## 4 Evaluation
### Performance of Trajectory Prediction  
The error between the ground truth and the predicted position of the adjacent vehicles was considered as the evaluation criterion of trajectory prediction. Considering that the proposed method predicts the future positions until 2 s with increments of 0.04 s, the root-mean-squared error (RSME) of all predicted positions was considered as the criterion. Let \(n\) be the index of the predicted position, and then the RMSE can be calculated as follows,  
\[\text{RMSE}=\sqrt{\frac{1}{N}\Sigma_{n=1}^{N}[(x_{n}-\hat{x}_{n})^{2}+(y_{n}- \hat{y}_{n})^{2}]}, \tag{19}\]  
where \(x_{n}\) and \(y_{n}\) denote the position at the incremental step \(n\), which is used as the ground truth. \(\hat{x}_{n}\) and \(\hat{y}_{n}\) represent the predicted position obtained using the proposed method. However, the error of lateral positions was excluded from the evaluation scope. \(N\) is the number of predicted positions. The future positions are predicted until two seconds with increments of 0.04 s; therefore, \(N\) is equal to 50. Figure 12 shows an example of the predicted future positions of the adjacent vehicles obtained using the proposed method. The green vehicle indicates the ego vehicle, whereas the blue ones represent the adjacent vehicles for which the ego vehicle is monitoring intentions and behavior. The blue rectangles show the predicted lane-keeping trajectories, and the red ones represent the lane-changing trajectory. The figure shows the future positions at five prediction terms: 0.4 s, 0.8 s, 1.2 s, 1.6 s, and 2 s. From this figure, it can be seen that the cut-in vehicle is detected, and the trajectory of that vehicle is successfully predicted. Consequently, it is possible to ensure sufficient response time for the ego vehicle based on the predicted future positions of the adjacent vehicles. Figure 11: Examples of the operation characteristic estimation using the proposed method: the blue line indicates \(\alpha\), the green one is \(l\), and the black line shows \(m\). These parameters do not have units. In addition, the red line indicates the reaction time (in seconds). It is confirmed that the reaction time is distributed around 1.5 s.  
Figure 12: Example of trajectory prediction: the blue rectangles show the predicted lane-keeping trajectories, and the red ones represent the lane-changing trajectory. It is confirmed that the cut-in vehicle is detected, and the trajectory of that vehicle is successfully predicted. To evaluate the effectiveness of the real-time estimation of operation characteristics, the prediction accuracy was compared to those of the previous methods that employ constant values of the operation characteristic variables, as shown in Table 1. As the previous methods cannot predict the lane-changing trajectory, only lane-keeping events were used for the performance comparison. It is clearly evident that the proposed method with the adjustment of operation characteristics significantly improves the prediction accuracy. In Table 1, the minimum error for each location is shown in bold. Compared to the results obtained using the previous methods, the proposed method considerably reduced the errors by almost the half of the number of errors reported for the previous method in [21]. The average error of the proposed method was 0.065 m, whereas that of [21] was 0.139 m.  
Considering the results of the three previous methods, it can be seen that the performance is largely affected by the values of the parameters. Among the previous methods, the values of the operation characteristic variables in [21] showed the best accuracy. However, it was confirmed that the average errors varied depending on the location. Therefore, it is concluded that the constant values cannot be adjusted according to the change in the driving conditions, which may lead to a deterioration of the performance. By contrast, the proposed method showed the robust performance in various driving conditions owing to the real time estimation of the parameter values.