## 2 Construction Method of EMR-SF along the Road Collection Data
### LRBF Interpolation Method  
The sampled EMR data are distributed along the road at the boundary of the study area, and thus, there are no data in the center region. If the sampled data are used to construct the EMR-SF directly, this will lead to a low accuracy of the space field construction because of the lack of data. Therefore, the LRBF interpolation method is proposed to improve the accuracy of the construction of EMR-SF, in which the EMR values are generated by interpolating the data collected along the road in a layered manner from the outside to the inside. Grid point G needs to be constructed within the study area before using the LRBF. With the sampling data as the boundary, grid point G is divided into \(m\) layers from the boundary inward, \(G=\{L_{1}\cup L_{2}\cup\cdots\cup L_{m}\}\). The value of each layer of grid points is generated according to the sampling data. Meanwhile, each layer of the grid points that are generated is added to the sampling dataset, and they are interpolated as the sample points to generate values for the next layer of grid points. The LRBF interpolation method is as follows:  
\[F_{n}(\mathrm{x})=\sum\limits_{i=1}^{k}c_{i}\varphi(r)+p(\mathrm{x})=\sum \limits_{i=1}^{k}c_{i}\varphi(\|\mathrm{x}-\mathrm{x}_{i}\|)+p(\mathrm{x}),n=1,2,\cdots m,\ \mathrm{x}_{i}\in L_{0}\cup L_{1}\cup\cdots\cup L_{n-1} \tag{1}\]  
where \(x\) represents the grid points, and \(x_{i}\) represents the sample points. \(L_{0}\) is the data points sampled along the road, and \(L_{n}\) is the \(n\)th level grid point. \(F_{n}(\mathrm{x})\) is the value of the \(n\)th-level grid point. \(\mathrm{x}_{i}\in L_{0}\cup L_{1}\cup\cdots\cup L_{n-1}\) indicates that when the nth layer grid points are calculated, the sample point \(x_{i}\) belongs to the dataset after the sample data are combined with the previous \(n-1\) grid point data. \(c_{i}\) is the linear combination coefficient, \(r=\|\mathrm{x}-\mathrm{x}_{i}\|\) is the Euclidean distance from the grid point to the sample point \(x_{i}\), and \(\varphi(r)\) is the basis function. \(p(\mathrm{x})=a_{0}+a_{1}x+a_{2}y\) is a polynomial function, and \(\sum\limits_{i=1}^{k}c_{i}=\sum\limits_{i=1}^{k}c_{i}x_{i}=\sum\limits_{i=1}^ {k}c_{i}y_{i}=0\). The Gaussian basis function is often used in interpolation with less data [20], so the Gaussian basis function is used for LRBF interpolation. The expression of the Gaussian basis function is \(\varphi(r)=e^{-x^{2}r^{2}}\). \(\varepsilon\) is the shape parameter, which will affect the result of LRBF interpolation. Because too-small shape parameters will produce a significant pathological matrix, resulting in unstable interpolation results, too-large shape parameters will affect the interpolation accuracy [21; 22; 23]. To solve the value of the optimized shape parameter, it is optimized by particle swarm optimization (PSO) during the calculation [24; 25]. Figure 1: Construction of the EMR-SF by LRBF. According to the LRBF interpolation Equation (1), the interpolation accuracy is mainly affected by two factors. 1. Grid point density: the density of the grid points depends on the spacing distance between the grid points. If the spacing distance is large, the grid point density is small; otherwise, the density is large. The increase in the number of sample points \(x_{i}\) is affected by the density of the grid points in the LRBF interpolation process. Too few grid points will cause the loss of data in the center of the sampling range, while too many grid points will cause data redundancy, both of which are not conducive to the construction of a space field by the LRBF. After determining the density of the grid point, it is necessary to determine the number of layers \(m\) of the grid point, which is affected by the interval distance between layers. 2. Layered interval distance: the distance between the adjacent two layers represents the layered interval distance. The layered interval distance of the grid points affects the number of layers \(m\), which determines the number of grid points in each layer.