# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
From each dataset, three representative routes were selected for testing, referred to as Path #1, Path #2, and Path #3. The experiments on Path #1 demonstrate that neural networks can effectively mitigate error amplification during GNSS outages. However, on the stable Path #1, the performance gap between all models is minimal, with the proposed method in this paper reducing the error by 97.5% compared to the INS system. Experiments on Path #2 show that during sharp turns in the trajectory, the attention mechanism plays a significant role in modeling IMU and GNSS signals. The performance of LSTM and GRU on this route is notably inferior to that of the iTransformer and FECAM-iTransformer. The FECAM-iTransformer, which places additional emphasis on multi-channel frequency-domain features, achieved higher positioning accuracy than the iTransformer. Compared to INS, the positioning error of the FECAM-iTransformer is reduced by 98.3%. Experiments on Path #3 demonstrate that neural networks with attention mechanisms perform better on low-cost sensor platforms, regardless of whether the vehicle is turning or traveling in a straight line. The FECAM-iTransformer reduced the positioning error by 99.9% compared to the INS. Compared to traditional deep learning models, the FECAM-iTransformer demonstrates superior navigation accuracy and stability. Current neural network solutions generally fail to deeply and specifically capture and extract the time and frequency characteristics of the IMU data, as they typically model all sequence information solely in the time domain. Therefore, further research in this area, focusing on detailed feature analysis and extraction of sensor data, represents a promising direction for improvement. However, there are areas for further enhancement in this work: the training and test datasets do not cover all possible application scenarios. Although experiments have shown that the method is effective on both professional and low-cost equipment platforms for land vehicles, future studies could extend experimental vehicles to surface, underwater, aerial, and other scenarios. As the volume of data increases, the proposed method is expected to achieve even better adaptability. ## 6 Conclusions

In this paper, a novel method for estimating the GNSS location measurements using the FECAM-iTransformer algorithm is proposed to mitigate the accumulated INS errors during GNSS signal interruptions. The iTransformer and FECAM algorithms are employed to extract time-domain and frequency-domain features from multi-channel IMU sensor data, enabling the stable output of reliable GNSS positioning signals even in the event of a complete GNSS outage. This approach significantly reduces vehicle position errors. Additionally, this study provides a detailed analysis of the model's input features and outputs. The model dynamically learns and predicts changes in vehicle position using IMU inputs, specifically triaxial acceleration and triaxial angular velocity. Compared to existing LSTM and GRU models, the FECAM-iTransformer achieves more accurate and stable navigation prediction results. **Author Contributions:** Conceptualization, X.K. and B.Y. ; methodology, B.Y. ; software, B.Y. ; validation, X.K. and B.Y. ; formal analysis, B.Y. ; investigation, B.Y. ; resources, X.K. ; data curation, B.Y. ; writing--original draft preparation, B.Y. ; writing--review and editing, X.K. ; visualization, B.Y. ; supervision, X.K. ; project administration, X.K. ; funding acquisition, X.K. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Key Research and Development Program of China: Design and Development of High Performance Marine Electric Field Sensor, grant number 2022 YFC3104001. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data are available from the corresponding authors. **Conflicts of Interest:** The authors declare no conflicts of interest.