## 5 Results and Discussion
### MDDA with TC Integration Scenario  
In the present scenario, the MDDA-TC algorithm demonstrated a significant enhancement, resulting in an increase that exceeded 75.5% in 2D and 90% in 3D position RMSE over the solution from all visible satellites based on the Google matrix in Table 2, in addition to an improvement of about 78% in 2D and 83% in 3D position RMSE against the MDDA only scenario, and about 2.5% in 2D and 1.7% in 3D position RMSE over the solution from all satellites, shown in Table 4. Additionally, with the limited channel receiver, the 10 MDDA-TC algorithm improved the 2D and 3D position RMSE, with the same improvements over 10 MDDA, shown in Table 2, and about 10% and 4% in 3D position RMSE over 10 EL-TC and 10 CNR-TC, respectively. The results are included in Table 4.  
Similarly, Figures 12 and 13 demonstrate the improvement in position RMSE achieved by the MDDA-TC algorithm compared to the CNR and EL biased algorithms. Figure 11: CDF vs 3D-osition RMSE for LC. Figure 10: The 3D position RMSE. Furthermore, an additional analysis is depicted in Figure 14, which features the CDF curve in conjunction with the 3D position RMSE for TC integration. The comparison reveals that the MDDA demonstrated optimum accuracy in comparison to all satellites on the horizon. Moreover, in situations requiring the reduction of satellites to align with the maximum number of receiver channels, the MDDA exhibited superior performance compared to alternative methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **East** & **North** & **Down** & **2D Position** & **3D Position** \\ \hline \multicolumn{5}{c}{**All Visible Satellites**} \\ \hline All Satellites & 0.66 & 0.54 & 0.82 & 0.86 & 1.19 \\ \hline MDDA-TC-Based & 0.64 & 0.54 & 0.82 & 0.84 & 1.17 \\ \hline \multicolumn{5}{c}{**Selected Satellites**} & **According to Max. Number of Rx Channels (10 Satellites)**} \\ \hline
10 EL-TC-Based & 0.64 & 0.73 & 1.05 & 0.97 & 1.43 \\ \hline
10 CNR-TC-Based & 0.63 & 0.72 & 0.94 & 0.95 & 1.34 \\ \hline
10 MDDA-TC-Based & 0.58 & 0.69 & 0.92 & 0.91 & 1.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MDDA-TC algorithm 2D and 3D position RMSE in meters. Figure 12: The 2D position RMSE. Figure 13: The 3D position RMSE. Hence, Figure 15 clarifies the optimization of the MDDA-TC over MDDA-LC algorithms and demonstrates the substantial improvement in the positional RMSE during the whole trajectory. Figure 16 illustrates the differences between the MDDA-LC and MDDA-TC trajectories in comparison to the reference trajectory, using a real-world map as context. Both methods exhibited satisfactory positioning accuracy, with MDDA-TC demonstrating comparatively enhanced performance. Figure 14: CDF vs 3D position RMSE for LC. Figure 15: The 3D position error using MDDA-(LC and TC) revealed a noteworthy improvement achieved by utilizing MDDA-TC with a restricted set of 10 visible satellites. As shown in Figure 17, the NED position error for the MDDA-TC algorithm, which represented the optimized approach, demonstrated the lowest error compared to the other algorithm. Furthermore, an essential question arose, warranting a comprehensive examination: Among the visible satellites, which one was selected by the satellite selection (SS) techniques, and what were the underlying reasons? In order to provide an elucidating response, two distinct epochs are chosen as illustrative examples. The skyplot of the first epoch is presented on the left Figure 18, while the skyplot of the final epoch is displayed on the right  
Figure 16: Trajectory depicted on Google earth map. Figure 17: The MDDA-TC position error in (north, east, down) NED. in Figure 19. This visual representation facilitates the analysis of the SS techniques and their impact on satellite selection. In the first epoch, the MDDA algorithm prioritized satellites 6, 18, 22, and 32 based on their optimal horizon geometry. However, despite having favorable EL angles and CNR, satellites 2 and 11 were excluded from the selection process.