## 1 Introduction  
Lane width is a critical parameter in road geometric design. If the lane width is excessively wide, while traffic capacity can be ensured, the excessive lateral clearance may lead to a rapid decline in drivers' lane-keeping sensitivity and increase the risk of distracted driving. Conversely, if the lane width is too narrow, it can significantly impede the free flow of vehicles and increase the likelihood of collisions between vehicles and with roadside obstacles. Therefore, designing an appropriate lane width is essential to ensure both traffic safety and efficient vehicle operation. In recent years, China's freeway network has been gradually improved. To meet the increasing transportation requirements of the masses, freeway reconstruction and expansion projects have been gradually put on the agenda, and the design of passenger-dedicated lanes has become a focus of attention [1]. However, the current established Chinese technical standards for lane widths are mainly for mixed passenger and freight traffic, with trucks rather than passenger cars as the design vehicle. The external dimensions and dynamic characteristics of cars are quite different from trucks, and whether and to what extent the width of their dedicated lanes can be reduced are yet to be analyzed and justified by relevant studies. Understanding and mastering the driving behavior of highway vehicles, particularly their overtaking maneuvers, are essential for the design of appropriate lane widths. Overtaking is a complex process where vehicles have certain speed differences and are spatially close to each other, which can easily lead to accidents such as scratches, rollovers and rear-end collisions [2]. According to statistics, 4-10% of all traffic accidents occur in the overtaking process [3,4]. Therefore, mastering the motion characteristics of vehicles along the cross-section of the road in the overtaking scenario not only helps to deeply understand the formation mechanism of vehicle overtaking risk but also provides data support for lane width design. However, most data acquisition methods in previous studies have relied on real-vehicle driving [5] and simulation [6], and the former approach struggles to capture comprehensive dynamic and static parameters of surrounding vehicles, while the latter faces challenges in ensuring the reliability and applicability of the results. Moreover, these traditional data collection methods often fail to provide a sufficiently large sample size, thereby limiting the generalizability of the research findings. With the rapid advancement of artificial intelligence in recent years, computer vision technology has become increasingly sophisticated, making it feasible to extract high-precision vehicle trajectories [7]. Utilizing UAV video-based vehicle detection and tracking algorithms can yield micro-traffic information characterized by large sample sizes and multiple parameters [8]. This study aims to propose a passenger lane width calculation method for freeways based on overtaking behavior. UAVs are used to record videos on the common two-way six-lane freeways in China. Parameters such as the position and outermost dimensions of the vehicle are extracted from the aerial video based on computer vision technology. After screening the eligible overtaking events, the lateral motion and lateral distance of vehicles during the overtaking process are analyzed. The main contributions of this research work are as follows:  
* To intuitively express the relative motion between vehicles, a vehicle coordinate system is established at the geometric center of the overtaken vehicle. * To describe the lateral motion of a vehicle during overtaking, the absolute lateral displacement is defined in the road coordinate system and the relative lateral displacement is defined in the vehicle coordinate system.