## 3 Satellite Selection Algorithm
### Geometric Dilution Precision  
The Dilution of Precision (DOP) is an important physical quantity for measuring the satellite positioning accuracy, which is affected by the geometric structure of the satellites. The effect of the satellite geometric structure on the position error is also called the GDOP, which represents the ratio of the position error to the ranging error [24], and is also an important evaluation index in the satellite selection algorithm. The relationship between the positioning accuracy of the satellite navigation system and the Geometric Dilution of Precision can be expressed by the formula  
\[\sigma_{G}=GDOP\times\sigma_{\rho} \tag{17}\]  
where \(\sigma_{G}\) is the standard deviation of the navigation error, and \(\sigma_{\rho}\) is the uncertainty error of the pseudo-distance measurement value, also known as User Equivalent Range Error (UERE). It can be seen that when \(\sigma_{\rho}\) is certain, the GDOP is smaller, and the smaller the \(\sigma_{G}\) is, the higher the navigation accuracy is. However, different positioning satellites' \(\sigma_{\rho}\) values are generally not the same, and a smaller GDOP does not guarantee higher navigation and positioning accuracy. In certain situations, when a satellite cluster at a low elevation angle can provide a better geometric structure, it is more affected by the ionosphere and troposphere compared to satellites at high elevation angles. It also experiences stronger multipath interference [5]. The uncertainty error of the pseudo-range measurement will be significantly larger than that of other satellites, and the positioning accuracy will be greatly affected at this time. Nevertheless, selecting a satellite combination with a smaller GDOP is still an important step to improve the integrated navigation accuracy. The GDOP is defined in detail as  
\[GDOP=\sqrt{trace(G_{u}^{T}G_{u})^{-1}}=\sqrt{g_{11}+g_{22}+g_{33}+g_{44}} \tag{18}\]  
where \(\left(G_{u}^{T}G_{u}\right)^{-1}\) can be expressed in the form of the matrix  
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\(G_{u}\) is the matrix associated with the satellite line-of-sight vector  
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