## 3 Vehicle Pose Estimation Method
### Point Tracking Based on Local Search Area  
Tracking edge points form the foundational basis for calculating the unknown structural parameters delineated in Equations (1)-(3). Given that MI\(-\)CNN effectively identifies the frontal vehicle and its corresponding edge points within each frame, this section of the paper is dedicated to elucidating the optimal approach for inter-frame matching. In scenarios characterized by high video frame rates, the intervals between frames translate to minimal inter\(-\)vehicle distances, resulting in relatively minor changes in pixel displacement within the image. Consequently, the conventional practice of globally matching target vehicles on a one\(-\)by\(-\)one basis is deemed unnecessary [27]. The decomposition of motion and the statistical analysis of pixel displacement for select frontal vehicles across frames are vividly depicted in Figure 6. The abscissa represents the frontal vehicles' pixeldisplacement component in the horizontal or vertical directions in the previous frame (\(\Delta x_{1}\) or \(\Delta y_{1}\)), while the ordinate represents the displacement component of the current frame (\(\Delta x_{2}\) or \(\Delta y_{2}\)). In Figure 5, the dotted black lines demarcate the upper and lower envelopes of the scatter diagram. The range \(R\) delineated by the black dashed lines defines the local tracking search area, meticulously aligning with the prerequisites of vehicle matching. Given the inherent limitations of prior datasets to encompass the entirety of working conditions, a redundant variable \(b\) is introduced. This variable dynamically adjusts the search area in real time, guaranteeing continuous adequacy for \(R\) to encompass the upcoming target. Suppose the resolved motion of the frontal vehicle is approximately equal to the linear motion with uniform speed. In that case, \(\Delta y_{pre}\) is the displacement of the previous frame, \(a\) is the acceleration, and \(\Delta t\) is the fixed inter\(-\)frame time; then, the current displacement \(\Delta y\) is:  
\[\Delta y=\Delta y_{pre}+a\Delta t^{2} \tag{9}\]  
Due to the interference caused by system delays, measurement errors, or other factors, a linear fitting model of the local tracking search area can be established according to Equation (3):  
\[\Delta y=k_{1}\Delta y_{pre}+k_{2}+b \tag{10}\]  
where \(k_{1}\) and \(k_{2}\) can be obtained after fitting the scatter plot data, and \(b\) can be corrected with the calculated redundancy distance after vehicle matching. It will keep the redundancy constant. When the tracking search areas overlap with each other or the number of vehicles to be matched is greater than one, the optimal matching association can be obtained by combining motion and texture similarity. Given that the number of vehicles in the current search area is \(N_{1}\), \(M_{ij}=1\) represents that vehicle \(I\) in frame \(t\) matches vehicle \(j\) in frame \(t+1\), while \(M_{ij}=0\) represents that they do not match. The set \(\Delta=\{M_{ij}\}\in\{0,1\}^{N\times N}\) represents all matching combinations, and the optimal association can be calculated as:  
\[\Delta_{\rm op}=\underset{\Delta}{\rm argmax}\sum_{i=1}^{N}\sum_{j=1}^{N}s_{ i,j}M_{i,j} \tag{11}\]  
Figure 6: Displacement’s scatter plot of the edge points and analysis of the vehicle’s displacement. The red dot is the statistical analysis of pixel displacement for select frontal vehicles across frames. The redundancy is the search area. The search area is the area that completes the cut to the vehicle and the target vehicle. \[\left\{ \begin{array}{l}\sum_{i=1}^{N}\Delta_{i,j}=1i\in\{1,2,\ldots N\}\\ \\ \sum_{j=1}^{N}\Delta_{i,j}=1j\in\{1,2,\ldots N\}\\ \\ \Delta_{i,j}\in\{0,1\}\end{array} \right. \tag{12}\]  
where 0 is filled in when the number of vehicles is insufficient, and \(s_{ij}\) represents the matching confidence between vehicles \(i\) and \(j\). It can be calculated as follows:  
\[s_{i,j}=\alpha s_{m,ij}-(1-\alpha)s_{p,ij} \tag{13}\]  
\[\left\{