## 4 Experiment and Analysis
### Performance Comparison: With VG vs. without VG  
For the same dataset as in Section 4.2, this study verified the robustness of the VG pitch and roll observations on the attitude filtering results under GNSS denial conditions through simulation of the dataset. The error comparison charts shown in Figure 7a-c, respectively, demonstrate the performance of the TC integrated navigation algorithm in terms of horizontal and vertical attitude angle errors, velocity errors, and position errors for this set of data with and without VG correction. From the experimental attitude error in Figure 7a, it can be clearly observed that during the long period of GNSS denial from 1500 s to 1700 s, the correction effect of the VG on the estimation of the horizontal attitude angle is quite significant, with the peak of the maximum error being significantly lower than that of the filtering scheme without VG correction. However, there is no significant improvement in the vertical attitude error, velocity error, or position error. To more accurately quantify the effect of VG correction, Table 4 summarizes the RMSE of the two observation schemes in the estimation of the AVP (attitude, velocity, position). Consistent with the analysis of various error result graphs, Table 4 shows that the VG has a certain optimization effect on the AVP estimation accuracy of the carrier, with significant optimization in the horizontal attitude angle. Specifically, the VG scheme reduced the RMSE of the horizontal attitude from 0.108 degrees to 0.078 degrees, the RMSE of the vertical attitude from 0.80 degrees to 0.76 degrees, the RMSE of velocity from 0.031 m/s to 0.028 m/s, and the RMSE of position from 2.69 m to 2.39 m. These improvements correspond to approximately 27.78%, 5.00%, 9.68%, and 11.09% increases in accuracy, respectively. Based on the aforementioned analysis, we have recognized the significant effect of the VG in optimizing the estimation of the horizontal attitude. Given that the improvement effects of the VG on the estimation of other state quantities are not obvious, this study will not delve further into these aspects. To further verify the optimizing effect of the VG on the estimation of the horizontal attitude angle and to examine its ability to suppress the \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Without VG** & **With VG** \\ \hline Horizontal attitude (deg) & 0.108 & 0.078 \\ Vertical attitude (deg) & 0.80 & 0.76 \\ Velocity (m/s) & 0.031 & 0.028 \\ Position (m) & 2.69 & 2.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of AVP RMSE with and without VG correction. Figure 7: Performance comparison between with VG and without VG. (**a**) Comparison chart of attitude errors in horizontal and vertical directions. (**b**) Comparison chart of velocity errors in eastward, northward, and vertical directions. (**c**) Comparison chart of positional errors in the three spatial dimensions of longitude, latitude, and altitude. divergence of the estimation in the carrier under conditions of weakened or denied GNSS signals, this study intentionally introduced periods where GNSS signals are unavailable to simulate extreme situations of GNSS signal denial and conduct a detailed analysis. To this end, we actively added four periods of GNSS signal denial to the experimental data, located at 500 to 600 s, 2500 to 2600 s, 3400 to 3500 s, and 4000 to 4100 s, each lasting for 100 s. Figure 8 presents the horizontal attitude estimation results obtained through simulation during these specific periods. The conclusion remains within our expectations: Figure 8 shows that the VG has a positive optimizing effect on the estimation of the horizontal attitude angle during each long period of GNSS denial. Table 5 summarizes the RMSE of attitude estimation for the two observation schemes in both the global time period and the period containing only GNSS denial.