## 4 Naturalistic Driving Data-Based Longitudinal Driver Model Parameter Design
### Analysis of Free Acceleration/Deceleration Point  
Using the pre-processed data in Section 4.1, we analyzed the human drivers' free acceleration/deceleration driving data in a situation where the vehicle in front is far away and not obstructed. Figure 4 shows the maximum acceleration/deceleration distributions of vehicles driven by human drivers derived from the randomly chosen 300 free acceleration/deceleration datasets. The speed, acceleration, and jerk data used for the analysis are presented in Figure A2. Moreover, the distributions of maximum acceleration/deceleration for each maximum section during free acceleration/deceleration are summarized in Tables A1 and A2. With the analysis of the free acceleration/deceleration data, human drivers generally have similar patterns during free acceleration/deceleration (see Figure A2), and the mean values of maximum acceleration/deceleration are 2.30 m/s\({}^{2}\) and \(-\)2.16 m/s\({}^{2}\), respectively. Longitudinal driving characteristics of human drivers can be derived mainly from the mean and median values of acceleration/deceleration, and the mean was used in this study [47,48]. Figure 5 shows the driving of different drivers arbitrarily selected to see the human drivers' free acceleration/deceleration patterns in detail, and the maximum speed and maximum acceleration/deceleration for each driver are expressed in Table 3.  
Figure 4: Distribution of maximum acceleration/deceleration (300 random vehicles): (**a**) case of free acceleration; (**b**) case of free deceleration. Figure 3: Example of pre-processed driving data: (**a**) speed; (**b**) acceleration. To analyze the driving characteristics at the beginning of the time of braking, the required deceleration for braking is calculated and analyzed from data. The required deceleration means the deceleration required for a complete stop when the relative distance is \(R\) and the relative speed is \(\dot{R}\). Figure 6 and Equation (10) express the required deceleration calculation. \[a_{req}=sign\left(\dot{R}\right)\frac{\dot{R}^{2}}{2R} \tag{10}\]  
The beginning point of braking is defined as the point at which the first brake pedal signal occurs in the deceleration section before stopping. For the case where there is no leading vehicle, it is assumed that the virtual vehicle is stopped at the stop position of the ego vehicle. The analysis of the required deceleration calculated from the data at the beginning point of braking is specified in Figure 7a. The required deceleration at the start point of braking is \(-1.37\) m/s\({}^{2}\) on average with a 0.55 m/s\({}^{2}\) standard deviation. In the same way, the required deceleration at the sailing start point before braking is analyzed. The sailing start point can be expressed as the time when the acceleration pedal is released to brake, and this can be regarded as the start point of braking. As described in Equations (2) and (3), the rolling/aerodynamic resistances affect the motion of the vehicle. Therefore, the tendency to decelerate during sailing is different depending on the size or type of the vehicle. As this study develops the longitudinal motion scenario by imitating the overall driving pattern of a human driver, the sailing behaviors of various vehicles can be expressed with the variation of the required deceleration at the sailing start point. The analysis result of the required deceleration at the start of sailing is specified in Figure 7b, and the average value is \(-0.89\) m/s\({}^{2}\) with a standard deviation of 0.44 m/s\({}^{2}\). Moreover, the distributions of required deceleration at braking/sailing start point are summarized in Tables A3 and A4. Figure 6: Scheme of required deceleration. Figure 7: Distribution of required deceleration (300 random vehicles): (**a**) case of braking start point; (**b**) case of sailing start point.