# VEPO-S2S: A VESsel Portrait Oriented Trajectory Prediction Model Based on S2S Framework
## 5 Experiments
### Model Performance Comparison  
#### 5.2.1 Comparison Results  
Through comparisons with the baselines using the evaluation metrics of the RMSE, MAE, and ADE, our model demonstrated strong robustness, as shown in Tables 2-4. The LSTM, BiLSTM, GRU, and BiGRU employ a sliding window approach for the prediction of multiple points, while the other six Seq2 Seq models do not. Our model outperformed the baselines in the third to fifth trajectory points. However, the GRU achieved better results in the MAE in Table 3 and the ADE in Table 4, regarding the first and second points. This is mainly because the GRU has a structural advantage in predicting short-term sequences due to its simplicity. However, VEPO-S2S experiences a slight decrease when handling short-term predictions, as the portrait of the vessel may not be easily discernible. When the prediction length increases, our model performs better than the baseline models, according to the RMSE, MAE, and ADE. Simultaneously, considering that trajectory prediction is also a time series forecasting problem, we compared VEPO-S2S with several time series forecasting models, including the ARIMA, Kalman Filter, and VAR. As Tables 2-4 show, our model was superior to others; the three-time series prediction models performed well in short-term forecasting, but the accuracy rapidly declined as the forecast horizon increased. Specifically, the VAR model became ineffective after the third time step because it failed to capture long-term complex nonlinear relationships. Different from time series models that only utilize position sequences, VEPO-S2S benefits from additional prior information, such as the ship length and width, as well as its powerful ability to construct spatiotemporal correlations from historical trajectory points, making it more advantageous in forecasting tasks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Name** & **10->1** & **10->2** & **10->3** & **10->4** & **10->5** \\ \hline Kalman & \(3.42\times 10^{-4}\) & \(4.62\times 10^{-4}\) & \(8.22\times 10^{-4}\) & \(11.52\times 10^{-4}\) & \(14.29\times 10^{-4}\) \\ VAR & \(1.38\times 10^{-4}\) & \(5.60\times 10^{-4}\) & \(123.53\times 10^{-4}\) & - & - \\ ARIMA & \(4.83\times 10^{-4}\) & \(7.11\times 10^{-4}\) & \(9.42\times 10^{-4}\) & \(11.76\times 10^{-4}\) & \(14.14\times 10^{-4}\) \\ LSTM & \(0.68\times 10^{-4}\) & \(1.22\times 10^{-4}\) & \(1.87\times 10^{-4}\) & \(2.64\times 10^{-4}\) & \(3.51\times 10^{-4}\) \\ BiLSTM & \(2.37\times 10^{-4}\) & \(2.38\times 10^{-4}\) & \(2.99\times 10^{-4}\) & \(3.74\times 10^{-4}\) & \(4.56\times 10^{-4}\) \\ GRU & \(\mathbf{0.59\times 10^{-4}}\) & \(\mathbf{1.05\times 10^{-4}}\) & \(1.62\times 10^{-4}\) & \(2.27\times 10^{-4}\) & \(2.99\times 10^{-4}\) \\ BiGRU & \(2.42\times 10^{-4}\) & \(2.73\times 10^{-4}\) & \(4.00\times 10^{-4}\) & \(4.91\times 10^{-4}\) & \(5.20\times 10^{-4}\) \\ LSTM-LSTM & \(1.11\times 10^{-4}\) & \(1.59\times 10^{-4}\) & \(2.13\times 10^{-4}\) & \(2.73\times 10^{-4}\) & \(3.38\times 10^{-4}\) \\ BiLSTM-LSTM & \(1.39\times 10^{-4}\) & \(1.90\times 10^{-4}\) & \(2.47\times 10^{-4}\) & \(3.07\times 10^{-4}\) & \(3.72\times 10^{-4}\) \\ GRU-GRU & \(0.80\times 10^{-4}\) & \(1.23\times 10^{-4}\) & \(1.74\times 10^{-4}\) & \(2.31\times 10^{-4}\) & \(2.93\times 10^{-4}\) \\ BiGRU-GRU & \(1.16\times 10^{-4}\) & \(1.75\times 10^{-4}\) & \(2.38\times 10^{-4}\) & \(3.05\times 10^{-4}\) & \(3.76\times 10^{-4}\) \\ Transformer & \(1.28\times 10^{-4}\) & \(1.50\times 10^{-4}\) & \(1.83\times 10^{-4}\) & \(2.25\times 10^{-4}\) & \(2.73\times 10^{-4}\) \\ METO-S2S & \(2.26\times 10^{-4}\) & \(2.30\times 10^{-4}\) & \(2.41\times 10^{-4}\) & \(2.68\times 10^{-4}\) & \(3.07\times 10^{-4}\) \\ Ours & \(0.83\times 10^{-4}\) & \(1.17\times 10^{-4}\) & \(\mathbf{1.52\times 10^{-4}}\) & \(\mathbf{2.01\times 10^{-4}}\) & \(\mathbf{2.52\times 10^{-4}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison results of VEPO-S2S with various baselines under ADE evaluation metric. Here, 10->5 means predicted through 10 historical trajectories.