# Predictive Analysis of Vehicular Lane Changes: An Integrated LSTM Approach
## 3 Results and Analysis
### Integrated Prediction Model  
The optimal models identified from prior sections were integrated into a unified prediction model. For individual vehicles, the maneuver at each time step was initially predicted using the linear SVC model. If the prediction yielded a result of zero, then the LK-LSTM model was employed to forecast the longitudinal (\(pos_{y}\)) and lateral (\(pos_{x}\)) positions. Otherwise, the LC-LSTM model was utilized for position predictions. This approach enables the reconstruction of a vehicle's complete trajectory. For comparison, trajectories were also reconstructed using the Simple-LSTM model, serving as a baseline. The actual positional data, spanning 10,000 time steps, was employed to assess model performance. Table 12 presents a comparative analysis between the Simple-LSTM and Integrated-LSTM models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**LC-LSTM RMSE**} & \multicolumn{2}{c}{**Training Set**} & \multicolumn{2}{c}{**Testing Set**} \\ \cline{2-5}  & **Actual (ft)** & **Normalized** & **Actual (ft)** & **Normalized** \\ \hline \(y\) & 7.811 & \(5.0337\times 10^{-3}\) & 11.451 & \(7.3794\times 10^{-3}\) \\ \(x\) & 0.444 & \(4.9811\times 10^{-3}\) & 0.617 & \(6.9247\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results for LC-LSTM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**LC-LSTM RMSE**} & \multicolumn{2}{c}{**Training Set**} & \multicolumn{2}{c}{**Testing Set**} \\ \cline{2-5}  & **Actual (ft)** & **Normalized** & **Actual (ft)** & **Normalized** \\ \hline \(y\) & 11.030 & \(7.1081\times 10^{-3}\) & 8.844 & \(5.6989\times 10^{-3}\) \\ \(x\) & 0.752 & \(8.4409\times 10^{-3}\) & 0.427 & \(4.7940\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Results for LK-LSTM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Comparison**} & \multicolumn{2}{c}{**Simple-LSTM**} & \multicolumn{2}{c}{**Integrated-LSTM**} \\ \cline{2-5}  & \(y\) & \(x\) & \(y\) & \(x\) \\ \hline RMSE (ft) & \(10.576\) & \(1.870\) & \(16.621\) & \(1.401\) \\ Normalized RMSE & \(6.815\times 10^{-3}\) & \(20.987\times 10^{-3}\) & \(10.711\times 10^{-3}\) & \(15.731\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Results for LK-LSTM. In an evaluation of model accuracy, Figures 8 and 9 present the actual and predicted vehicle positions obtained using both the Simple-LSTM and Integrated-LSTM models, respectively. Figure 8 specifically focuses on the point-wise comparison of the true and estimated positions for several vehicle examples. Figure 8 displays the actual and predicted vehicular positions for IDs \(31,54,90\), and \(100\). The left column features the predictions generated by the Simple-LSTM model, whereas the right column showcases the results obtained via the Integrated-LSTM model. The first row of the figure is dedicated to illustrating the relationship between time and longitudinal positions, while the second row focuses on time versus lateral positions. Within each subplot, the red line represents the predicted positions, while the blue line delineates the actual positions. Figure 9 extends the analysis by depicting the full trajectories under both modeling paradigms. Figure 9 also displays the actual and predicted vehicular trajectories for IDs \(31,54,90\), and \(100\). The left figure features the predictions generated by the Simple-LSTM model, whereas the right figure showcases the results obtained via the Integrated-LSTM model, wherein the red line represents the predicted trajectory while the blue line delineates the actual trajectory. A closer examination of the figures reveals distinct differences in performance between the two models. Notably, the Integrated-LSTM model exhibited a greater variance in longitudinal positioning compared with its Simple-LSTM counterpart. On the other hand, the variance in lateral positioning was notably lower when using the Integrated-LSTM model.