# A Method to Reduce Non-Nominal Troposphere Error
## 5 Method to Reduce the Non-Nominal Troposphere Error
### Simulation Results
Given that the number of satellites in the optimal subset is 16, it is necessary to select four, eight and four satellites in the elevation ranges of (5\({}^{\circ}\), 30\({}^{\circ}\)), (30\({}^{\circ}\), 60\({}^{\circ}\)) and (60\({}^{\circ}\), 90\({}^{\circ}\)), respectively. Based on the current GPS constellation and the global BDS constellation, the numbers of satellites in different elevation ranges are shown in Table 7 for the case in which the number of visible satellites at the Linzhi airport is minimized. Table 7 shows that the requirements of satellite selection can be met when the number of visible satellites at the Linzhi airport is minimized. Figure 19 presents a skylpot of the optimal satellite subset obtained by the brute method corresponding to the epoch in which the number of visible satellites at the Linzhi airport is minimized. Figure 20 shows a skylpot for the optimal satellite subset obtained by the greedy method corresponding to the epoch in which the number of visible satellites at the Linzhi airport is minimized. \begin{table}
\begin{tabular}{c c} \hline
**Elevation Range** & **Distribution Ratio** \\ \hline (5\({}^{\circ}\), 30\({}^{\circ}\)) & 25.7\% \\ (30\({}^{\circ}\), 60\({}^{\circ}\)) & 49.5\% \\ (60\({}^{\circ}\), 90\({}^{\circ}\)) & 24.8\% \\ \hline \end{tabular}
\end{table} 
Table 6: Average distribution of the optimal satellite subsets under the greedy method. \begin{table}
\begin{tabular}{c c} \hline
**Elevation Range** & **Number of Satellites** \\ \hline (5\({}^{\circ}\), 30\({}^{\circ}\)) & 11 \\ (30\({}^{\circ}\), 60\({}^{\circ}\)) & 8 \\ (60\({}^{\circ}\), 90\({}^{\circ}\)) & 5 \\ \hline \end{tabular}
\end{table} 
Table 7: Number of satellites in different elevation ranges when the number of visible satellites at the Linzhi airport is minimized. Figure 19: Skylpot of the optimal satellite subset obtained by the brute method. The colors represent the non-nominal troposphere error for every satellite, and red crosses indicate that the corresponding satellites are selected. Table 8 presents the satellites that were removed from the optimal satellite subset by the greedy and brute methods. According to Table 8, the optimal satellite subset selected by the greedy method exchanges satellite No. 55 with satellite No. 70 compared with the subset obtained by the brute method. The other satellites in the optimal subsets are all the same. Satellites No. 55 and No. 70 have approximately equal non-nominal troposphere errors, confirming the effectiveness of determining the distribution of optimal satellite subsets based on the brute and greedy methods. Figure 21 shows a skylpot of the optimal satellite subset obtained by the proposed method corresponding to the epoch in which the number of visible satellites at the Linzhi airport is minimized. The colors represent the non-nominal troposphere error for every satellite, and red crosses indicate that the corresponding satellites are selected. Figure 21 shows that the optimal satellite subset selected by the new method exchanges satellite No. 68 with satellite No. 72 compared with the subset obtained by the brute method. The non-nominal troposphere error of satellite No. 68 is smaller than that of satellite No. 72. The other satellites are all the same. This slight difference indicates that the geometry of the satellite subset obtained by the new method is as good as the satellite subset obtained by the brute method. Figure 22 presents the \(VPL_{\text{C}}\) of the new method under non-nominal troposphere, with the following results. * \(VPL_{\text{C\_new}}\) is the \(VPL_{\text{C}}\) of the new method. From Figure 22, we can derive the following inequality:  
\[VPL_{\text{C\_Brute}}<VPL_{\text{C\_Greedy}}<VPL_{\text{C\_new}}<VPL_{\text{C \_GDOP}}<VPL_{\text{C\_all}}<VPL_{\text{C\_deviation}} \tag{23}\]