## 3 Experimental Results and Analysis
### Simulated Signal Experiments
#### 3.1.2 Poor Satellite Geometry  
It is well established that satellite geometry and signal strength significantly influence the multimodality of the cost function in DPE [3]. Poor satellite geometry increases the number of local optima within the search area, while lower signal strength raises the ratio of local optima to the global optimum, thereby increasing the search difficulty. To create a more challenging reception scenario, we simulated an indoor near-window environment characterized by poor satellite geometry and a low \(C/N_{0}\) level of 25 dB/Hz. In this scenario, only satellites with elevations between 20\({}^{\circ}\) and 75\({}^{\circ}\) and azimuths between 0\({}^{\circ}\) and 180\({}^{\circ}\) were used. The corresponding PRN code numbers, azimuths, and elevations of the satellites are summarized in Table 8.  
The results are presented in Table 9. In harsh environments, the 2 SP method exhibits the greatest decline in performance, as low \(C/N_{0}\) and poor satellite geometry impair the accuracy of the acquisition and tracking process, resulting in lower positioning accuracy compared with DPE-SI methods. This demonstrates that the proposed framework retains the ability of DPE to handle weak signals [1]. Among the DPE methods, traditional search algorithms exhibit the most pronounced performance degradation under challenging conditions, which is consistent with their iterative design. As previously discussed in Section 2.1, the search space contains numerous secondary peaks, posing significant challenges for search-based methods such as ARS. Due to the necessity of reverting to the initial search radius multiple times, its search accuracy experiences a substantial decline. Similarly, MRG encounters the same set of challenges. In the strategy of MRG, the search is conducted iteratively, with the search center being relocated and the search boundaries reduced after each iteration. If the highest peak is excluded from the search space after adjustments, the search may fail to locate the receiver's accurate position. In contrast, swarm intelligence algorithms search over a bounded set of real numbers, ensuring that the highest peak is always within the search space, thus overcoming the inherent limitations of traditional search algorithms. Additionally, these traditional search algorithms are computationally expensive, especially as the number of dimensions increases. Swarm intelligence algorithms, however, can control the number of points evaluated by adjusting the number of individuals and iterations, leading to more efficient and consistent performance. As observed, GWO, DBO, and ADBO all achieve better performance than traditional search algorithms in terms of precision, stability, and execution time. Notably, while ADBO and 2 SP exhibit comparably high positioning accuracy under fine satellite geometry, the ADBO algorithm shows the smallest reduction in accuracy under poor satellite geometry, which can be attributed to its effective navigation solution search capability within DPE, allowing it to better exploit the advantages of the DPE-SI framework. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**PRN** & **2** & **4** & **26** & **31** \\ \hline Azimuth & 27.5 & 195.4 & 205.4 & 152.4 \\ Elevation & 29.9 & 46.5 & 38.5 & 53.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Azimuth and elevations of satellites with poor geometry. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Algs.** & **2 SP** & **MRG** & **ARS** & **PSO** & **SSA** & **GWO** & **HHO** & **PIO** & **PO** & **DBO** & **ADBO** \\ \hline PE (m) & 170.0 & 169.3 & 273.4 & 1231.2 & 999.9 & 164.3 & 1162.9 & 1346.9 & 542.8 & 90.5 & 49.3 \\ CBE (m) & 10.2 & 19.4 & 36.2 & 51.0 & 40.0 & 17.3 & 59.3 & 66.4 & 24.8 & 12.0 & 7.5 \\ PN (10\({}^{3}\)) & \(-\) & 400 & 400 & 50 & 50 & 50 & 50 & 50 & 50 & 50 \\ ET (s) & \(-\) & 89.0 & 91.5 & 11.1 & 11.0 & 11.0 & 26.0 & 14.6 & 11.0 & 12.1 & 13.0 \\ \hline \hline \end{tabular}
\end{table}