## 2 Data Collection and Analysis
### Data Analysis  
The processed aerial video enables the extraction of trajectory data for individual vehicles through analysis using image recognition software. By employing the YOLOv3 target detection algorithm, a trained vehicle detection model facilitates the comprehensive analysis of video frames, facilitating the extraction of crucial vehicle operation data, such as vehicle identification numbers, world coordinates (x and y), vehicle models, and velocities. To ensure data accuracy, anomalous data are meticulously addressed:  
* Datasets in which trajectories began and ended nearby, including those encompassing road markings within the detection range, were discarded. * Iteration through each frame of the vehicle trajectory was conducted to eliminate data points with x-coordinates that were less than their predecessors. * Vehicle trajectory data located on the paved shoulder were excluded. Following the aforementioned data-processing methodology, 280 sets of vehicle operation trajectories were obtained. Among these, 78 sets pertained to lane-change trajectory data, comprising 64 sets of right lane changes and 14 sets of left lane changes. Due to the possibility of errors in image detection caused by screen jitter resulting from high-altitude  
Figure 1: Data collection sites and devices. airflow, Kalman filtering was employed to refine trajectory data and minimize decision errors, as illustrated in Equation (1):  
\[ \begin{array}{l}\hat{x}_{t}^{-}=F\hat{x}_{t-1}+Bu_{t-1}\\ P_{t}^{-}=FP_{t-1}F^{T}+Q\\ K_{t}=P_{t}^{-}H^{T}\big{(}HP_{t}^{-}H^{T}+R\big{)}^{-1}\\ \hat{x}_{t}=\hat{x}_{t}^{-}+K_{t}\big{(}z_{t}-H\hat{x}_{t}^{-}\big{)}\\ P_{t}=(I-K_{t}H)P_{t}^{-}\end{array}  \tag{1}\]  
where \(\hat{x}_{t}^{-}\) denotes the predicted system state at moment \(t\), \(F\) and \(B\) serve as the state transfer matrix. \(\hat{x}_{t}\) denotes the optimal estimate values of the system state at moment \(t\), \(u_{t}\) denotes the acceleration at moment \(t\), \(P_{t}^{-}\) and \(P_{t}\) represent the covariance estimation matrix and the optimal estimation matrix, respectively, \(Q\) is the predicted noise covariance matrix, and the Kalman coefficient is denoted as \(K_{t}\). The observed matrix and observed noise covariance matrix are represented by \(H\) and \(R\), respectively. \(z_{t}\) denotes the measured position value at moment \(t\) and \(I\), serves as the unit matrix. Assuming that the state of the system at time \(t\) is represented by a three-dimensional vector \(x(t)=(x_{t}y_{t}v_{t})^{T}\), where \(x_{t}\) signifies the world \(x\) coordinate, \(y_{t}\) denotes the world \(y\) coordinate, \(v_{t}\) is the vehicle speed, and \(\theta_{t}\) is the vehicle speed declination. The state transfer equation is expressed in Equation (2). \[\left\{ \begin{array}{l}x_{t}=x_{t-1}+v_{t-1}\Delta t\cos\theta_{t-1}+\frac{ \Delta t^{2}}{2}u_{t}\cos\theta_{t-1}\\ y_{t}=y_{t-1}+v_{t-1}\Delta t\sin\theta_{t-1}+\frac{\Delta t^{2}}{2}u_{t}\sin \theta_{t-1}\\ v_{t}=v_{t-1}+u_{t}\Delta t\end{array} \right. \tag{2}\]  
The video recording is operated at a frame rate of 30 frames per second, allowing the assumption of negligible vehicle acceleration between consecutive intervals. Consequently, the state transfer matrix is depicted in Equation (3). Additionally, the trajectory prediction curve is based on a third-degree polynomial fit of the scattered data points. This curve ensures a smooth and uninterrupted representation, aligning the vehicle's instantaneous speed direction tangential to the trajectory curve. Subsequently, the calculation of the vehicle speed deflection angle is presented in Equation (4). \[\left[ \begin{array}{c}x_{t}\\ y_{t}\\ v_{t}\end{array} \right]=\left[ \begin{array}{ccc}1&0&\Delta t\cos\theta_{t-1 }\\ 0&1&\Delta t\sin\theta_{t-1}\\ 0&0&1\end{array} \right]\left[ \begin{array}{c}x_{t-1}\\ y_{t-1}\\ v_{t-1}\end{array}