## 4 Target State Prediction with Uncertainty Estimation
### Driving Mode Decision  
Constraints for SMPC are highly related to the driving mode because intersection cross priority decides the boundaries of constraints. Therefore, the driving mode should be determined before defining the constraints for SMPC. In this study, driving modes are composed of three modes: 'Approach', 'Cross', and 'Yield'. The approach mode is prepared to provide safe approaching behavior at the uncontrolled intersection until the target is detected. It means that the driver's deceleration characteristics are reflected in autonomous driving as an approach mode to avoid the inevitable collision with targets appearing from a blind spot. The deceleration command of the approach mode is determined based on the shape of the occluded region, the possible target-appearing position, and the nominal braking characteristics of the human driver. Meanwhile, the cross and yield modes are declared when the autonomous vehicles detect other intersection-approaching targets. In these driving modes, the risk caused by the target vehicle should be properly managed by the interaction between the autonomous vehicle and targets. Then, an SMPC-based motion planner is used to determine the desired acceleration. Particularly, yield mode is the replacement of the stop mode of the previous studies to cover most driving situations except when the ego vehicle has a cross priority. Therefore, an autonomous vehicle in yield mode does not simply stop but determines various behaviors according to the driving situation. A mode transition condition between the cross and yield modes is defined based on the uncontrolled intersection theory. The uncontrolled intersection theory has been used to analyze the driving behavior of human drivers who are interacting with each other in uncontrolled intersections. The concepts of critical gap and follow-up gap have been used to define the mode transition condition between the cross and yield modes. In the uncontrolled intersection theory, the critical gap is the threshold for the time gap between higher-rank stream vehicles. It means that no driver will split the vehicle stream from a higher-rank road unless the gap between the vehicle in a higher priority stream is at least equal to the critical gap. The follow-up gap is the threshold to follow the preceding vehicle that enters the intersection. The driver will enter the intersection if the headway time with a preceding vehicle is less than the follow-up gap. This concept has been modified to define the mode transition condition for the proposed driving-mode decision algorithm. First, the approaching targets have been classified into three groups, primary, secondary, and in-lane targets, as shown in Figure 9. The first vehicle entering the intersection from other branches of the ego vehicle is denoted as a primary target. Then, the next vehicle immediately following the primary target is classified as a secondary target. The in-lane target means the preceding target of the ego vehicle. Based on the target classification, a time gap between primary and secondary targets is compared to the critical gap. A headway time between the in-lane target and ego vehicle is compared to the follow-up gap. When calculating the time gap and headway time, the predicted states of the ego and the target vehicle have been used to overcome the limitations of the constant velocity assumption. The driving mode is changed to yield mode if one of the following conditions is satisfied: (1) The remaining time to the intersection is larger than the primary target, (2) the time gap between primary and secondary target is smaller than the critical gap threshold, or (3) the headway time to the preceding vehicle is larger than the follow-up gap threshold. On the contrary, the cross mode is only declared if the opposites of the aforementioned conditions are all satisfied simultaneously. This hard condition for the cross mode is introduced to prevent a dangerous situation caused by misjudgment of the driving mode.