# An Extended Car-Following Model Considering Generalized Preceding Vehicles in V2X Environment
## 3 Parameter Calibration  
NGSIM project initiated by the American Federal Highway Administration provides large-scale, high-precision vehicle trajectory data for the study of traffic flow theory, including the car-following model. The US101 data set of NGSIM is employed to celebrate the GPV model constructed in the previous section and then verify the celebration. To obtain suitable data for this specific work, selection of US101 data set need to be taken according to the following rules:  
Rule 1: Lane number. The highway section where the US101 data set is collected is divided into 4 lanes, and 1 ramp numbered 1-5, as shown in Figure 1. Considering that lane 4 is next to ramp 5 and lane-changing behavior is frequent, vehicles in lane 4 and ramp 5 will not be regarded as object vehicle to eliminate interference on car-following behavior exerted by lane-changing behavior. Further considering that the front vehicles in the adjacent lanes are introduced into the GPV model, vehicles only in lane 2 can be regarded as an object vehicle. Rule 2: Integrity of the vehicle group. GPV is comprehensively considered in our model, and thus the object vehicle for this research should have a complete GPV group. Based on this, the object vehicle for this research should have the front vehicle, non-neighboring front vehicle and left/right front vehicle to meet the integrity standard of the vehicle group. Rule 3: Time headway between the object vehicle and its front vehicle. If time headway between the vehicle and its front vehicle exceeds 5 s [39], movement of the vehicle is no longer restricted by its front vehicle, and the vehicle will not be considered to be in a car-following state. Vehicles which are in the car-following state can be regarded as an object vehicle for our study. Rule 4: Duration of car-following state. To ensure that the amount of data contained in each set of trajectory data are consistent and sufficient, the duration of the car-following behavior is set as 30 s considering characteristics of the US101 data set and its collection section. Figure 1: Lane setting of US101 collection section. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & \(\mathbf{V_{1}}\) & \(\mathbf{V_{2}}\) & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(l_{c}\) \\ \hline  & 6.75 & 7.91 & 0.13 & 1.57 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters value in Equation (5). According to rules 1-4, data filtering progress can be determined, as shown in Figure 2. Based on these, a selection of the US101 dataset is carried out, and 162 sets of trajectory data suitable for our research are obtained. Half of the datasets are randomly selected for calibrating model parameters, and the others are used to verify calibration results. Calibration of parameters in the car-following model is a kind of optimum solution for nonlinear programming problems. In this work, the objective function is calculation error between actual data and model output, variables to be optimized are parameters in the model, and constraints are the physical boundaries of these parameters. The genetic algorithm is widely used and has shown high performance in dealing with this kind of problems [40; 41]; parameters in the genetic algorithm used in this research are set as follows:  
1. population size: 60;
2. crossover probability: 0.9;
3. mutation probability: 0.2;
4. iteration number: 500;
5. value range of parameters to be celebrated: \(a\in[0,2]\), \(\lambda\in[0,1]\), \(p\in[0,1]\). Utilizing MATLAB (Version 9.6) software, parameters in the GPV model is calibrated. The FVD model constructed in [36] is also calibrated for comparison and further exploration in the following sections. Calibration results are as shown in Table 2.  
To verify the calibration results of parameters in the GPV model and the FVD model, mean absolute error (MAE) and mean absolute relative error (MARE) are employed as the performance index. The equations of MAE and MARE are as follows:  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-y_{i}^{m}\right| \tag{7}\]