## 3 Results and Discussion
It is worth mentioning that the MCC is considered for all the EKF-based approaches in this study; however, nonlinear regression with MCC is considered for MCCEKF-NR, and MCC with a mixture of Gaussian noises is considered for Mixture-LRMCCEKF. The noise strength changes with respect to time appeared more in the case of EKF as compared to other filters. However, the EKF can enhance performance even further by considering the MCC. According to a different perspective, the MCC mechanism helped the EKF's noise variance adaptability performance. The MCC-based nonlinear regression method offers superior computational efficiency along with comparable positioning accuracy when compared to MCC-based EKFs. Moreover, with only a slight increase in execution time over Mixture-LRMCCEKF, the MCCEKF-NR method offers the best positioning accuracy among the approaches. Figure 4: _Cont._  
The six different filtering approaches' precision in terms of mean errors for different positioning comparisons, such as EKF, MCCEKF-BC, MCCEKF-DS, MCCEKF-GL, MCCEKF-NR, and Mixture-LRMCCEKF are presented in Figure 5a-c. The performance comparisons for different algorithms are shown in Table 1 for different positions in terms of MEs, which reveals that Mixture-LRMCCEKF and MCCEKF-NR offer the best positioning accuracy among the approaches. \begin{table}
\begin{tabular}{c c c c} \hline
**Filters** & **East (m)** & **North (m)** & **Altitude (m)** \\ \hline EKF [29] & 28.5627 & 21.7379 & 40.5981 \\ MCCEKF-BC [31] & 19.3647 & 16.6939 & 25.4365 \\ MCCEKF-DS [34] & 16.5144 & 15.4960 & 24.1786 \\ MCCEKF-GL [32] & 16.5886 & 15.6737 & 24.4489 \\
**MCCEKF-NR [Present]** & **16.4092** & **15.3790** & **24.0792** \\
**Mixture-LRMCCEKF [Present]** & **16.4124** & **15.3989** & **24.1061** \\ \hline \end{tabular}
\end{table} 
Table 1: The performance comparison in terms of mean errors (MEs) for different filters with respect to different positions. Figure 4: The error for different MCCEKF with respect to different positions: (**a**) east, (**b**) north, and (**c**) altitude. Figure 5: The minimum error (ME) for different MCCEKF with respect to different positions: (**a**) east, (**b**) north, and (**c**) altitude. The six different filtering approaches' precision in terms of mean square errors for different positioning comparisons, such as EKF, MCCEKF-BC, MCCEKF-DS, MCCEKF-GL, MCCEKF-NR, and Mixture-LRMCCEKF are presented in Figure 6a-c. The performance comparison for different algorithms is shown in Table 2, which reveals that Mixture-LRMCCEKF and MCCEKF-NR offer the best positioning accuracy among the approaches in terms of MSE. Figure 6: The mean square error (MSE) for different MCCEKF with respect to different positions: (**a**) east, (**b**) north, and (**c**) altitude. The six different filtering approaches' precision in terms of root mean square errors for different positioning comparisons, such as EKF, MCCEKF-BC, MCCEKF-DS, MCCEKF-GL, MCCEKF-NR, and Mixture-LRMCCEKF, are presented in Figure 7a-c. The performance comparison for different algorithms is shown in Table 3, which reveals that Mixture-LRMCCEKF and NRMCCEKF offer the best positioning accuracy among the approaches in terms of RMSEs. In the meantime, MCCEKF-NR performs better than the EKF and the other MCCEKF's studied here, and estimates more accurately than the Mixture-LRMCCEKF. Furthermore, it is worth noting that the fixed-point algorithms in Mixture-LRMCCEKF and MCCEKF-NR are based on the iterative EKF converging to the most ideal result for the application in the GPS satellite navigations.