## 4 Trajectory Prediction Performance Evaluation
Figure 5: The target intersection and recorded data of an example case from the intersection right turning experiments. (a) Bird’s-eye view; (b) Observed experiment vehicle trajectory; (c) Observed velocity of the experiment vehicle; (d) Observed steering wheel angle of the experiment vehicle. Figure 6: An example of the trajectory prediction in a real intersection by the trajectory prediction methods: (**a**) circular arc with constant radius; (**b**) circular arc considering the steering angle; (**c**) Barc curve; (**d**) Clothoidal curve; and (**e**) Triclothoidal curve. The prediction methods that require definition of the terminal point could predict the trajectory with high accuracy before getting into the intersection. The Triclothoidal curve, especially, could predict the trajectory with fewer deviations from the actual path. We can see from Figures 6 and 7 that, while the methods using circular arc trajectories (a) and (b) were not required to define the position of the terminal point, the prediction accuracy was lower, especially before entering the intersection. The deviations of the  
Figure 7: An example of the trajectory prediction in a real intersection by trajectory prediction methods: (**a**) circular arc with constant radius; (**b**) circular arc considering the steering angle; (**c**) Biare curve; (**d**) Clothoidal curve; and (**e**) Triclothoidal curve. The prediction methods that require definition of the terminal point could predict the trajectory with high accuracy before getting into the intersection. The Triclothoidal curve, especially, could predict the trajectory with fewer deviations from the actual path. curvature between observed data and prediction were large. The prediction accuracy of the (c) Biarc curve, (d) clothoidal curve, and (e) Triclothoidal curve was higher; however, the (c) Biarc curve and (d) clothoidal curve swelled out to the left at the beginning of the prediction because the predicted curvature of those curves were positive values at the beginning. On the other hand, because (e) the Triclothoidal curve considers the current steering angle of the vehicle, this method could predict the curvature as negative values so that the predicted trajectory does not swell out to the left. In addition, the Triclothoidal curve could predict the curvature of the driver's intersection right-turn accurately. Figure 8 shows the comparison of the absolute prediction error between the trajectory prediction methods, (c) Biarc curve, (d) clothoidal curve, and (e) Triclothoidal curve, from the driving experiments at 31 urban intersections in Tokyo. In the evaluation, prediction curves were generated every 5 m the ego vehicle travelled, and errors between the predicted trajectory and the observed actual path were calculated every 1 m step. The absolute errors were the measured deviations in the normal direction from the actual driving path of the ego vehicle and the errors were only used before and during the time the vehicle passed through the intersection. Therefore, the prediction errors after turning right were not considered. From the result, more than 70% of the predictions by the Triclothoidal curve had less than 0.3 m of absolute error. Comparing to the other prediction methods, the Triclothoidal curve was overwhelmingly accurate. In order to evaluate another aspect of the prediction performance by the Triclothoidal curve, we statistically estimated the trajectory prediction accuracy at the population of the urban intersection right-turn. We introduced the maximum absolute prediction errors as another index to evaluate the prediction performance and measured them from the lateral distance between the first trajectory prediction at the entrance of the intersection and the actual driving trajectory.