# Fast Screening Algorithm for Satellites Based on Multi-Constellation System
## 3 Fast Satellite Screening Algorithm Based on Multi-Threshold Optimization
### Modeling the Relationship between GDOP Values and Star Selection Ratios  
According to the multi-constellation combination of the satellite guidance system for satellite selection before and after the GDOP value changes to determine the number of suboptimally distributed satellites, three systems, GPS/Galileo/BeiDou, were selected to establish a simulation platform based on ephemeris parameters and actual observations, and the elevation angle of the masking satellite is set to \(5^{\circ}\). The relationship between the results of the optimal GDOP value selection method in Nanjing and the value of the ratio of the selected satellites \(p\) is shown in Table 1, and the observation time is a total of 2.5 h, the observation interval is 5 s, and the total number of observable ephemeris is 1800. The ratio \(p\) is the ratio of the total number of retained satellites \(m\) and the total number of observed satellites \(K\). The GDOP value before and after selection is the GDOP value. \(\Delta\)GDOP is the amount of loss of GDOP value before and after star selection.  
It can be seen that the GDOP value of the multi-constellation positioning system increases with the decrease in the star selection ratio, but the two do not form a linear relationship [13] However, the GDOP value decreases less when the proportion of the selected stars is larger (\(\geq\)70%), which does not cause much loss of positioning accuracy, whereas the GDOP value increases significantly when the proportion of the selected stars is lower than 70%. From this, it is conjectured that the GDOP value and the proportion of selected stars follow the negative exponential decay law [14]. The GDOP value star selection ratio model is assumed to be as follows:  
\[\mathrm{GDOP^{\prime}}=\mathrm{GDOP*}k_{1}e^{(k_{2})}+k_{3} \tag{14}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline Star selection ratio & 1 & 0.90 & 0.80 & 0.70 & 0.6 & 0.50 \\ \hline Number of stars selected & 22 & 19 & 17 & 15 & 13 & 11 \\ \hline GDOP & 1.661 & 1.779 & 1.818 & 1.919 & 2.143 & 2.686 \\ \hline \(\Delta\)GDOP & 0 & 0.118 & 0.157 & 0.258 & 0.482 & 1.025 \\ \hline \end{tabular}
\end{table}
Table 1: The relationship between GDOP value changes and satellite selection ratios.  
where GDOP\({}^{\prime}\) denotes the GDOP value after the star selection, \(k_{1}\), \(k_{2}\) and \(k_{3}\) are related to the number of visible stars of the navigation system, and the selected value is determined by a large number of a priori measured data. In this paper, the traditional minimum GDOP value selection method to traverse the simulation of the satellite data of multiple observation calendar elements within 3 h was used to analyze a large amount of data to obtain the GDOP value model as  
\[\text{GDOP}^{\prime}\approx K/8.2*e^{\left(-0.2K*p\left(1-0.178p\right)\right) }+0.97 \tag{15}\]  
\(K\) is the total number of observable satellites, and \(p\) is the selection ratio. Users can use this model to determine the selection ratio by the number of satellites to optimize the positioning accuracy in real time. The star selection algorithm studied in the following section is affected by the observation time, and the star selection ratio is determined to be 70% on the premise of ensuring a small loss of positioning accuracy.