## 2 Methodology
### Data Collection and Analysis  
Since the optimized design has never been constructed yet, it is essential to develop and calibrate an accurate and stable simulation model to recreate the real traffic scenario. Thus, actual traffic data should be collected to create a simulation model for evaluating each design. The following data were collected:  
* Vehicle speed and volume, which were used to calculate traffic density.
* Time headway and lane change trajectories are used to calibrate vehicles' behavior in simulation.
* The diverging ratio of the investigated interchange.
* The proportion of passenger vehicles and trucks in the investigated section.  
Furthermore, optimal conditions required to conduct this task include peak hours of several levels of service (LOS), clear weather, free from any unforeseen crashes or facility maintenance, and avoidance of obvious congestion [38]. Therefore, a preliminary investigation is imperative to determine specific details. Notably, roadside radar equipment can be replaced with UAVs for efficient data collection, as it always attracts drivers' attention and disrupts the normal traffic flow.  
The use of UAVs provides a cost-effective solution for data collection since their compact and portable size enables up to 30 min of continuous aerial photography per battery charge. Additionally, it offers a wide field of view, enhancing the spatial coverage of data measurement. However, this method necessitates more stringent image processing requirements, which can be addressed through the use of an image recognition tool based  
Figure 4: Optimized design scheme B, with both left and right side exit ramps (LRER).  
Figure 3: Optimized design scheme A, with lane separation around the interchange (LSI).  
on the YOLOv3 target detection algorithm. To establish an accurate coordinate network in the video, it is necessary to first employ a GPS-RTK mobile station to measure the coordinate information of string feature points along the roadside. Figure 5 shows the used devices and tools.  
Obtained vehicle trajectory data frequently contains errors that could result from UAV in-flight jitter, and these errors may be further amplified at speed and acceleration. To eliminate this effect, the authors propose the application of the Kalman filter, which serves as an optimal autoregressive data processing algorithm that leverages the linear system state equation to estimate the system state optimally from input and output observations [39]. Equation (1) shows the Kalman filter process.  
\[\left\{\begin{array}{l}\hat{\pi}_{t}^{-}=F\hat{x}_{t-1}+Bu_{t-1}\\ P_{t}^{-}=FP_{t-1}F^{T}+Q\\ K_{t}=P_{t}^{-}H^{T}(HP_{t}^{-}H^{T}+R)^{-1}\\ \hat{x}_{t}=\hat{x}_{t}^{-}+K_{t}(z_{t}-H\hat{x}_{t}^{-})\\ P_{t}=(I-K_{t}H)P_{t}^{-}\end{array}\right. \tag{1}\]  
The Kalman filter process involves several components. \(\hat{x}_{t}^{-}\) and \(\hat{x}_{t}\) denote the predicted and optimal estimate values of the system state at moment \(t\), respectively. \(U_{t-1}\) denotes the acceleration at moment \(t\). \(F\) and \(B\) serve as the state transfer matrix, \(P_{t}^{-}\) and \(P_{t}\) represent the covariance estimation matrix and the optimal estimation matrix, respectively. The Kalman coefficient is denoted as \(K_{t}\), and \(Q\) is the predicted noise covariance matrix. The observed matrix and observed noise covariance matrix are represented by \(H\) and \(R\), respectively. \(Z_{t}\) denotes the measured position value, and \(I\) serves as the unit matrix.  
The optimal predicted trajectory can be obtained by utilizing the Kalman filter, which further solves for several critical parameters, including vehicle speed, density, volume, and time headway.