## 6 Conclusions  
This paper mainly studies the ASV maritime positioning and state estimation based on LiDAR, where the poses are obtained by scan matching. We introduced ICP, NDT, and their variants in detail and selected 10 different registration methods for testing and evaluation, including ICP, LMICP, GICP, FastGICP, FastVGICP, and PTPLICP, PTPLCOMP1C, NDT, NDTOMP1, and NDTOMP7. The performance test experiment of the algorithm is divided into single-frame experiments and continuous-frame experiments. Single-frame experiments involved the registration of two adjacent frames, and continuous-frame experiments used scan-to-map registration. The accuracy of the single-frame experiment is evaluated by the \(RMSE\), and the parameters of the algorithm are selected at the same time. The continuous-frame experiment uses the registration output overall trajectory, XYZ direction trajectory, Euler angle, ATE, and RPE to evaluate each registration algorithm.  
The experimental results show that the single-frame registration ICP and LMICP have high accuracy, and the mean values of \(RMSE\) on 10 pairs of data are 0.965926 and 0.966460, respectively. NDTOMP1 and VGICP are fast in registration, and the average registration time is 19 ms and 31.4 ms, but the registration accuracy is much lower than ICP. For continuous-frame registration, the registration results of ICP, LMICP, GICP, and NDTOMP1 differ greatly from the truth values, especially ICP and GICP. VGICP and multi-threaded optimization GICP have the best effect, and the \(RMSE\) of ATE is 1.862248 and 2.199127, respectively. Compared with straight-line navigation, the distance between the corresponding points of two adjacent frames of point clouds increases and becomes more discrete when USV turns, and the registration accuracy is worse.  
However, there are still some defects in this paper owing to the limitations of experimental conditions. The mechanism of loss of registration accuracy at turning could be revealed by more abundant data sets, such as different maneuvers, ASVs of different sizes, and LiDAR of different types. In addition, the influence of dynamic objects from a busy port on point cloud registration is the focus of our future study.  
Writing--original draft preparation, H.W.; writing--review and editing, Y.Y. and Q.J.; methodology, H.W., Y.Y. and Q.J.; software, H.W. and Q.J.; formal analysis, H.W.; validation, H.W.; investigation, H.W. and Q.J.; resources, Y.Y. and Q.J.; data curation, H.W., Y.Y. and Q.J.; visualization, H.W.; funding acquisition, Y.Y. and Q.J.; supervision, Y.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52071049; the Doctoral Scientific Research Foundation of Liaoning Province of China, grant number 2020-BS-070; Ministry of Industry and Information Technology Letter \"Intelligent Ship Comprehensive Test and Verification Research\", grant number No. 2018(473); the Fundamental Research Funds for the Central Universities, grant number 3132022131, and the 2022 Liaoning Provincial Science and Technology Plan (Key) Project: R&D and Application of Autonomous Navigation System for Smart Ships in Complex Waters, grant number 2022 jH1/10800096.  
Not applicable.  
The authors declare no conflict of interest.