# Fast Lidar Inertial Odometry and Mapping for Mobile Robot SE(2) Navigation
## 2 Related Work  
The iterative closest point (ICP) [19; 20] methods were introduced to achieve rigid transformation between two Lidar frames in back-end optimization by finding their correspondences at a point-wise or feature-wise level. However, due to the sensor motion and the rotation mechanism of 3D Lidar, the first step of Lidar SLAM is to eliminate the point-cloud distortion. Lidar odometry and mapping (LOAM) [18], as one of the representative methods of 3D Lidar SLAM, was proposed by [PERSON] in 2014 for low-drift and real-time state estimation and mapping. The linear interpolation method used IMU measurements to correct point-cloud distortion. LOAM extracted features (edge/planar) by calculating the smoothness of a point in its local Lidar scan and subjected edge and planar features to scan-matching to find correspondences between scans. In order to achieve real-time requirements, the two threads were designed to return low-precision odometry with a high frequency and high-precision mapping with a low frequency, respectively. A lightweight and ground-optimized Lidar odometry and mapping (LeGO-LOAM) method was proposed in [12] for real-time six-degree-of-freedom mobile robot state estimation. On the one hand, LeGO-LOAM adapted the primary pipeline of [18] and designed a more advanced feature segmentation method at the front end and two steps for state optimization at the back end. On the other hand, the loop closure module was integrated into LeGO-LOAM to make it more robust in complex environments. A general approach that aimed to achieve an accurate framework was provided in [13] for Lidar SLAM, where the local smoothness was taken into account for iterative pose optimization. Compared with the loosely coupled scheme, the Lidar inertial odometry via smoothing and mapping (LIO-SAM) adapted tightly coupled system framework was proposed in [14], which applied a factor graph to optimize the robot state using incremental smoothing and mapping. A versatile Lidar SLAM system based on the efficient multi-metric linear least-squares ICP was presented in [15]. LINS was proposed in [21] as a lightweight Lidar inertial state estimator for the real-time navigation of ground vehicles. It was also based on a tightly coupled framework and introduced an error-state Kalman filter to compensate for the estimated motion state recursivity. IMU measurements have been used to characterize system motion at any time to correct point-cloud distortion [22; 23; 24]. Traditional Lidar SLAM methods are corrupted by noise, and the estimated trajectories have drift issues in the z axis. Ground parameters have been extracted to build ground factors in order to eliminate the drift in the altitude direction [25]. The concept of continuous time was proposed in [26] to present mobile robot trajectory estimation and state prediction, a non-parametric robotic state estimation method based on the GP. [PERSON] [27] derived a mathematical model of the GP based on the weight-space and function-space methods and proposed an efficient approach that could provide robot state predictions at any time of interest. In addition, the GP [28] can estimate the probability distribution (mean and variance) of the multi-dimensional navigation parameters of ground vehicles and has been widely involved in the domains of trajectory optimization [29], target tracking [30], fusion [31], and terrain modeling [32]. Although the lack of texture information in the point cloud makes it difficult to construct global descriptors, Lidar scanning is more robust due to its illumination- and viewpoint-invariant properties. For place recognition, the global descriptors were represented in the form of histograms in [33; 34]. The scan context (SC) was proposed in [35] as a non-histogram-based global descriptor from a 3D Lidar scan that encoded a point cloud of a 3D scan into a matrix by selecting the maximum height of the point in each bin.