## 3 Materials and Methods
### Position Algorithm Calculation
#### 3.1.2 Step 2: Positioning Process  
1. The dead reckoning positioning method is used to locate the moving point of the vehicle with the information of only one base station [46]. The positioning principle calculates the vehicle position at the next time based on the vehicle location, driving direction, and vehicle speed at the previous time. Since the position and direction at the previous moment determine the position at the current moment, positioning errors may continue to accumulate as the positioning updates. When the dead reckoning positioning method is adopted, the initial coordinate is known as \((x_{0},y_{0})\) and the initial azimuth is \(\theta_{0}\), and the dead reckoning positioning coordinates \((x_{a},y_{a})\) can be calculated by:  
\[\left\{ \begin{array}{l}x_{a}=x_{0}+S_{0}\sin\theta_{0}\\ y_{a}=y_{0}+S_{0}\cos\theta_{0}\end{array} \right. \tag{3}\]  
\[S_{0}=v_{0}t \tag{4}\]  
where \(S_{0}\) indicates the real-time measurement of vehicle travel distance, unit: m; \(t\) indicates the vehicle movement time, \(t=1\) s; and \(\theta\) indicates the included angle between the vehicle driving direction and the horizontal direction. 2. The plane positioning method calculates the vehicle position for the data group that receives two base station signals in one second [47]. The positioning principle is to measures the linear distance between the target and the two base stations with known positions. Under the condition of no measurement error, the target vehicle will be located at the intersection point of the circle, with each base station as the center and the signal propagation distance as the radius. If two circles intersect and there are two intersections, the intersection close to the vehicle position at the previous time is judged as the estimated vehicle position. If there is only one intersection point between two circles, the intersection point is the estimated vehicle position. If two circles intersect without intersection, it is considered that the data at that time cannot be located. When the plane positioning method is adopted, the positioning coordinate \((x_{b},y_{b})\) can be obtained by:  
\[ \begin{array}{l}\min\sqrt{\left(x_{b}-x_{0}\right)^{2}+\left(y_{b}-y_{0} \right)^{2}}\\ s.t.\left\{\begin{array}{l}\left(x_{b}-x_{1}\right)^{2}+\left(y_{b}-y_{1} \right)^{2}=d_{1}^{2}\\ \left(x_{b}-x_{2}\right)^{2}+\left(y_{b}-y_{2}\right)^{2}=d_{2}^{2}\end{array}\right.\end{array}  \tag{5}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Model Parameter** & **Calibration Results** \\ \hline Environmental factor (A) & 180.61 \\ Path loss coefficient (n) & 8.19 \\ Related coefficient (R) & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model fitting formula-related parameters. 3. The trilateration method is the most used node positioning method in wireless positioning [48]. Taking the distance obtained by the distance propagation model as the radius and the base station coordinates as the center of the circle, the intersection of the circles or the centroid of the intersecting area is the vehicle position. In practical applications, if the three circles cannot intersect at one point due to errors, the position of the target to be measured may not be located. When the trilateral measurement positioning method is adopted, the vehicle receives signals from three or more base stations, the base station coordinates are represented by \((x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})\), and the positioning coordinate \((x_{c},y_{c})\) can be obtained by: \[\left\{ \begin{array}{c}(x_{c}-x_{1})^{2}+(y_{c}-y_{1})^{2}=d_{1}^{2}\\ (x_{c}-x_{2})^{2}+(y_{c}-y_{2})^{2}=d_{2}^{2}\\ (x_{c}-x_{3})^{2}+(y_{c}-y_{3})^{2}=d_{3}^{2}\end{array} \right.\] (6)
4. The least-squares method establishes the corresponding characteristic equation according to the positioning distance and obtains the vehicle position by solving the minimum value of the error square sum [25].