## 1 Introduction  
Autonomous surface vehicles (ASVs) have the characteristics of high autonomy and intelligence [1] and can perform a variety of high-risk tasks in harsh or inaccessible marine environments [2]. Its low weight and compact size make it highly mobile [3]. Since there is no crew onboard, personnel safety is higher [4]. Besides, they can also be deployed in numerous applications involving many fields, such as the civil, industrial, and military fields [5], such as environmental monitoring [6], coastal surveillance [4], resource exploration [7], reconnaissance [8], and rescue [9]. In general, ASVs are extremely suitable for eliminating personal hazards and improving safety in dangerous and rough marine missions. In addition, it is expected that the market for ASVs will proliferate shortly. State estimation is one of the most studied issues in the field of ASV [10]. It is a prerequisite for ships to achieve genuine autonomy. At present, most ships mainly rely on the global navigation satellite system (GNSS) and inertial measurement unit (IMU) to obtain their pose. When the ship is sailing in the harbor, GNSS performance is seriously affected by the multipath (MP) effect and the non-line-of-sight (NLOS) reception, and the positioning error may increase to several meters [11] or even tens of meters [12]. IMU has a cumulative error, and the reliability decreases with time [13]. Therefore, an alternative state estimation system is needed to estimate the ship's motion by using the surrounding environment. When the GNSS and IMU information is inaccurate or interrupted, it provides accurate position and motion estimation for the ship to avoid collisions and other accidents. To solve the above problems, ASV usually relies on the data collected by its sensors to apply the Simultaneous Localization and Mapping (SLAM) method for positioning. The sensors used in ASV mainly include GNSS, IMU, gyro compass, magnetic compass, camera, radar, LiDAR, geomagnetic direction sensor (GDS), and fiber-optic gyro (FOG). GNSS, IMU, camera, radar, and LiDAR can be used for ship positioning. Gyro compass, magnetic compass, GDS, and FOG are mainly used for azimuth measurement. In addition, GNSS and IMU are the basic sensors to ensure the safe operation of USV, which can be called safety sensors. Camera [14], radar [15], and LiDAR [16] can use the scan matching between consecutive frames for ASV state estimation. However, the camera is easily affected by illumination and weather conditions, resulting in large registration errors and inaccurate state estimation [17]. The low resolution of radar output also affects the accuracy of registration and state estimation [18]. Compared with the camera and radar, LiDAR can provide reliable and accurate distance measurement and is more robust to the environment with poor lighting conditions or less optical texture [19]. State estimation accuracy is usually higher. It has been a research hotspot in recent years. This paper mainly describes the autonomous positioning scheme based on 3D LiDAR. Scan matching is the core module of the LiDAR SLAM [20]. It uses the relationship between adjacent frames to estimate the motion pose of the current frame. Depending on this process, the current robot pose will be incrementally updated. Scan matching is commonly used in positioning and six-degree-of-freedom (6 DOF) state estimation of unmanned aerial vehicles [21], unmanned ground vehicles [22], and ASV [23]. For some applications that require precise positioning, scan matching can further refine the positioning accuracy, especially for scenarios such as berthing that require high position and rotation accuracy. Iterative closest point (ICP) [24] and normal distribution transformation (NDT) [25] are classic scan-matching algorithms. The ICP algorithm aligns two frames of point clouds by distance judgment, and the NDT algorithm uses a Gaussian distribution to model point clouds.