## 4 Results and Discussion
### Lateral Displacement for Lane-Keeping Overtaking
#### 4.2.2 Factors Affecting Lateral Displacement  
The results in Figure 8 and Table 4 show that there is some difference in the distribution of absolute displacement of vehicles during overtaking, but specifically what kind of difference exists in each overtaking process has not been clarified. According to Equation (5), the relative displacement is formed by stacking the absolute displacements of the two vehicles. Thus, the relative displacement of vehicles is grouped at an interval of 0.5 m and the absolute displacements corresponding to each relative displacement are counted, and the results are shown in Figure 9.  
As can be seen from the line connecting the mean values of absolute displacements of each group in Figure 9a, the absolute displacement of the overtaking vehicle shows a monotonically increasing relationship with the change in relative displacement. The amplitude of its absolute displacement at the same level of relative displacement is significantly higher than that of the overtaken vehicle, which indicates that the relative displacement before overtaking is mainly contributed by the overtaking vehicle. The results in Figure 9b show that when the two vehicles are laterally close to each other (negative relative displacement), the overtaking vehicle is still the main contributor to the relative displacement because the overtaking vehicle that deviates from the lane center before overtaking will return to travel near the lane center after overtaking. However, when the two vehicles move away from each other, the absolute displacement of the overtaken vehicle was not significantly weaker than that of the overtaking vehicle, and even the mean value of some groups was slightly higher than that of the overtaking vehicle, most likely because the front-to-back positional relationship of the vehicles after overtaking has been reversed, and the overtaken vehicle was able to see the overtaking vehicle directly in front of it and adopted moving away behavior to maintain a safe lateral distance. Taken together, in addition to the obvious lane-changing behavior, the lateral displacement of the vehicles is also related to the lateral distance-keeping behavior and lane-keeping behavior. According to the statistical results of the cumulative frequency, both before and after overtaking vehicles are not uniformly shown to be laterally close to or moving away from each other, and there are some differences in the amplitude of the lateral displacements, which are likely to be related to the initial lateral distance of the vehicles at the beginning of each phase. To verify the above conjecture, the initial geometric center distances as well as the relative displacements of the Class I trajectories at the beginning of the overtaking phase were extracted in the vehicle reference frame. Figure 10 shows the two-dimensional  
Figure 9: The relationship between absolute displacement and relative displacement of vehicles. (**a**) Before overtaking; (**b**) After overtaking. scatter distribution of relative displacement versus initial geometric center distance. It can be found that the relative displacement changes from positive to negative as the initial geometric center distance increases, indicating that the two vehicles tend to move away from each other when the initial geometric center distance is small. A linear function was used to fit the scatter points, and the results are shown in Table 5. According to the parameters obtained by fitting, the lateral displacement zeros of the two phases before and after overtaking can be calculated as 4.24 m and 3.75 m. The lateral displacement zero reflects the driver's expectation of lateral distance in different overtaking stages. The expected lateral distance before overtaking is 0.49 m more than the lane width of 3.75 m, which indicates that the vehicle tends to keep a larger lateral distance than the lane width to ensure the safety of overtaking.