## 1 Introduction  
Every year, the lives of approximately 1.35 million people are cut short as a result of road traffic crashes. The road traffic safety situation is severe worldwide [1]. According to statistics from the National Safety Council of the United States, there were 32,744 fatalities due to traffic accidents in 2014, which increased to 35,398 in 2015 and further rose to 40,200 in 2017, indicating an overall upward trend in casualties [2]. Additionally, data from the South Korean National Police Agency's investigation reported 45,921 pedestrian traffic accidents in 2019, resulting in 1487 fatalities and 46,400 injuries [3]. Advanced Driver Assistance Systems (ADASs) have experienced rapid development over the past decade, playing a crucial role in improving traffic safety [4, 5]. Research indicates that comprehensive deployment of the six most common ADASs would reduce the frequency of road accidents in the UK by 23.8%, translating to a yearly reduction of 18,925 accidents [6]. In Europe, light vehicles produced after 2022 are required to be equipped with Lane Keeping Assist (LKA) and Autonomous Emergency Braking (AEB) functionalities [7]. As one crucial component of ADASs, the Autonomous Emergency Braking System (AEBS) is a vehicle control system designed to assist drivers in avoiding and reducing the severity of traffic accidents. It detects potential collisions and activates the brakes automatically without requiring the driver's foot pedal action to initiate the braking. The LKAS alleviates the operational burden on drivers, curbing inadvertent lane departure and enhancing the vehicle's travel safety and lateral stability [8; 9; 10]. In the research on the collision avoidance effects of the AEBS, [PERSON] et al. evaluated the collision mitigation effects of the automatic emergency braking system based on data reported by insurance companies. The results indicated that vehicles equipped with AEB showed a 27% reduction in rear-end collisions compared to those without the AEB system [11]. The safety benefits of AEB for a country are closely related to the market penetration rate of active safety systems. [PERSON] et al. assessed the safety benefits of AEB in China using historical accident data and found that, compared to scenarios without AEB, with a 100% AEB penetration rate, the potential maximum reductions in deaths and injuries in China by 2030 could be 7.98% and 5.47%, respectively [12]. Furthermore, research by [PERSON] et al. demonstrated that vehicles equipped with AEB had a 38% lower probability of rear-end collisions compared to vehicles without AEB [13]. The study by [PERSON] et al. indicated that vehicles equipped with AEB systems could prevent 40% to 50% of rear-end collision accidents. The widespread adoption of AEB technology has the potential to prevent thousands of related fatalities and injury accidents each year [14]. Based on the actual data of thirty traffic accidents, it was confirmed that a total of twenty-seven accidents could have been prevented with the AEBS. Furthermore, it also demonstrated that the collision avoidance rate of vehicles gradually increased as the radar angle increased [15]. [PERSON] et al. showed that low-speed AEB systems could reduce the rates of rear-end collisions and rear-end injury collisions by 43% and 45%, respectively [16]. [PERSON] et al. indicated that the overall reduction in crash risk for AEB with pedestrian detection was 8%, and for AEB with bicyclist detection, it was 21% [17]. These findings underscore the significant importance of automatic emergency braking systems in collision avoidance. In the realm of collision avoidance control algorithms, [PERSON] et al. proposed an automatic emergency braking algorithm based on Time to Collision (TTC), which could satisfy both safety and ride comfort of a vehicle [18]. [PERSON] et al. developed an automatic emergency collision avoidance system designed to reduce rear-end collisions.