# Research on the SSUKF Integrated Navigation Algorithm Based on Adaptive Factors
## 4 Simulation Experiment
Through this mechanism, ASSUKF not only effectively handles dynamic noise variations but also maintains high-precision state estimation under various complex environmental conditions, significantly reducing navigation errors. Figure 3: Roll angle error. Figure 2: Pitch angle error. Figure 4: Heading angle error. Figure 5: Eastward velocity error. Figure 6: Northward velocity error. Figure 8: Latitude direction position error. Figure 7: Upward velocity error. Figure 9: Longitude direction position error. To further validate the reliability of the results and avoid errors caused by random factors in a single trial, we conducted ten independent trials, each using the same parameter settings. For each trial, the measurement errors followed the same distribution. We then compiled the relevant experimental results and averaged the outcomes of the ten trials. Table 2, comparison of root mean square errors (RMSEs) for different algorithms, shows the Root Mean Square Error (RMSE) of the navigation results for the three methods. In terms of position error, UKF and SSUKF have similar accuracy, while ASSUKF, with the addition of adaptive filtering, effectively handles abnormal noise and significantly improves accuracy. Specifically, ASSUKF improves position accuracy in the latitude direction by 18.10% and in the longitude direction by 20.6%. Regarding velocity error, the velocity estimation capabilities of the three methods are relatively similar, with good accuracy. For attitude error, ASSUKF performs exceptionally well. Specifically, the pitch angle error improves by 27.6% compared to UKF and by 27.1% compared to SSUKF. The roll angle error improves by 29.9% compared to UKF and by 20.1% compared to SSUKF. The heading angle error improves by 24.3% compared to SSUKF but is slightly worse than UKF. By comparing the RMSEs of UKF, SSUKF, and ASSUKF, it is clear that the proposed ASSUKF significantly outperforms both UKF and SSUKF in terms of position and attitude accuracy. The introduction of the adaptive factor effectively improves the filtering accuracy of the integrated navigation system, ensuring that the system provides more accurate and reliable navigation results in complex dynamic environments. Another important metric for evaluating the algorithm is its running efficiency. While the UKF is relatively simple in implementation, it requires direct handling of the covariance matrix and its inversion operations, which results in higher computational complexity, especially when dealing with high-dimensional systems or environments with significant noise variations. This makes UKF's run time noticeably longer, particularly when the state \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Filter**} & \multicolumn{3}{c}{**Position Error/m**} & \multicolumn{3}{c}{**Velocity Error/m\(\cdot\)s\({}^{-1}\)**} & \multicolumn{3}{c}{**Attitude Error/(\({}^{\prime\prime}\)\({}^{\prime\prime}\)\({}^{\prime}\))**} \\ \cline{2-10}  & \(\Delta\)\(\Delta\)\(\Delta\) & \(\Delta\)\(H\) & \(\Delta\)\(V_{E}\) & \(\Delta\)\(V_{N}\) & \(\Delta\)\(V_{UI}\) & \(\Delta\)\(\theta\) & \(\Delta\)\(\gamma\) & \(\Delta\)\(\phi\) \\ \hline UKF & 1.04 & 1.78 & 2.31 & 0.093 & 0.077 & 0.012 & 132.4 & 190.4 & 76.4 \\ \hline SSUKF & 1.06 & 1.82 & 2.32 & 0.093 & 0.079 & 0.012 & 131.5 & 167.0 & 152.6 \\ \hline ASSUKF & 0.86 & 1.43 & 2.24 & 0.092 & 0.074 & 0.007 & 95.9 & 133.5 & 115.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of root mean square errors (RMSE) for different algorithms. Figure 10: Altitude direction position error. dimension is large. In contrast, SSUKF and ASSUKF use the spherical simplex sampling strategy, which effectively reduces numerical instability and memory consumption. These methods improve running efficiency while maintaining high accuracy. Table 3, comparison of running times for different algorithms, shows the running times of the three algorithms.