## 4 Discussion  
This study aims to address the issue of error accumulation in standalone INS and the challenges related to fusion optimization and disruption in integrated navigation systems. A new INS/MNS combined navigation system was proposed, utilizing LSTM with an adaptive CKF algorithm. The proposed seamless IM-NN fusion structure developed during MNS data loss correlates current input information with prior model information to compensate for the loss of heading accuracy. Field tests and simulations were performed to confirm the effectiveness of the suggested strategy.  
The experimental results demonstrated that the proposed Method 5 fusion algorithm significantly improved heading accuracy compared to Method 2 in magnetic normal environment experiments. Method 3 improved by 76.93%, Method 4 by 83.36%, and Method 5 by 83.72%. In the magnetic anomaly environment experiment, Method 6 increased heading accuracy by 83.50% compared to pure INS Method 2. The results proved that the designed IM-NN based on an LSTM network successfully captured the inherent nonlinear relationship between INS output and heading information, delivering precise navigation information in the event of MNS interruption.  
Novel fusion filtering algorithms need to be investigated in the future to further optimize the combined navigation. The proposed IM-NN still has limitations: for example, it can only compensate for the prediction using deep learning network algorithms when the directional accuracy decreases significantly, but the magnitude of the decrease in directional  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Median** & **Max** & **Min** & **RMS** & **Improve (RMS)** \\ \hline Method 2 & 10.00 & 29.20 & \(2.6\times 10^{-4}\) & 13.94 & \(\backslash\) \\ Method 6 & \(-\)0.14 & 6.86 & \(7.9\times 10^{-5}\) & 2.30 & 83.50\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Median, Max, Min, and Rms of The Yaw Obtained by Two Methods in The Magnetic Anomaly Experiment (Unit \({}^{\circ}\)).  
Figure 8: (**a**) Analysis of heading angle during periods containing geomagnetic disruptions. (**b**) Analysis of heading angle errors during periods containing geomagnetic disruptions.  
accuracy in the initial stage is small and cannot be detected by active sensing. At the same time, the predicted values output by the deep learning network algorithm are still in error compared to the observed values.  
In a future research direction, fault detection algorithms will be considered to assist the deep learning network, and optimized Kalman fusion filtering algorithms will be explored to reduce the error in the nonlinear system of combinatorial navigation and further improve the orientation accuracy of integrated navigation.  
Conceptualization, T.L. and H.Z.; Methodology, T.L., T.Z. and H.Z.; Validation, T.L., T.Z. and C.W.; Investigation, T.Z. and H.Z.; Resources, C.W.; Data curation, T.Z.; Writing--original draft, T.L. and T.Z.; Writing--review & editing, C.W.; Visualization, T.L. and T.Z.; Supervision, C.W.; Project administration, C.W.; Funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
The data that support the findings of this study are available on reasonable request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.