# GAT-ABiGRU Based Prediction Model for AUV Trajectory
## 4 Experiments and Results
### Analysis of Forecast Results
#### 4.4.2 Analysis of Ablation Experiments  
In this experiment, we focused on validating the impact of GAT (graph attention network) and its attention mechanism on model performance. To this end, we selected three models, ABiGRU, GAT-BiGRU, and GAT-ABiGRU, and conducted detailed experimental analyses. To maintain consistency in the experiments, the same dataset of 2000 entries is selected to ensure that all models are evaluated on the identical test and validation sets. Figure 8a,b demonstrate the prediction results of the ABiGRU model for the drift trajectories in latitude and longitude, respectively. Figure 9a,b show the prediction results of the GAT-BiGRU model for the drift trajectories in latitude and longitude. Finally, Figure 10a,b present a comprehensive comparison of the prediction results of the three models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Metrics** & **Latitude (*N)** & **Longitude (*E)** \\ \hline \multirow{3}{*}{RNN} & MSE & 0.009232 & 0.007548 \\  & RMSE & 0.096083 & 0.086879 \\  & MAE & 0.135882 & 0.122865 \\ \hline \multirow{3}{*}{GRU} & MSE & 0.003807 & 0.002014 \\  & RMSE & 0.061700 & 0.044877 \\  & MAE & 0.087258 & 0.063466 \\ \hline \multirow{3}{*}{CNN-LSTM} & MSE & 0.002324 & 0.001847 \\  & RMSE & 0.048207 & 0.042976 \\ \cline{1-1}  & MAE & 0.068176 & 0.060778 \\ \hline \multirow{3}{*}{GAT-ABiGRU} & MSE & **0.000163** & **0.000142** \\ \cline{1-1}  & RMSE & **0.012767** & **0.011916** \\ \cline{1-1}  & MAE & **0.018055** & **0.016852** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MSE, RMSE, and MAE value comparison among different models. Figure 8: (a) Latitude prediction results from the ABiGRU model; (b) Longitude prediction results from the ABiGRU model. From Figures 8-10, comparing the prediction results of latitude and longitude, it can be observed that the GAT-ABiGRU model achieves the most excellent fitting effect with the real trajectory. This model demonstrates high accuracy in predicting latitude and longitude, closely matching the real trajectory. Following it are the GAT-BiGRU model and the ABiGRU model, which although not as accurate as the GAT-ABiGRU model, still exhibit relatively outstanding performance compared to other models used in previous experiments. However, it is worth mentioning that the performance of the GAT-ABiGRU model surpasses both the GAT-BiGRU model and the ABiGRU model. This result fully demonstrates the effectiveness of the GAT network and attention mechanism in enhancing the model's performance. By introducing the GAT network and attention mechanism, the GAT-ABiGRU model can better capture the key information in the input. From the data in Table 2, we can observe a significant improvement in the trajectory prediction performance of the GAT-ABiGRU model compared to other models. Specifically, compared to the ABiGRU model, the GAT-ABiGRU model reduces 0.018601 in RMSE (root mean square error) for latitude and 0.016806 for longitude. This remarkable improvement demonstrates that introducing graph neural networks (GAT) effectively enhances the model's prediction accuracy. Furthermore, when comparing the GAT-ABiGRU model with the GAT-BiGRU model, we can see that the GAT-ABiGRU model achieves a reduction of 0.005065 in RMSE for latitude and 0.002401 for longitude. This result indicates that incorporating an attention mechanism before the bidirectional GRU (BiGRU) output enables more precise prediction results. The attention mechanism allows the model to focus more on critical information during prediction, thus enhancing accuracy. Therefore, by combining graph neural networks and attention mechanisms, the GAT-ABiGRU model significantly  
Figure 10: (**a**) Latitude prediction results from the GAT-ABiGRU, GAT-BiGRU, and ABiGRU models; (**b**) Longitude prediction results from the GAT-ABiGRU, GAT-BiGRU, and ABiGRU models. Figure 9: (**a**) Latitude prediction results from the GAT-BiGRU model; (**b**) Longitude prediction results from the GAT-BiGRU model.