## 3 Methods
### Model Parameter Identification
#### 3.2.2 Identification of Microcharacteristic Parameters of Driver Braking Behavior  
1. Data Collection  
1. Data set selection To deeply explore the characteristics of driver braking behavior from a microscopic perspective, a large- and wide-scale data set of driver behavior is required. This not only requires advanced data acquisition devices but also accumulates data over time and space dimensions. Therefore, for this study, we have chosen the publicly available naturalistic driving behavior data set (HighD) published by the Institute for Automotive Engineering at RWTH Aachen University in Germany [51]. The reasons for selecting this database are threefold: (1) the university has long-standing research expertise and advantages in the fields of automotive engineering and autonomous driving; (2) the database can meet the precision and breadth requirements of this study; and (3) it has been widely utilized by many researchers in the study of driver behavior [25; 26]. 2. Data set introduction The HighD data set is a new collection of natural vehicle trajectories on German highways. It overcomes limitations of traditional traffic data collection methods by using a drone's aerial perspective, which eliminates occlusions. The data set automatically extracts vehicle trajectories, including type, size, and maneuvers. It is also useful for tasks like analyzing traffic patterns and parameterizing driver models. The HighD data set includes a total of 60 highway sections. Each section data consists of four files, namely \"_highway.png\", \"_recordingMeta.csv\", \"_tracks.csv\", and \"_tracksMeta.csv\". For specific explanations and the coordinate system used for data collection, please refer to the official website. 3. Data collection In this study, the data of eight highway sections (sections 12, 17, 20, 32, 36, 42, 47, 60) were selected due to their wider range of braking acceleration distribution. Each highway section is 420 m long. 2. Data Reading and Processing This step involves data reading and processing, as shown in Figure 6.  
1. Utilizing Python programming, the data were compiled based on the data file ***_tracks.csv\". Within the recorded timeframe, the max-xAcceleration (maximum x Acceleration) for each vehicle (corresponding to each ID) was retrieved. 2. The filtering process is carried out to retain the arrays where the direction of max-xAcceleration is opposite to that of xvelocity. 3. The retrieved and filtered values of the max-xAcceleration are read into the data file ***_tracksMeta.csv\". A new data file ***_tracksMeta.new.csv\" was created. 4. A further filtering process is conducted. The arrays that did not record TTC (time to collision) or had abnormal TTC values were removed in data file ***_tracksMeta.new.csv\". 5. Finally, the data file ***_tracksMeta.new.csv\" from the eight highway sections were integrated into the data file \"all_tracksMeta.csv\". Data Analysis and Parameter Identification. The TTC is used to quantify the urgency of driving conditions, with a smaller TTC indicating a more urgent situation. As a result, drivers tend to take more urgent braking maneuvers. To analyze the data, we conducted density-based clustering analysis using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and implemented it in Matlab programming. The data set used for analysis includes the files ***_tracksMeta1.csv\" and \"all_tracksMeta.csv\". The _x_-axis and _y_-axis are the minTTC (minimum time to collision) and max-xAcceleration, respectively. The data analysis results are shown in Figures 7 and 8. Some preliminary conclusions can be drawn. (1) The data distribution of driver braking behavior is roughly the same in two driving directions on each highway section, (2) the max-xAcceleration values range from 0 to 5.5 m/s\({}^{2}\), and (3) the data are clustered into eight clusters. The max-xAcceleration values ranges for clusters 1 to 8 are as follows: [4.5, 5.5], [3, 4.5], [1, 3), [0, 1), (\(-\)1, 0], (\(-\)3, \(-\)1], (\(-\)4.5, \(-\)3], [\(-\)5.5, \(-\)4.5].