## 4 Results Analysis and Discussion
### Complete Trajectory Prediction  
In this study, we compared the performance of the Decision Tree, Gradient Boosting Regressor, and Random Forest models in predicting the outcomes for two ships of different sizes, drafts, and types, particularly during maneuvers involving various turning angles. One ship has the following specifications: a length of 199 m, a beam of 32 m, a draft of 13.1 m, and is a bulk carrier. The other ship has a length of 115 m, a beam of 20 m, a draft of 9.3 m, and is a general cargo vessel. Figure 14 and Table 3 compares the predictions for the bulk carrier in terms of position, Course Over Ground (COG), and Speed Over Ground (SOG). Panel (a) compares the predicted ship positions across different models, where the Random Forest model's predicted trajectory aligns most closely with the actual trajectory, indicating higher prediction accuracy and stability. The Gradient Boosting Regressor shows some deviation from the actual position, while the Decision Tree model exhibits larger discrepancies from the actual trajectory. Panel (b) compares the predicted COG across different models, with both the Random Forest and Gradient Boosting Regressor models closely matching the actual COG, demonstrating strong predictive performance; however, the Decision Tree model shows \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Parameter** & **MSE** & **Adjusted \(R^{2}\)** \\ \hline \multirow{3}{*}{Random Forest} & LON & 2293.8592 & 0.9999 \\  & LAT & 6790.8516 & 0.9999 \\  & SOG & 6.0709 & 0.9957 \\  & COG & 33.2415 & 0.9727 \\ \hline \multirow{3}{*}{Random Forest} & LON & 18,823.2767 & 0.9998 \\  & LAT & 27,791.3605 & 0.9996 \\  & SOG & 38.9861 & 0.9923 \\  & COG & 160.2386 & 0.9812 \\ \hline \multirow{3}{*}{Decision Tree} & LON & 23,957.7198 & 0.9979 \\  & LAT & 18,916.4763 & 0.9978 \\ \cline{1-1}  & SOG & 19.0222 & 0.9871 \\ \cline{1-1}  & COG & 259.5119 & 0.9359 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction Error Summary. a significant gap compared to the actual COG, indicating poorer performance. Panel (c) compares the SOG predictions across different models, where the Random Forest model's prediction curve closely aligns with the actual values at most data points, demonstrating very high prediction accuracy. In contrast, the Decision Tree model shows considerable deviation, and the Gradient Boosting Regressor provides moderate prediction accuracy. Figure 15 and Table 4 compares the predictions for the general cargo vessel in terms of position, COG, and SOG. Panel (a) contrasts the actual ship trajectory with the predicted positions from different models, where the Random Forest model shows very close alignment with the actual trajectory, indicating high prediction accuracy. The Gradient Boosting Regressor also performs well, closely aligning with the actual trajectory. The Decision Tree model, however, shows significant deviations from the actual trajectory in some regions, indicating poorer performance. Panel (b) compares COG predictions across different models, where the Random Forest model closely matches the actual COG, showing excellent predictive performance. The Gradient Boosting Regressor's predictions are also close to the actual values at most data points, while the Decision Tree model's predictions deviate more significantly. Panel (c) compares SOG predictions across different models, with the Random Forest model's prediction curve aligning very closely with the actual values at most data points, indicating very high prediction accuracy. In contrast, the Decision Tree model shows significant deviation, and the Gradient Boosting Regressor provides moderate prediction accuracy. The comparison across these three aspects reveals that the Random Forest Regressor consistently outperforms in predicting ship trajectories, COG, and SOG, with prediction results that fit the actual values most accurately.