# Evaluation of Network RTK Positioning Performance Based on BDS-3 New Signal System
## 2 Network RTK Positioning Algorithm
### Classification Modeling of Ionospheric and Tropospheric Delay  
Regional atmospheric modeling is a key factor affecting the accuracy of network RTK service [26]. Literature [27] compares the commonly used atmospheric delay modeling methods and points out that the modeling accuracy of all methods is similar, and the interpolation accuracy of 2-3 cm can be obtained for medium and short baseline networks within 100 km. After a comprehensive comparison of various atmospheric modeling strategies, this paper draws on the solution strategy of the horizontal gradient factor of FKP. Namely, FKP broadcasts correct information for the geometric level gradient factor and the ionosphere horizontal gradient factor. The geometric horizontal gradient factor is used to correct non-dispersion errors such as the tropospheric residual, and it should be pointed out that the tropospheric delay has a strong correlation with the height of the station [17; 27]. This paper adopts the strategy of combining prior tropospheric model correction with atmospheric modeling. Firstly, the tropospheric delay extracted from the baseline of each reference station is compensated with an a priori high-precision tropospheric model (such as GPT2 [28]), which is related to altitude difference. In other words, the tropospheric delay of each baseline involved in modeling is normalized to a unified elevation plane before modeling. There is no need to consider elevation normalization before ionospheric horizontal gradient factor modeling, but different from conventional planar modeling strategy methods, this method will determine the weight according to the elevation angle of the satellite under each modeling baseline before ionospheric interpolation [29]. In addition, before modeling, the weights of modeling baselines should be determined according to the distance between each baseline and the rover station, which is inversely proportional to the weight. If p is a reference satellite, the regional double-difference atmospheric modeling method of \(q\), which is a non-reference satellite, is shown in Equations (7) and (8):  
\[\left[ \begin{array}{c}T_{H,1}^{pq}\\ \cdots\\ T_{H,n}^{pq}\\ I_{1}^{pq}\\ \cdots\\ I_{n}^{pq}\\ \end{array} \right]=6.37\left[ \begin{array}{c}w_{1}\\ \cdots\\ w_{n}\\ w_{1}\\ \cdots\\ w_{n}\\ \end{array} \right]\cdot\left[ \begin{array}{cccc}dB_{1}&dL_{1}\cdot\cos\left(B _{1,ref}\right)&0&0\\ \cdots&\cdots&\cdots&\cdots\\ dB_{n}&dL_{n}\cdot\cos\left(B_{n,ref}\right)&0&0\\ 0&0&H_{1}^{q}\cdot dB_{1}&H_{1}^{q}\cdot dL_{1}\cdot\cos\left(B_{1,ref}\right) \\ \cdots&\cdots&\cdots&\cdots\\ 0&0&H_{n}^{q}\cdot dB_{n}&H_{n}^{q}\cdot dL_{n}\cdot\cos\left(B_{n,ref}\right) \\ \end{array} \right]\left[ \begin{array}{c}trop_{H}^{pq}\\ trop_{H}^{pq}\\ trop_{H}^{pq}\\ ionb^{pq}\\ ionl^{pq}\end{array} \right] \tag{7}\]  
\[H_{n}^{q}=1+16\cdot\left[0.53-\frac{el_{n}^{q}}{\pi}\right]^{3} \tag{8}\]  
where, \(T_{H,n}^{pq}\) is the double-difference tropospheric delay of the nth modeling baseline of satellite \(q\), which has been naturalized to the standard elevation H; \(l_{n}^{pq}\) is the double-difference ionospheric delay at the \(L_{1}\) frequency signal of the nth satellite \(q\) participating in the modeling baseline; \(w_{n}\) is the weight of the nth baseline involved in modeling for satellite \(q\); \(dB_{n}\) and \(dL_{n}\) are the latitude and longitude span of the nth baseline involved in modeling for satellite \(q\); \(B_{n,ref}\) is the latitude of the nth baseline reference station. \(el_{n}^{q}\) is the elevation angle of the rover terminal of satellite \(q\) at the nth baseline. All the angle information in the Equation is in radians. \(trop_{H}^{pq}\) and \(trop_{H}^{pq}\) are the north-south and east-west gradients of the geometric horizontal gradient factor of satellite \(q\). \(ionb^{pq}\) and \(ionl^{pq}\) are the north-south and east-west gradients of the ionospheric gradient factor of satellite \(q\).