated pipelines with thresholds \(el_{th}\) for the GNSS-RTK availability assessment equals 90\({}^{\circ}\), 35\({}^{\circ}\), 20\({}^{\circ}\), and 15\({}^{\circ}\) are presented respectively in Figure 9a-d. Different from urban-1, fixed u-blox RTK solutions processed by RTKLIB [2] are reported on urban-2. Among the fixed ones, the corresponding mean elevation angle mask of which is smaller than \(el_{th}\), are fused with LiDAR and IMU measurements as Equation (11) in our experiments. It is noteworthy that when fixed solutions are developed, the surroundings are relatively empty. The mean elevation angle mask of such places would be relatively small. Specifically, on urban-2 only one fixed solution has a mean elevation angle mask larger than 35\({}^{\circ}\). Therefore, trajectories estimated by pipelines with \(el_{th}\) set to 90\({}^{\circ}\) and 35\({}^{\circ}\) achieves similar accuracy as plotted in Figure 9a,b. As \(el_{th}\) decreasing, the percentage of available GNSS RTK solutions to integrate with LiDAR and IMU measurements increases. As a consequence, the estimated trajectory achieves better accuracy. As shown in Figure 9c,d, the estimated trajectories are in better agreement with the ground truth. The box plot in Figure 9d compares the precision of the four trajectories quantitatively.  
Table 4 shows the precision of the positioning results from alone GNSS-RTK measurements, the LIO, and the four adaptive integrated pipelines quantitatively. Overall speaking, the positioning results on urban-2 are more accurate compared to that on urban-1 thanks to fixed solutions. The ATE of the pure GNSS-RTK is still large with an RMSE of 15.75 m. The LIO achieves the next best precision with the RMSE of 1.80 m. The RMSE of ATE of the position estimated by LIO-SAM is improved compared with GNSS RTK alone but still large due to the reliability of the fused GNSS RTK solutions is not proved. Among the four adaptive integrated pipelines, when \(el_{th}\) equals 90\({}^{\circ}\) and 35\({}^{\circ}\), comparable positioning precision is achieved. The RMSE of ATE is about 8.6 m. By decreasing the \(el_{th}\) to 20\({}^{\circ}\), the  
Figure 9: (**a–d**) plots the trajectory generated by pipelines with the thresholds \(el_{th}\) for the GNSS-RTK availability assessment set as 90\({}^{\circ}\), 35\({}^{\circ}\), 20\({}^{\circ}\) and 15\({}^{\circ}\) respectively on urban-2. The black trajectory is the ground truth. The ATE of each estimated position is mapped on the trajectory referring to the color bar with the same scale on the right, on which the largest and the smallest tick label represent the maximum and the minimum ATE respectively while the middle one represents the midrange of them. (**e**) shows the boxplot of the ATE on the whole trajectory produced by the four pipelines.  
RMSE is significantly improved by 50% to 4.86 m. The pipeline with \(el_{th}\) set to 15\({}^{\circ}\) achieves the best precision with the RMSE of 1.738 m as marked in bold font in Table 2.