## 1 Introduction  
Decreasing the number of intersection accidents has been one of the most important challenges in ensuring traffic safety. According to the National Highway Safety Transportation Administration (NHTSA), from 2009 to 2018, the number of fatalities and injuries from accidents at intersections accounted for 26% of total fatalities and injuries from traffic accidents, and the number of fatalities and injuries at intersection accidents is slightly increasing [1]. In Japan, 42% of traffic accidents have occurred at intersections; however, excluding cases when the signals were ignored, right-turn accidents accounted for nearly 47% of those that occurred at intersections, which is the highest percentage in terms of intersection accidents [2]. Generally, an intersection right-turn (or left-turn in right-hand traffic) is a difficult task for drivers because drivers must be aware of oncoming traffic and crossing bycycles and pedestrians. Both cyclists and pedestrians may cross the road from the right and left sides, and these unpredictable situations can easily affect the judgement of drivers, thus increasing the risk of accidents [3]. From these facts, reducing right-turn accidents can be an important goal in reducing the overall traffic accidents. Further, this paper is particularly focused on right-turn accidents as recent statistical data have revealed that the accident rates for left-turns are not relatively high in Japan. To reduce the number of accidents at intersections, especially when vehicles make right-turns, extensive research on advanced driver assistance systems (ADAS) has been conducted from the perspective of active driver assistance. Research on ADAS that use vehicle-to-vehicle (V2V) or vehicle-to-infrastructure (V2I) communication was expected to reduce the number of accidents at intersections. By obtaining information on oncoming traffic and crossing pedestrians from transmitters fitted on infrastructure or other traffic communication participants, the systems alert to avoid collisions with objects coming from blind spots [4; 5; 6; 7; 8; 9; 10; 11]. V2I communication has also been used for a highly automated driving function to determine the right timing to turn at an intersection [12; 13]. Systems dependent on communication facilities are effective when both the surrounding vehicles and infrastructures have communication devices; however, it requires wide-ranging cooperation including manufacturers and local government. Therefore, it may take several years to deploy such facilities to entire city roads. It is against this backdrop that we found the need to develop and put more value on the ADAS without depending on the V2V or V2I communication. For the challenge of avoiding collisions while turning right at intersections, without depending on communication technology, ADAS or other risk prediction methods have been proposed [14; 15; 16; 17; 18; 19; 20; 21]. Our research group proposed an ADAS that enables the prediction of the potential risk of objects darting out from the blind spot during intersection right-turning [22; 23]. This ADAS assists deceleration to a moderate, safe speed by determining the potential risk by predicting the conflict point between the ego vehicle and the blinded darting-out object. These studies required a high-accuracy trajectory to predict the conflict point. The trajectory prediction method we have proposed in this paper is expected to fulfill the requirement. In the following text, we briefly review previous studies that have correctly predicted the trajectory of the vehicle. Some researchers took the approach of planning the intersection turning path for automated vehicles by generating the target path from digital maps [24; 25]. However, for most driver assistance systems, especially for systems in urban areas including intersection turnings, drivers were required to hold the steering wheel even during the assistance. Hence, the design of the ADAS requires the driver's input, such as dynamic steering wheel motion.