# Use of a Weighted ICP Algorithm to Precisely Determine USV Movement Parameters
## 2 Evaluation of the Accuracy of Determining the Coordinates of a Position Using LIDAR
### Weighted Matching Point Clouds Using the Mean Direction Error
Figure 14 shows that the accuracy of determination of the \(\mathrm{\Delta COG}\) using the K_ICP method significantly decreases, as in the case of the SOG, for scans in the intervals of \(\left\langle 220,\ 365\right\rangle\) and \(\left\langle 720,\ 825\right\rangle\). The HD_ICP method also proved to be the best in determining the \(\mathrm{\Delta COG}\) in this case. This was also confirmed by the lowest values of the mean error, equal to \(0.03^{\circ}\), and of the standard deviation, equal to \(0.11^{\circ}\), presented in Table 1. Figure 15 shows a histogram representing the frequency of occurrence of \(\mathrm{\Delta COG_{ICP}}-\mathrm{\Delta COG_{R}}\) increment differences. The histogram representing the frequency of the occurrence of differences \(\mathrm{\Delta COG_{ICP}}-\mathrm{\Delta COG_{R}}\) shown in Figure 15 enables the conclusion that the HD_ICP method is also the best in terms of the accuracy of determining the \(\mathrm{\Delta COG}\). Its advantage over the others can be clearly seen in the interval of differences \(\mathrm{\Delta COG_{ICP}}-\mathrm{\Delta COG_{R}}\)\(\left\langle-0.05,\ 0.05\right\rangle\). Given that the \(\mathrm{\Delta ROT}\) results are identical with the \(\mathrm{\Delta COG}\) results, their presentation and analysis have been omitted. Differences in the algorithms' accuracy are shown at Figure 16 (presenting results of H_ICP and HD_ICP). Differences between HD_ICP and HM_ICP versions are barely visible, so they were omitted. Figure 12: A graph of \(\mathrm{SOG_{ICP}}-\mathrm{SOG_{R}}\) differences. Figure 13: Histogram representing the frequency of occurrence of \(\mathrm{SOG_{ICP}}-\mathrm{SOG_{R}}\) differences. ## 4 Conclusions

As the study attempted to prove, an ICP algorithm that matches point clouds from a laser scanner can effectively generate USV movement parameters. The proposed weighting factor based on the mean error in the specified direction of the determination of the coordinates of the positions of

Figure 16: (**a**) Grid map computed by ICP with proposed directional weighting—HD_ICP; (**b**) grid map computed standard H_ICP. Figure 7:0 A graph of \(\Delta\)COG\({}_{\text{ICP}}-\Delta\)COG\({}_{\text{R}}\) increment differences. Figure 7:1 A histogram representing the frequency of occurrence of \(\Delta\)COG\({}_{\text{ICP}}-\Delta\)COG\({}_{\text{R}}\) increments. scan points enables more realistic (corresponding to the actual movement) matching of subsequent maps of the surrounding environment. This helps to determine the USV movement parameters with a higher accuracy. This was confirmed by the study results--inter alia the values of statistical indices in the form of mean \(\text{SOG}_{\text{ICP}}-\text{SOG}_{\text{R}}=0.007\ \frac{\text{m}}{\text{s}}\ (-0.014\ \text{kts})\) and standard deviation \(\text{SOG}_{\text{ICP}}-\text{SOG}_{\text{R}}=0.0025\ \frac{\text{m}}{\text{s}}\ (0.05\ \text{kts})\) and \(\Delta\text{COG}_{\text{ICP}}-\Delta\text{COG}_{\text{R}}=0.03^{\circ}\) and standard deviation \(\Delta\text{COG}_{\text{ICP}}\ -\ \Delta\text{COG}_{\text{R}}=0.11^{\circ}\). However, it should be noted that the authors' original weighting factor should be used in combination with a robust criterion function to reduce measurements with gross errors (e.g., based on Huber's function), as only such a solution can be fully applicable. The indicated mean error values lead us to a generalized statement that the developed method allows measuring SOG and COG with the accuracy required by the IMO. It should be noted, however, that the test was carried out in confined waters (harbors, channels, berths, marinas), beyond which the method would not be effective due to the low LIDAR range. All data used in publication is available at [51]. L.M., methodology, investigation, writing-original draft preparation, writing-review and editing, K.N., supervision, formal analysis, validation and funding acquisition. The article has been funded by a statutory research on marine optical navigation systems conducted in Polish Naval Academy.