## 4 Naturalistic Driving Data-Based Longitudinal Driver Model Parameter Design  
### Driving Data Pre-Processing  
The safety pilot model deployment (SPMD) database, an open naturalistic driving database, is used to derive the driving characteristics of human drivers [35]. SPMD consists of data acquisition systems (DAS), basic safety messages (BSM), roadside equipment (RSE), and contextual data. Among the vast amount of data in this database, only a part of DAS, which is closely related to this paper, is selected for human driving characteristics analysis. DAS consists of DAS1 and DAS2. Both DAS1 and DAS2 provide data for ego vehicles and GPS measurements for each vehicle. However, for measurement of the vehicle in front, DAS1 used a vision sensor and DAS2 used a radar sensor. Between them, only the radar sensor-based DAS2, which has relatively high measurement accuracy for longitudinal driving, is used. In DAS2, 14,346 driving datapoints of 64 vehicles are measured at a 10 Hz cycle. It is confirmed that there are omissions or noise in some of the data. Therefore, the data are preferentially classified through a classification process shown in Table 2 in consideration of its reliability and efficiency. For more detail, the data classification process is described in Appendix A.  
A smoothing process is performed to remove noise from the classified data. For this purpose, the locally estimated scatterplot smoothing (LOESS) algorithm, which is a widely known local regression method, is used [49]. LOESS is a regression method that constructs a quadratic polynomial using a weight function \(w\) for regression smoothing and a robust weight function \(G\) based on median values (see Equations (7)-(9)). In Equation (9), the coefficients \(a,b\), and \(c\) of the quadratic polynomial are derived in the direction of minimizing the product of the weights and the square error of the actual data and the quadratic polynomial.  
\[w(x_{k})=\bigg{(}1-\bigg{|}\frac{x_{i}-x_{k}}{d_{i}}\bigg{|}^{3}\bigg{)}^{3} for\ k=1,\ldots,\ n \tag{7}\]  
\[G(x_{k})=\begin{cases}1-6 MID&|6 MID|<1\\ 0&|6 MID|\geq 1\\ \frac{|y_{i}-\theta_{i}|}{6\ \text{median}\ (|y_{i}-\theta_{i}|)}\end{cases} \tag{8}\]  
\[RSS_{x}(a,b,c)=\sum_{k}w(x_{k})G(x_{k})\Big{(}y_{k}-a-bx_{k}-cx_{k}^{2}\Big{)}^ {2} \tag{9}\]  
Figure 3 is an example of smoothing results obtained by applying LOESS to the classified data. As shown in Figure 3, the smoothing process was carried out only to the extent that the characteristics of the data were not loose. In the case of the acceleration data, there is an offset within the data, thus there is an error even when the smoothing process is performed. For example, although the speed increases in the 65-70 s section in Figure 3a, the acceleration in the same section in Figure 3b is shown as 0, indicating that there exists an offset of the acceleration data. It is judged that this offset is caused by problems such as  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Step** & **Exclusion Conditions** & **Remain Time (s)** \\ \hline (1) Original & - & 8,338,419.4 \\ (2) Trip time & Trip data less than 300 s & 7,589,392.0 \\ (3) Radar & Radar data nonexistence & 7,523,291.5 \\ (4) 0 to 0 & Zero speed nonexistence & 7,277,452.8 \\ (5) Data & Continuous data nonexistence over 10 s & 6,884,491.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data classification process to ensure reliability.  
the measurement equipment setting and the mounting error when gathering the SPMD data set. However, in the case of the speed data, the smoothing processing showed a better result than the acceleration data. For this reason, acceleration for the data analysis is used by differentiating the smoothed speed of the data.