## 3 Case Analysis and Discussion
### Data Preprocessing
#### 3.2.2 Trajectory Data Preprocessing  
According to existing research literature, there are some outliers and measurement errors in the NGSIM trajectory data, which have a great negative impact on the calibration and verification of the models. Furthermore, the vehicles' speed and acceleration in NGSIM are obtained from first-order and second-order derivatives of longitudinal displacement, respectively. The error of speed and acceleration will be magnified 10 times and 100 times if the longitudinal displacement contains errors. Therefore, it was necessary to smooth the NGSIM data. Figure 1: Schematic diagram of the I-80 detection section. Many existing methods can be used for processing the NGSIM data, but most of them directly smooth the speed and acceleration obtained from the derivation of the longitudinal trajectory of vehicles, which will lead to overprocessing and affect the actual accuracy of trajectory to a certain extent. To meet the research needs of this study, some processing on the dataset was first carried out. The specific treatment scheme was as follows:  
1. Convert the imperial units in the dataset into international standard units, exclude the data of trucks and motorcycles, and only keep the data of small cars in the I-80 highway as the research object. 2. Handling abnormal data in NGSIM dataset. The data marked with the same vehicle ID under different vehicle trajectories are relabeled, and then abnormal vehicles with mismatched framerates are eliminated due to lane-changing behavior. Abnormal data in the data collection, such as negative vehicle spacing, are also eliminated. 3. Renumber the vehicle ID of the sample data and recalculate the speed, acceleration, and following distance of each vehicle in each frame according to \"Local_X\" and \"Local_Y\" in the dataset. The formula is shown in Equations (15)-(19). \[V_{xi}(t) =\frac{X_{i}(t+n)-X_{i}(t)}{0.1n}\] (15) \[V_{yi}(t) =\frac{Y_{i}(t+n)-Y_{i}(t)}{0.1n}\] (16) \[A_{xi}(t) =\frac{V_{xi}(t+n)-V_{xi}(t)}{0.1n}\] (17) \[A_{yi}(t) =\frac{V_{yi}(t+n)-V_{yi}(t)}{0.1n}\] (18) \[D_{i}(t) =Y_{j}(t)-Y_{i}(t)-L_{j}(t)\] (19) where \(V_{xi}(t)\) and \(V_{yi}(t)\) represent the lateral and the longitudinal speed of vehicle \(i\) at frame \(t\), respectively, \(X_{i}(t)\) and \(Y_{i}(t)\) represent the lateral and the longitudinal coordinates of vehicle \(i\) at frame \(t\), respectively, \(A_{xi}(t)\) and \(A_{yi}(t)\) represent the lateral and the longitudinal acceleration of vehicle \(i\) at frame \(t\), respectively, \(n\) represents the difference between the frames, \(D_{i}(t)\) represents the car-following distance, \(Y_{j}(t)\) and \(L_{j}(t)\) represent the longitudinal coordinate and the length of the vehicle \(j\) being followed, and \(Y_{i}(t)\) represents the longitudinal coordinate of the following vehicle \(i\). 4. This study did not consider the collector-distributor lanes and the entrance and exit ramps. Thus, only lanes 1-5 were reserved as the research object. The front and rear vehicle information of vehicle \(i\) is searched through data matching, and only the \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Describes** & **Unit** \\ \hline Vehicle\_ID & vehicle identification number & / \\ Frame\_ID & frame of data at a certain moment & 0.1 s \\ Total\_Frame & total of frames of the target car in the dataset & 0.1 s \\ Global\_Time & timestamp & Ms \\ Local\_X & lateral coordinate of the front center of the vehicle & Feet \\ Local\_Y & longitudinal coordinate of the front center of the vehicle & Feet \\ v\_length & vehicle length & Feet \\ v\_Class & vehicle type & 1-Motorcycle, 2-Car, 3-Truck \\ Lane\_ID & current lane position of the vehicle & / \\ Preceding & vehicle ID number of the preceding vehicle on the same lane & / \\ Following & vehicle ID number of the rear vehicle on the same lane & / \\ Location & street name or highway name & / \\ \hline \end{tabular}
\end{table} 
Table 1: Original data of the NGSIM dataset.