## 4 Simulations and Experiments on Tri-Axis RINS
### Experiments and Discussion  
In the dynamic environment, the carrier angular and line motions are coupled with IMU-related errors to excite new navigation errors, which are not only caused by the rotation scheme but are also associated with the calibration accuracy and control method of the RINS. At present, the same static navigation experiments using Schemes A, B, and C are sufficient to prove the advantages of the improved rotational modulation scheme proposed in this manuscript. As shown in Figure 12, the tri-axis RINS was fixed on a single-axis speed turntable, and a DC voltage regulator supplied the power. The laptop recorded the original data from the IMU and drew the 1 Hz navigation data on the screen. The design of different rotation schemes requires determining the command angles for the three motors. In our current test environment, which is mainly static, we use the high-precision encoder output as feedback for motor control instructions. However, when the structure of the tri-axis RINS changes or the carrier is in a dynamic environment, we need to reallocate the motor control command angles. Our ultimate goal is to achieve the rotational modulation scheme of the IMU in the geographic coordinate system. Since this manuscript mainly demonstrates the advantages of the improved rotational modulation scheme, there is no strict requirement on the initial attitudes and heading angle of RINS, and it is enough to ensure that the turntable is locked during the static navigation experiments. The model of initial alignment and the rotation scheme during alignment were the same, so we mainly focused on the effect of the rotation schemes on navigation accuracy. The navigation time of each test is more than 6 h because more than 1/4 of the Earth's cycle is convenient to observe the error pattern. Figure 11: Position errors of different rotation schemes. Figure 12: Experimental environment. Under the same initial alignment conditions and navigation environment, we obtained the following navigation results: The position errors of the three schemes for a certain navigation test were plotted in Figure 13, and it is obvious that Scheme C has the smallest position error. The CEP was calculated to compare the navigation performance of different rotation schemes. The CEPs for all tests are tabulated in Table 7, and the mean values of the three schemes are 0.109 n mile/h, 0.070 n mile/h, and 0.053 n mile/h, respectively. By using Scheme C, we can significantly improve navigation performance compared to Schemes A and B, with improvements of 51% and 25%, respectively. To compare the navigation results from multiple perspectives, we also list the maximum radial position errors \(\left(\Delta R_{i}\right)_{\text{max}}\) for each group of navigation experiments within 6 h in Table 8 and it is evident that the average value of the maximum radial position error of Scheme C is less than half of the other two schemes. In conclusion, it is quite visible from the results of simulations and actual navigation tests that the improved rotational modulation scheme can effectively reduce navigation errors despite the poor temperature stability of FOG. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Experiment Number**} & \multicolumn{3}{c}{**Circular Error Probability (n Mile/h)**} \\ \cline{2-4}  & **Scheme A** & **Scheme B** & **Scheme C** \\ \hline
1 & 0.140 & 0.069 & 0.054 \\
2 & 0.083 & 0.072 & 0.055 \\
3 & 0.105 & 0.068 & 0.049 \\ Mean value & 0.109 & 0.070 & 0.053 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Circular Error Probability of the three schemes. Figure 13: Navigation test position errors for three rotation schemes.