## 4 Experiments
### Model Performance Comparison
#### 4.2.3 Quantitative Analysis  
To further explore the detailed prediction error, we performed experiments from the first to the fifth track point and calculated the metrics of RMSE, MAE, and FDE. The prediction results are displayed in Tables 7-9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Name** & **Enc** & **Dec** & **RMSE** & **MAE** & **ADE** & **FDE** \\ \hline PESO & LSTM & LSTM & _0.000466_ & _0.000327_ & _0.000523_ & _0.000681_ \\ PESO-GRU-GRU & GRU & GRU & 0.000552 & 0.000399 & 0.000646 & 0.000817 \\ PESO-BiGRU-GRU & BiGRU & GRU & 0.000531 & 0.000387 & 0.000617 & 0.000766 \\ PESO-BiLSTM-LSTM & BiLSTM & LSTM & 0.000511 & 0.000380 & 0.000562 & 0.000704 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Exploration results on different Seq2 Seq structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Name** & **First** & **Second** & **Third** & **Fourth** & **Fifth** \\ \hline LSTM & 0.000389 & 0.000649 & 0.001000 & 0.001359 & 0.001710 \\ BiLSTM & 0.000499 & 0.000757 & 0.001092 & 0.001441 & 0.001785 \\ GRU & 0.000395 & 0.000651 & 0.001000 & 0.001358 & 0.001708 \\ BiGRU & 0.000434 & 0.000672 & 0.001011 & 0.001366 & 0.001712 \\ LSTM-LSTM-LSTM & 0.000380 & 0.000592 & 0.000893 & 0.001245 & 0.001639 \\ GRU-GRU & _0.000326_ & 0.000719 & 0.001235 & 0.001801 & 0.002396 \\ BiGRU-GRU & 0.000730 & 0.000897 & 0.001133 & 0.001574 & 0.002280 \\ BiLSTM-LSTM & 0.000571 & 0.000618 & 0.000772 & 0.000952 & 0.001210 \\ PESO & 0.000333 & _0.000367_ & _0.000425_ & _0.000511_ & _0.000620_ \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantitative results on each track point under the metric of RMSE. \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 LSTM & 0.000493 & 0.000651 & 0.000842 & 0.001043 & 0.001245 \\ BiLSTM & 0.000611 & 0.000769 & 0.000956 & 0.001152 & 0.001350 \\ GRU & 0.000495 & 0.000650 & 0.000839 & 0.001037 & 0.001238 \\ BiGRU & 0.000528 & 0.000677 & 0.000860 & 0.001056 & 0.001254 \\ LSTM-LSTM & 0.000462 & 0.000587 & 0.000748 & 0.000935 & 0.001139 \\ GRU-GRU & _0.000399_ & 0.000649 & 0.000953 & 0.001290 & 0.001649 \\ BiGRU-GRU & 0.000914 & 0.000995 & 0.001096 & 0.001256 & 0.001499 \\ BiLSTM-LSTM & 0.000740 & 0.000753 & 0.000818 & 0.000900 & 0.001007 \\ PESO & 0.000412 & _0.000429_ & _0.000453_ & _0.000484_ & _0.000523_ \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison results with time-series forecasting models under four metrics of RMSE, MAE, ADE, and FDE. The experiments were conducted in the most typical scenario in this paper: predicting the following 5 track points with the previous 10. In these three tables, we can see that the baseline models have advantages in predicting the first track point, but PESO outperforms other models in the prediction of the next track points, and the prediction errors of all models obviously increase from the first to fifth points. That is because from the first prediction to the last, the amount of information available for a single prediction is obviously decreasing. RNN-baseline models, such as LSTM, use a sliding window manner to predict, which will gradually increase the error and accumulate inaccuracy for each prediction. Seq2 Seq-baseline models, such as BiLSTM-LSTM, are capable of predicting several points at one time, reducing the tendency of the increasing error compared to RNN-baseline models. Our proposed model, PESO, is specially designed with Parallel Encoders and a Ship-Oriented Decoder. The Parallel Encoders are targeted to capture more feature information by using different encoders to obtain multiple feature representations, which include the Location Encoder and the Sailing Status Encoder. The Parallel Encoders embed different types of features at the same time, avoiding the noise generation of different types of features and enriching feature representation.