## 4 Expressway PTV Detection Algorithm for Over-the-Horizon
### PTV Quantitative Evaluation Algorithm
#### 4.5.3 Construction of PTV Evaluation Algorithm  
In order to better evaluate the PTV of expressway sections, a comprehensive comparative analysis was conducted on PTVs, and their severity ratings were evaluated. It is necessary to further determine the weight impact of different indicators on PTV threat assessment, that is, the degree to which different indicators have an impact on the results. The core of AHP is to apply a hierarchy to the problem to be analyzed. Based on the nature of the problem and the overall goal to be achieved, the problem is decomposed into different factors, and the factors are aggregated and combined at different levels according to their correlation, influence, and membership relationships, forming a multi-level analytical structural model. This method is applied to the multi-objective comprehensive evaluation method for hierarchical weight decision analysis. In the field of intelligent driving, PTV threat assessment is regarded as a multi-objective comprehensive evaluation, and it is difficult to quantitatively describe what threat is. AHP is very suitable for this type of problem. Therefore, this article uses the structure of AHP to describe the modeling of threat assessment levels. Figure 7 is the analytic hierarchy process structure diagram. Figure 6: Schematic diagram of S-type membership function. Figure 7: Analytic hierarchy process structure. Due to the consideration of multiple characteristic indicators in PTV evaluation, it is not possible to accurately calculate the degree of influence of each factor. When assigning weights to obtain weight vectors, subjective factors account for a large proportion and can select the factors that have the greatest impact on danger. Corresponding weights can be given based on the importance of the indicators. Therefore, it is necessary to establish a judgment matrix to compare the importance of any two factors, avoiding the computational difficulty of comparing all factors together. Table 2 represents the quantitative criteria for the importance between elements, which divides the importance scale of elements into 1-9. The larger the importance scale, the more important the element is relative to another element. The judgement matrix R= rij(n \(\times\) n) is constructed by filling in the values comparing the importance of two elements, as shown in Table 3.  
After the construction of the judgement matrix is completed, the matrix needs to be tested for consistency, which refers to the permissible range of inconsistency determined by pairwise comparison of the matrices. The final weights can be obtained only after passing the consistency test of the judgement matrix. Calculate the consistency index (CI) with Formula (9), as shown below:  
\[\text{CI}=\frac{\lambda_{\text{max}}-\text{n}}{\text{n}-1} \tag{9}\]  
where \(\lambda_{\text{max}}\) is the maximum eigenvalue of the matrix. When CI = 0, there is complete consistency; when CI approaches 0, there is satisfactory consistency. The larger the CI, the more severe the inconsistency. In order to measure the size of CI, a random consistency indicator RI was introduced, and the statistical data of RI is shown in Table 4. Finally, the consistency ratio CR is obtained and calculated as shown in Formula (10). \[\text{CR}=\frac{\text{CI}}{\text{RI}} \tag{10}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Scale** & **Meaning** \\ \hline
1 & Equally important \\
3 & One factor is slightly more important than the other \\
5 & One factor is obviously more important than the other \\
7 & One factor is strongly more important than the other \\
9 & One factor is extremely more important than the other \\
2, 4, 6, 8 & Intermediate value of two adjacent judgments \\ Reciprocal & A is compared with B; if the scale is 3, then B compared with A is 1/3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proportional scale table.