## 3 Results
### Fixed Satellite Selection Experiment  
For dynamic users, the expected positioning accuracy permits the use of a fixed-number satellite selection strategy, simplifying the problem from multi-objective to single-objective optimization. At each epoch, five satellites are selected--four to satisfy the minimum navigation requirement (position and clock bias estimation) and one additional satellite to enhance geometric distribution. This approach also ensures manageable computational and data overhead, making it suitable for deployment on large unmanned aerial vehicles. As shown in Equation (6), the goal is to minimize \(\underset{x\in\mathbb{R}}{\min}f(x)=\underset{x\in\mathbb{R}}{\min}f_{1}(x)\) to determine the minimum DGDOP value. The iterative characteristics of the DGDOP within the observation epochs of the unmanned aerial vehicle's flight trajectory are shown in Figure 5a, and the variation of the DGDOP values across the epochs is illustrated in Figure 5b. Figure 4: The IGD results of the dynamic scene satellite selection algorithm over 2185 epochs. (**a**) Boxplot of IGD values: In the box plot, the red line represents the median, while the upper and lower edges of the box correspond to the first and third quartiles of the IGD values. The height of the box reflects the interquartile range (IQR). The whiskers extend to 1.5 times the IQR, and red plus signs indicate outliers beyond the whiskers. (**b**) Statistical results of IGD values: The comparison of algorithms is based on the average, median, standard deviation, best, and worst IGD values. The height of the histogram bars represents the magnitude of these metrics. Figure 5 illustrates the iteration results and the DGDOP convergence of each satellite selection algorithm. It can be observed that the DGDOP values in the observation epochs converge rapidly when the proposed NSWOA is applied. The iteration statistics are shown in Table 6.  
As shown in Figure 5a and Table 6, the minimum number of iterations required by the NSWOA to achieve a DGDOP value below 150 is 11, which is two and one fewer than the iterations required by the GWO and NSGA-II algorithms, respectively. When the DGDOP value is reduced to below 148, the NSWOA still requires four fewer iterations than GWO but exceeds PSO and NSGA-II by four and five iterations, respectively. Further iteration to a DGDOP value below 147.5 results in NSWOA matching the performance of GWO, outperforming PSO, but falling short of NSGA-II. Based on this analysis, it can be concluded that when computational resources are limited and fewer iterations are allowed, the NSWOA converges faster than the GWO and NSGA-II algorithms. As the optimization target (DGDOP) decreases, the required number of iterations increases. However, NSWOA still exhibits faster convergence than GWO, eventually surpassing PSO. Overall, the NSWOA optimization algorithm demonstrates strong performance in the fixed satellite selection dynamic scenario. Figure 5b shows that the DGDOP values optimized by each algorithm in the fixed satellite selection dynamic scenario are generally within the same range throughout the entire flight process. A more detailed statistical analysis is provided in Table 7.  
The results shown in Figure 5b and Table 7 indicate that, in the single-objective fixed satellite selection dynamic scenario with 2,185 observation epochs, the proposed NSWOA demonstrates strong competitiveness. The percentage of epochs with DGDOP values between 130 and 170 is lower than that of GWO and NSGA-II, but overall higher than PSO, \begin{table}
\begin{tabular}{c c c c c c} \hline
**DGDOP** & **Less Than 150** & **Less Than 149** & **Less Than 148** & **Less Than 147.5** & **Less Than 147** \\ \hline NSWOA & 11 & 22 & 31 & 51 & \\ GWO & 13 & 26 & 35 & 51 & 88 \\ PSO & 7 & 16 & 27 & 58 & \\ NSGAII & 12 & 21 & 26 & 36 & 67 \\ \hline \end{tabular}
\end{table} 
Table 6: Minimum iteration count corresponding to DGDOP results (unit: iterations). Figure 5: Fixed number of satellites selection algorithm comparison.