# IMU-Aided High-Frequency Lidar Odometry for Autonomous Driving
## 1 Introduction  
Precise and high-frequency localization is one of the key problems for autonomous vehicles. In recent years, the fusion of Global Navigation Satellite System (GNSS) and Inertial Measurement Unit (IMU) has been the most popular localization method. However, the GNSS/IMU system will fail in some environments where GNSS signals suffer from satellite blockage or multipath propagation [1], such when an autonomous vehicle is driving in a tunnel, in the mountains, or in an environment with electromagnetic interference. Thus, an alternative localization method is necessary when the GNSS signal is unavailable or is of poor quality. Currently, most autonomous vehicles are equipped with light detection and ranging (lidar) device, which is a promising sensor that could accurately calculate the range measurements of the surroundings. Some recent navigation approaches have begun to use lidar as a complementary sensor for the GNSS/IMU localization system. A typical lidar odometry algorithm could roughly be divided into three steps: a pre-processing step, which tries to compensate the intra-frame distortion caused by the vehicle's own movement; an intermediate step, which is the main body of the lidar odometry algorithm, and a last step, which outputs the localization result. As the lidar mostly spins at 10 Hz, its output frequency is thus less than 10 Hz, which might not be fast enough to meet the needs of other modules, like planning or control. To remedy this, some approaches try to combine the lidar with other sensors, such as IMU. In these approaches, the IMU and the lidar odometry are usually combined in an Extended Kalman Filter (EKF) framework, or by using a factor graph representation [2; 3; 4; 5; 6; 7] (as shown in the left of Figure 1). In this paper, we claim that IMUinformation can not only be fused with the lidar odometry at the output level, but it can also aid lidar odometry in the pre-processing level and the intermediate level (as shown in the right of Figure 1). In the pre-processing step, as the vehicle itself is moving during the lidar spin, the generated point clouds will be distorted. This intra-frame distortion is usually ignored. In this paper, we show that the high-frequency IMU information could naturally help correct this distortion, as long as the IMU and lidar are well-calibrated. We also claim that **the problem of intra-frame correction is in fact equivalent to inter-frame registration**, and propose an interesting two-step correction procedure which does not rely on the IMU. In the intermediate step, the IMU could also provide a good initial guess for the lidar odometry algorithm. Past works usually use the registration result from the previous two scans as the initial guess. We will do experiments to compare these two approaches. In the output step, we try to combine the lidar odometry with the IMU in the EKF framework. In summary, we make the following contributions in this paper:  
* We propose an efficient method for hand-eye calibration between the IMU and the lidar, which is a pre-requisite for making good use of the IMU. * In the pre-processing step of the lidar odometry algorithm, we emphasize that the intra-frame correction is equivalent to inter-frame registration, and propose an efficient method for utilizing the IMU information to rectify the distorted point clouds. * In the intermediate step, we use IMU to obtain the initial guess for the lidar odometry algorithm, and compare this approach with previous methods which usually use the registration results from the previous two scans as the initial guess. * By combining the lidar odometry with the IMU information, we obtain a complete localization system which can output stable, accurate, and high-frequency localization results at a frequency of around 40 Hz. The rest of this paper is organized as follows. In Section 2, we introduce some related works. Section 3.1 provides an overview of the proposed approach, and introduces the coordinate systems and notations in our approach.