# 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
To quantitatively test the effect of intra-frame correction, LOAM is also used as the lidar odometry algorithm, and the localization accuracy is compared with the ground-truth trajectory. Figure 11 compares the localization results with/without rectification. The trajectories generated by the three rectification methods and without rectification are compared with the ground truth in Figure 11a, where \"Method 1\" represents rectification by previous registration, \"Method 2\" is the approach of registering two distorted point clouds, and \"Method 3\" indicates rectification by IMU data. In addition, Figure 11b,c compare the translation error and rotation error of these approaches. Figure 9: The localization results before and after hand–eye calibration, where (**a**) compares the trajectories before/after hand–eye calibration with the ground truth; (**b**) compares the translation error before/after calibration, and rotation error is shown in (**c**). In this experiment, the UGV drives at a speed around 25 km/h, and the overall distance is about 1.1 km. Figure 11: The localization results with/without rectification, where (**a**) compares the trajectories generated by the three rectification methods (Methods 1–3 represent rectification by the previous registration result, by registering two distorted point clouds and by the IMU data, respectively), the trajectory generated without rectification (Origin) and the ground truth; and (**b,c**) compare the translation error and rotation error among them, respectively. In this experiment, the UGV drives at a speed of around 60 km/h. Figure 10: The 3D reconstruction results to test the three rectification methods. (**a**) represents the result without any rectification, and (**b–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, respectively. It can be seen that both the translation error and the rotation error are significantly reduced after rectification, and \"Method 3\" exhibits the best performance, followed by \"Method 1\" and \"Method 2\". A detailed error comparison is presented in Table 2.

### Experiments on Inter-Frame Registration

#### 4.3.1 Tests with Different Methods of Assigning Initial Guess

In this experiment, two methods of assigning initial guess for the lidar odometry algorithm are compared--namely, using the IMU data or the registration result from the previous two scans. In both approaches, the raw distorted point clouds are rectified by the IMU data, and LOAM is used as the lidar odometry algorithm. The tests are conducted when the vehicle drives at different speeds: a relatively slow speed of around 25 km/h, and a faster speed of around 60 km/h. A detailed error comparison is shown in Figure 6:0 It can be seen that using the IMU data as the initial guess always produces a better result than using the registration result from the previous two scans, especially when the vehicle drives at a faster speed. #### 4.3.2 Tests with Different Lidar Odometry Algorithms

Here, we compare three popular lidar odometry algorithms: ICP, NDT, and LOAM. During the experiments, the point clouds are rectified by the IMU data. The vehicle drives at a speed around 25 km/h, and the overall distance is about 1.1 km. A detailed error comparison is shown in Figure 6:1 It is obvious that LOAM performs much better than NDT and ICP. \begin{table}
\begin{tabular}{c c} \hline
**Rectification Methods** & **Average Processing Time (ms)** \\ \hline By previous registration & 2.565 \\ By registering two distorted point clouds & 68.504 \\ By IMU data & 4.546 \\ \hline \end{tabular}
\end{table} 
Table 1: Computational efficiency of three rectification methods. \begin{table}
\begin{tabular}{c c} \hline
**Rectification Methods** & **Mean Relative Position Error** \\ \hline Method 1 & 0.79\% \\ Method 2 & 0.94\% \\ Method 3 & 0.57\% \\ Without Rectification & 2.28\% \\ \hline \end{tabular}
\end{table} 
Table 2: Error comparison of three rectification methods.