# IMU-Aided High-Frequency Lidar Odometry for Autonomous Driving
## 3 The Proposed Approach
### Output Step: Fusion in an EKF Framework
#### 3.6.3 Measurement Model
### Experiments on Hand-Eye Calibration

As described in Section 3.3, in order to perform the lidar-IMU hand-eye calibration, we need to utilize multiple pairs of relative transformations \(\{\triangle\,T_{\rm k-1,k^{\prime}}^{\rm B}\,\triangle\,T_{\rm k-1,k}^{\rm L}\}\). We choose the frame pairs \(\{f_{1}^{\rm L},f_{1-1}^{\rm L}\}\) before and after the vehicle makes a turn. In addition, all the frames are collected when the vehicle is stationary. Figure 7 shows several transformation pairs we have chosen. In each sub-figure, the left part is the registration result before the hand-eye calibration, whilst the right half is the result after hand-eye calibration. It can be seen that \(f_{1}^{\rm L}\) and \(f_{1-1}^{\rm L}\) are much

Figure 6: Our experimental platform. It is equipped with a Velodyne HDL-64E Lidar, a Xsens MTI300 IMU, two photoelectric encoders, a NovAtel SPAN-CPT GNSS/INS system, and a Nova 5100 industrial computer. better-registered in the right half of Figure 7a-d than the left half, which indicates the importance of hand-eye calibration. Since the ground truth of \(\mathbf{T}^{\text{BL}}\) is impossible to be obtained, we could not verify the calibration result directly. However, we could use the IMU data to assemble different frames together, and the quality of the assembled scene can be used to evaluate the accuracy of the hand-eye calibration result. Figure 8 shows the assembled scene when the vehicle makes a turn at the intersection. Figure 8a is the assembled result before hand-eye calibration, which is very vague, while the result after the hand-eye calibration in Figure 8b is much clearer. This suggests that the result of our hand-eye calibration is accurate. To quantitatively test the effect of hand-eye calibration, we choose the LOAM algorithm as the lidar odometry algorithm, and compare the estimated trajectories with the ground-truth trajectory generated by the GNSS/INS system. Figure 9 illustrates the localization result before and after hand-eye calibration. The translation error and rotation error are shown in Figure 9b,c, where the horizontal axis represents the traveled distance and the vertical axis shows the errors. It is obvious that the translation error and the rotation error are significantly reduced after the hand-eye calibration. Figure 8: The 3D reconstruction result when the vehicle turns around at the intersection. The left (**a**) is the result before hand–eye calibration, and the right (**b**) is the result after hand–eye calibration. Figure 7: Four typical lidar pairs chosen to perform the hand–eye calibration. In each sub-figure, the left part is the registration result before the hand–eye calibration, whilst the right half is the result after hand–eye calibration. The yellow dotted line indicates the movement trajectory of the vehicle, while the yellow arrow and the blue arrow denote the orientation of the vehicle. ### Experiments on Intra-Frame Correction

Based on the hand-eye calibration results, we could also use the 3D reconstruction results to qualitatively test the three rectification methods introduced in Section 3.4. In order to test the result of the rectification, the vehicle should run fast to amplify the intra-frame distortion. Therefore, we carry out this experiment when the vehicle drives at around 60 km/h, and the results are shown in Figure 10.

Figure 10a-d represent different 3D reconstruction results when the vehicle is making a turn. Figure 10a is the result without any rectification, and the reconstructed scene is quite blurry. Figure 10b-d show the results when the distorted point clouds are rectified by the previous registration result, by registering two distorted point clouds and by the IMU data. The results obtained by these three approaches are all much better than the one without rectification. Moreover, the average processing time for these three methods applied on 2000 frames of point clouds is displayed in Table 1. It is seen that the approach of registering two distorted point clouds is the most computational expensive approach.