## 4 Experiments
### Experimental Results
#### 4.4.2 Continuous Frame Experiment Comparison  
In contrast to the single-frame experiment of scan-to-scan registration, in a continuous-frame experiment, we use scan-to-map registration. The LiDAR frequency is 10 Hz, the IMU frequency is 100 Hz, and the GNSS data is about 2 Hz (uneven). In order to facilitate the performance comparison of the algorithm, after aligning the initial timestamp of the data, we use GNSS as a benchmark to select data with a time difference of less than 0.05 from the LiDAR data. Similarly, for the IMU data, we select the data with the smallest time difference between the IMU and the GNSS, and the time difference is less than 0.05. The data that meet the above conditions are used as the reference value to evaluate the performance of the algorithm. Figure 4 is the trajectory comparison map of each registration algorithm, and the dotted line is the true value of the trajectory. From the diagram, it can be observed that the registration results of FastGICP, FastVGICP, PTPLICP, PTPLCOMPICP, NDT, and NOTOMP7 are better, and the coincidence between the trajectory and the real value is higher. The trajectories of ICP, LMICP, GICP, and NDTOMP1 are quite different from the real values, and the registration results are poor, especially for ICP and GICP. Some trajectories of the ICP and GICP algorithms have exceeded the port range, so they are not shown. The registration results of the six algorithms, such as FastGICP, are close to the true values, but it can be observed from the local enlarged image that the registration results of some regions are also significantly different from the true values. In the following, we further compare and analyze the registration algorithms with better results. The PTPLICP and PTPLOMPICP trajectories are completely coincident, so only one of the two is discussed. Figure 5 shows the comparison of the output trajectories of the registration algorithms in the x, y, and z directions. The trajectories of each registration algorithm in the x and y directions are under a high degree of coincidence with the true value of the trajectory, which proves that the registration algorithm has better registration results in the horizontal plane. It can be seen from the local graph that in the x and y directions, the algorithms with slightly worse registration results than other algorithms are FastGICP and PTPLOMPICP, respectively. The difference between the results in the z direction is obvious. Depending on the data analysis, the reason for this phenomenon should be that the observation information in the z direction is less, the observation incident angle in the z direction is large, and the precision is poor. FastGICP, FastVGICP, and PTPLOMPICP have better registration results in the z direction. Figure 3: Comparison of registration algorithm results. It can be seen from Figure 6 and the local graph that each registration algorithm has a similar performance on the yaw angle. The performance of each algorithm is different in terms of roll angle and pitch angle. Compared with FastGICP, FastVGICP, PTPLICP, and PTPLOMPICP, NDT and NDTOMP7 are more unstable than the actual value. The reason why the roll angle is not much larger than the pitch angle is that the two sides of the ship are equipped with yellow, which can reduce the frequency of roll. Figure 4: Comparison of output trajectories of registration algorithm. Figure 7 shows the roll and pitch error curves. For ease of viewing, the curves are smoothed by the Savitzky-Golay filter, where the window length and polynomial fitting order are 15 and 3, respectively. From the smoothed curve, it can be seen that the trend of roll and pitch is similar, and both contain multiple local gentle (small change range) and local steep (large change range) stages. Registration is an ongoing process of error accumulation. The gentle error curve indicates that the registration error is small and the registration result is good.