## 3 Materials and Methods
### Position Algorithm Calculation
#### 3.1.5 Step 5: Positioning Scheme Formulation  
According to the above weighting matrix, the two errors are taken as the main basis for determining the weight. It is distributed in multiple positioning methods to reduce the positioning error and improve the accuracy of coordinate positioning. The fusion coordinates are obtained by the following:  
\[\left\{\begin{array}{l}x=x_{c}\frac{w_{1}}{\sum_{j=1}^{3}w_{i}}+x_{d}\frac{ w_{2}}{\sum_{j=1}^{3}w_{i}}+x_{c}\frac{w_{3}}{\sum_{j=1}^{3}w_{i}}\\ y=y_{c}\frac{w_{1}}{\sum_{j=1}^{3}w_{i}}+y_{d}\frac{w_{2}}{\sum_{j=1}^{3}w_{i}} +y_{e}\frac{w_{3}}{\sum_{j=1}^{3}w_{i}}\end{array}\right.,\ i=1,\ 2,\ldots,n \tag{19}\]  
This article proposes the following three fusion positioning schemes based on the ranging positioning method, the non-ranging positioning method, and the ranging and non-ranging fusion positioning method.  
1. Comparison scheme 1: fusion positioning based on the ranging method  
In this scheme, trilateral measurement positioning and least-squares positioning are fused with dead reckoning positioning and plane positioning to obtain fusion positioning  
Figure 1: Error correction.  
algorithm A (WFA). According to the wireless location fusion algorithm formula, the algorithm formula of the WFA scheme can be obtained as follows:  
\[\left\{\begin{array}{l}x=x_{c}\frac{w_{1}}{w_{1}+w_{2}}+x_{d}\frac{w_{2}}{w_{1}+ w_{2}}\\ y=y_{c}\frac{w_{1}}{w_{1}+w_{2}}+y_{d}\frac{w_{2}}{w_{1}+w_{2}}\\ d=\sqrt{\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}}\end{array}\right. \tag{20}\]  
where \((x_{c},y_{c})\) and \((x_{d},y_{d})\) are the vehicle positioning coordinates located by the trilateral measurement method and the least-squares method, and \(w_{1},w_{2}\) are the weighting factors of the trilateral measurement method and the least-squares method. It can be obtained that the positioning coordinate of the WFA fusion positioning scheme is \((x,y)\). Furthermore, \(d\) indicates the positioning error distance, and \((x_{0},y_{0})\) indicates the real vehicle position.  
2. Comparison scheme 2: fusion location based on the non-ranging method  
In this scheme, centroid positioning, dead reckoning positioning, and plane positioning are selected to obtain the fusion positioning algorithm B (WFB). The algorithm formula of the WFB scheme can be obtained as follows:  
\[\left\{\begin{array}{c}x=x_{e}\cdot w_{3}\\ y=y_{e}\cdot w_{3}\\ d=\sqrt{\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}}\end{array}\right. \tag{21}\]  
where \((x_{e},y_{e})\) is the vehicle positioning coordinates of the centroid algorithm, and \(w_{3}\) is the weighting factor of centroid positioning. It can be obtained that the positioning coordinate of the WFB fusion positioning scheme is \((x,y)\).  
3. Fusion scheme: fusion location based on ranging and non-ranging methods  
Based on scheme (1) and scheme (2), considering the fusion of ranging-based and non-ranging-based positioning methods, the fusion positioning algorithm C (WFC) is obtained. The algorithm formula of the WFC scheme can be obtained as follows:  
\[\left\{\begin{array}{l}x=x_{c}\frac{w_{1}}{w_{1}+w_{2}+w_{3}}+x_{d}\frac{w_{2 }}{w_{1}+w_{2}+w_{3}}+x_{e}\frac{w_{3}}{w_{1}+w_{2}+w_{3}}\\ y=y_{c}\frac{w_{1}}{w_{1}+w_{2}+w_{3}}+y_{d}\frac{w_{2}}{w_{1}+w_{2}+w_{3}}+y_{ e}\frac{w_{3}}{w_{1}+w_{2}+w_{3}},\;i=1,2,3\\ d=\sqrt{\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}}\end{array}\right. \tag{22}\]  
where \((x_{c},y_{c})\),\((x_{d},y_{d})\), and \((x_{e},y_{e})\) are the vehicle positioning coordinates of the trilateration, least squares, and centroid algorithms, and \(w_{1},w_{2},w_{3}\) are the weighting factor of the trilateration, least squares, and centroid positioning. It can be obtained that the positioning coordinate of the WFC fusion positioning scheme is \((x,y)\).