## 5 Driver Acceptance Evaluation Model
### Parameter Selection
#### 5.1.1 Objective Parameters  
In the interaction database, each lane change case is described with various measurable, objective parameters. Table 1 shows the parameters selected for this study, including several representative parameters related to the control command, vehicle dynamic behavior, and relative relations with surrounding vehicles with their descriptive statistical values. To analyze the statistical significance and the acceptance sensitivity of the parameters associated with the spatial relationships between vehicles in terms of driver acceptance, the relative positions regarding three target vehicles are defined in Figure 3. Each surrounding vehicle was defined as follows: Target A represents the leading vehicle in the active lane, Target B represents the leading vehicle in the target lane, and Target C represents the following vehicle in the target lane. Figure 3: Relative positions between the ego-vehicle and the target vehicles. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Objective Factors**} & \multicolumn{1}{c}{**Description**} \\ \hline
**First Level** & **2 nd Level** & **3 rd Level** & \\ \hline \hline \multirow{8}{*}{Control Command} & \multirow{4}{*}{TPS} & Minimum & \multirow{2}{*}{Throttle position sensor} \\ \cline{3-3}  & & Maximum & \\ \cline{3-3}  & & Median & \\ \cline{3-3}  & & Mean & \\ \cline{3-3}  & & Standard Deviation & \\ \cline{2-3}  & \(\delta\) & \(\uparrow\) & Steering wheel angle \\ \cline{2-3}  & \(\dot{\delta}\) & \(\uparrow\) & Steering wheel angular velocity \\ \hline \multirow{8}{*}{Vehicle behavior} & Minimum & \multirow{2}{*}{Longitudinal velocity} \\ \cline{3-3}  & & Maximum & \\ \cline{3-3}  & & Median & \\ \cline{3-3}  & & Mean & \\ \cline{3-3}  & & Standard Deviation & \\ \cline{3-3}  & & \(Vy\) & \(\uparrow\) & Lateral velocity \\ \cline{3-3}  & & \(\dot{V}x\) & \(\uparrow\) & Longitudinal acceleration \\ \cline{3-3}  & \(\dot{V}y\) & \(\uparrow\) & Lateral acceleration \\ \cline{3-3}  & \(\ddot{V}x\) & \(\uparrow\) & Longitudinal jerk \\ \cline{3-3}  & \(\ddot{V}y\) & \(\uparrow\) & Lateral jerk \\ \cline{3-3}  & \(\dot{\psi}\) & \(\uparrow\) & Yaw angle \\ \cline{3-3}  & \(\dot{\psi}\) & \(\uparrow\) & Yaw angular velocity \\ \cline{3-3}  & \(\ddot{\psi}\) & \(\uparrow\) & Yaw angular acceleration \\ \cline{3-3}  & \(\dot{\phi}\) & \(\uparrow\) & Roll angle \\ \cline{3-3}  & \(\dot{\phi}\) & \(\uparrow\) & Roll angular velocity \\ \hline \multirow{8}{*}{Vehicle Relationships (Targets \(A\), \(B\), C)} & Minimum & \multirow{2}{*}{Time to collision} \\ \cline{3-3}  & Maximum & \\ \cline{3-3}  & Median & & \\ \cline{3-3}  & Mean & & \\ \cline{3-3}  & \multicolumn{3}{c}{Standard Deviation} \\ \cline{3-3}  & \(TTCx\) & \(\uparrow\) & Longitudinal time to collision \\ \cline{3-3}  & \(TTCy\) & \(\uparrow\) & Lateral time to collision \\ \cline{3-3}  & \(rtV\) & \(\uparrow\) & Relative velocity \\ \cline{3-3}  & \(rtVx\) & \(\uparrow\) & Longitudinal relative velocity \\ \cline{3-3}  & \(rtVy\) & \(\uparrow\) & Lateral relative velocity \\ \cline{3-3}  & \(D\) & \(\uparrow\) & Distance \\ \cline{3-3}  & \(Dx\) & \(\uparrow\) & Longitudinal distance \\ \cline{3-3}  & \(Dy\) & \(\uparrow\) & Lateral distance \\ \hline \hline \end{tabular} \(\dagger\) means ”same as above”.  
\end{table} 
Table 1: Parameters selected for the study, including several parameters related to the control command, vehicle dynamic behavior, and relative relations with surrounding vehicles. where \(TTC_{i}\) is the time to collision at the \(i\)th step; \(P_{ego}\) and \(P_{Target\ A,B,C}\) are the positions of the ego-vehicle and each target vehicle; and \(V_{ego}\) is the velocity of the driving vehicle. \[relV_{i}=V_{ego}-V_{TargetA,B,C} \tag{12}\]  
where \(relV_{i}\) is the relative velocity between the driving vehicle and the target vehicles at the \(i\)th step and \(V_{Target\ A,B,C}\) is the velocity of each target vehicle.