## 4 Experiments
### Orientation Estimation  
Given that the accurate structural parameters of vehicles within the video dataset remain undisclosed, a pertinent methodology is employed. The geometric characteristics of the test vehicles are meticulously measured beforehand, and, subsequently, these measurements are compared against the algorithm's outputs during experimentation. The test vehicles navigate across various scenarios, encompassing curves, intersections, and more. The derived statistical outcomes from the structural parameter estimation are summarized in Table 2. The tabulated results provide a comprehensive overview of the algorithm's performance in estimating structural parameters. A noteworthy observation from the table is that the proportion of estimated parameters whose errors fall below the threshold of 0.8 m consistently surpasses the 85% mark. When the error threshold is set at less than 0.12 m, the proportion of estimated parameters meeting this criterion consistently exceeds 90%. This finding substantiates the efficacy of the approach outlined in this paper, which leverages a mixed probability distribution to detect vehicle distance sequences reliably and accurately. This detection capability, in turn, lays a robust foundation for the subsequent optimization of structural parameters. In the course of the experiments, a discernible trend emerges: a higher probability associated with the distance sequence corresponds to dimin \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Proposed Method (\%)**} & \multicolumn{3}{c}{**Individual Kalman (\%)**} & \multicolumn{3}{c}{**Feature-Based (\%)**} \\ \cline{2-9}  & **MR** & **FPR** & **MMR** & **MR** & **FPR** & **MMR** & **MR** & **FPR** & **MMR** \\ \hline Video1 & 5.2 & 1.1 & 0.2 & 13.2 & 9.1 & 1.0 & 21.8 & 18.2 & 34.2 \\ \hline Video2 & 2.1 & 0.4 & 0.1 & 9.8 & 6.7 & 0.6 & 10.2 & 9.1 & 20.5 \\ \hline Video3 & 5.8 & 7.9 & 0.4 & 9.4 & 16.8 & 1.3 & 27.1 & 26.4 & 27.4 \\ \hline Video4 & 5.3 & 2.1 & 0 & 7.6 & 14.2 & 0.9 & 17.2 & 20.1 & 23.2 \\ \hline Video5 & 7.9 & 4.6 & 1.2 & 11.2 & 15.8 & 4.1 & 21.4 & 22.3 & 24.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative evaluation of different tracking methods. shed parameter estimation errors. However, this advantageous outcome is accompanied by an increased convergence time. Subsequent to the optimization of structural parameters, the distance measurement of target vehicle components is undertaken even under challenging operational conditions. In order to gauge the method's effectiveness, a comparison is made with two alternative measurement techniques within the same video dataset. These techniques entail shadow segmentation and external bounding box\(-\)based methods. To assess accuracy, a curve plotting the normalized ranging error along the horizontal axis and the cumulative proportion on the vertical axis is generated, as depicted in Figure 11. Remarkably, under equivalent measurement error thresholds, the method introduced in this paper consistently yields a notably higher count of vehicles compared to both the shadow segmentation and bounding box approaches. In scenarios where the shadow of the target vehicle is perturbed and becomes arduous to segment accurately, the corresponding shadow model exhibits greater errors. This phenomenon is depicted within Area A of Figure 12. When the lower edge of the target vehicle is obscured entirely, leaving the camera's view limited to the roof, both the shadow segmentation model and the bounding box method confront difficulties in identifying the horizontal reference area. Consequently, these methods need to improve in their ability to maintain accurate measurement, which is evident in Area B of Figure 12.  
In the ultimate phase of verification, an experiment is conducted to ascertain the robustness of our algorithm in the presence of vehicle turbulence. A test vehicle is driven in a straight path across a bumpy road.