## 4 Results and Discussion
### Lateral Displacement for Lane-Keeping Overtaking  
#### 4.2.1 Distribution Characteristics of Lateral Displacement  
In the vehicle reference frame, the \(Y\)-axis coordinates of overtaking vehicles at \(X=-100\) m and \(X=0\) m (before overtaking) or \(X=0\) m and \(X=100\) m (after overtaking) are extracted from the trajectories in Class I. The relative displacement of the overtaking vehicle within the range of 100 m is computed according to Equation (4), and the cumulative frequency statistics are shown in Figure 8a. It can be seen that the relative displacements before and after overtaking are roughly distributed in the ranges of \((-1.5,2.5)\) and \((-2,2)\) m. The relative displacement of the 85 th quantile before overtaking is 0.52 m, which is 0.28 m more than after overtaking, indicating that the lateral departing behavior is more obvious before overtaking. The relative displacement value of the 15 th quantile after overtaking is \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Classes**} & \multicolumn{4}{c}{**Before Overtaking**} & \multicolumn{4}{c}{**After Overtaking**} \\ \cline{2-10}  & **Sample Size** & **Initial Position** & **Driving Operation** & **Schema** & **Sample Size** & **Initial Position** & **Driving Operation** & **Schema** \\ \hline I & 1773 & Left lane & Straight ahead & & 1446 & Left lane & Straight ahead & \\ \hline II & 598 & Inside lane & Change lanes right & & 315 & Left lane & Change lanes left & \\ \hline III & 101 & Ego lane & Change lanes left & & 156 & Left lane & Change lanes right & \\ \hline IV & 8 & Right lane & Straight ahead & & 4 & Right lane & Straight ahead & \\ \hline V & 1 & Right lane & Continuous left lane & & 5 & Left lane & Continuous right lane & \\ \hline VI & 1 & Ego lane & Change lanes right & & 3 & Right lane & Straight ahead & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Different types of overtaking trajectories and their basic characteristics. \(-0.61\) m, which is 0.29 m less than before overtaking, meaning that vehicles approach each other more obviously after overtaking. Table 4 shows the proportion of lateral displacement behaviors in different overtaking phases. The proportion of lateral departing behavior before overtaking is higher, which indicates that vehicles tend to keep a constant lateral distance to ensure driving safety. The proportion of lateral approaching behavior after overtaking reaches 66%, mostly because the avoidance behavior in the previous phase makes the vehicle deviate from the centerline of the lane. Similarly, the absolute displacements of the overtaking vehicle and the overtaken vehicle in the road reference frame during the two phases are calculated according to Equations (2) and (3). The cumulative frequency statistics results in Figure 8b show that the absolute displacements in the 15 th quantile of the two vehicles before overtaking differ only by 0.03 m, which indicates that there is not much difference in their lateral approaching behaviors; the absolute displacements in the 85 th quantile of the overtaking vehicle are 0.16 m higher than that of the overtaken vehicle, and its lateral departing behavior is more obvious. It is worth noting that the absolute displacement of the 85 th quantile of the overtaken vehicle is 0.22 m higher than that of the overtaking vehicle, showing more obvious moving away behavior, which is reasonably explained by the fact that most of the overtaking vehicles have lateral approaching behaviors after they have moved to the front of the overtaken vehicle, and the overtaken vehicle has taken avoidance measures to ensure a safe lateral distance. Combined with the results in Table 4, the overtaking vehicles show more lateral departing behavior before overtaking and more lateral approaching behavior after overtaking; the overtaken vehicles have no obvious preference for lateral displacement behavior before overtaking and show more lateral departing behavior after overtaking.