## 3 The Influence of Satellite Elevation Angle on Positioning Accuracy  
For the convenience of analysis and calculation, this article mainly refers to the single satellite error amplification factor in the literature [27] to study the impact of the elevation of low orbit communication satellites relative to users on positioning accuracy as follows:  
\[\left|\frac{r}{V_{s}\cdot\sin\delta}\right|=\frac{R^{2}+(r_{s}+R)^{2}-2\cdot R \cdot(r_{s}+R)\cdot\cos\sigma}{\left[\frac{\mu}{(r_{s}+R)}\cdot\left(R^{2}+(r _{s}+R)^{2}-2\cdot R\cdot(r_{s}+R)\cdot\cos\sigma-R^{2}\cdot\sin^{2}\sigma \cdot\cos^{2}\varphi\right)\right]^{\frac{1}{2}}}, \tag{12}\]  
where \(\mu=3.986005\times 10^{14}\) is the gravitational constant, \(R=6.368\times 10^{6}\) is the Earth radius, \(V_{s}=\left(\sqrt{\frac{\mu}{r_{s}+R}},0,0\right)\) is the satellite vector velocity, \(U=\left(R\sin\sigma\cos\varphi,R\sin\sigma\sin\varphi,R\cos\sigma\right)\) is the position of the user, \(r_{s}\) is the satellite orbital altitude, and the definitions of \(\sigma\) and \(\varphi\) are shown in Figure 3.  
From Figure 3, it can be seen that, after the satellite is determined, the change in \(\sigma\) reflects the change in \(\varphi\); that is, the smaller the \(\sigma\), the larger the \(\varphi\). Therefore, the impact of satellite elevation \(\theta\) on positioning accuracy can be obtained by analyzing the impact  
Figure 3: The place schematic diagram of user U and satellite.  
of changes in \(\sigma\) on the positioning accuracy. The larger the elevation \(\theta\), the better the positioning accuracy.  
Figure 4 show the error amplification factors of a single satellite at satellite orbital altitudes of 340 km, 550 km, and 1150 km, respectively. Through comparative analysis of the three images, it can be seen that, as the satellite orbit height increases, the maximum error also decreases.  
As previously noted, the greater the satellite elevation angle, the lower the positioning error. The computation of the satellite elevation angle proceeds as follows:  
\[\mathbf{e}_{su,ECEF}=\frac{\mathbf{S}_{i}-\mathbf{\mathrm{P}}}{\|\mathbf{S}_{i}-\mathbf{\mathrm{P} }\|}, \tag{13}\]  
\[\mathbf{e}_{su,ENU}=\mathbf{M}\cdot\mathbf{e}_{su,ECEF}=[e_{E}\;e_{N}\;e_{U}]^{T}, \tag{14}\]  
\[\mathbf{M}=\begin{bmatrix}-\sin L&\cos L&0\\ -\sin B\cos L&-\sin B\sin L&\cos B\\ \cos B\cos L&\cos B\sin L&\sin B\end{bmatrix}, \tag{15}\]  
\[El=\arctan(e_{U}), \tag{16}\]  
where \(\mathbf{e}_{su,ECEF}\) is the unit vector of a satellite and user sight line direction in the Earth-centered Earth-fixed (ECEF) coordinate system. \(\mathbf{e}_{su,ENU}\) is the unit vector of a satellite and user sight line direction in the east-north-up (ENU) coordinate system. \(El\) is the elevation angle of the satellite relative to the user.  
Figure 4: The error amplification factors of a single satellite at different satellite orbital altitudes. (**a**) The error amplification factors of a single satellite at the satellite orbital altitude of 340 km. (**b**) The error amplification factors of a single satellite at the satellite orbital altitude of 550 km. (**c**) The error amplification factors of a single satellite at the satellite orbital altitude of 1150 km.