# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
The acquisition vehicle for the public dataset operates in a more complex environment and at higher speeds. In contrast, the robots using private datasets operate at a lower, steady speed, resulting in relatively smaller error fluctuations. Nevertheless, noise in the low-cost sensor measurements persisted and affected the performance of the LSTM and GRU models. However, the iTransformer and FECAM-iTransformer, with their attention mechanisms, mitigated the impact of these noises, achieving positioning accuracy comparable to the smooth driving on Path #1. Figure 17 shows the comparison of test tracks and horizontal errors for each method on Path #3. The test route includes multiple right-angle turns, and due to the mobile robot lacking a shock absorber, it experiences relatively high noise levels, posing a significant challenge for the neural network models. As seen in Figure 17a, LSTM and GRU are significantly affected, deviating considerably from the actual trajectory, while the iTransformer and FECAM-iTransformer align more closely with the real trajectory. Figure 17b shows that the fluctuations in the error graph are caused by the mobile robot's turns. The horizontal positioning errors accumulate more noticeably with the LSTM and GRU, whereas the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Method** & **East Error (m)** & **North Error (m)** & **Horizontal Error (m)** \\ \hline \multirow{4}{*}{MAX Error} & Our method & **2.9107** & **2.4888** & **3.7739** \\  & iTransformer & 6.0123 & 2.1510 & 6.0318 \\  & LSTM & 20.9941 & 11.4996 & 21.0050 \\  & GRU & 6.2305 & 20.5142 & 20.5985 \\  & INS & 200,340 & 1,493,000 & 1,495,300 \\ \hline \multirow{4}{*}{RMSE} & Our method & **1.5307** & **1.5734** & **2.1951** \\  & iTransformer & 3.3269 & 1.0635 & 3.4928 \\ \cline{1-1}  & LSTM & 10.8684 & 6.1222 & 12.4741 \\ \cline{1-1}  & GRU & 3.4413 & 9.4653 & 10.0715 \\ \cline{1-1}  & INS & 4959 & 2684 & 5639 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MAX Error and RMSE of different methods on Path #3. Figure 16: The box plot and bar chart of position error on Path #3: (**a**) The box plot shows the horizontal position error distribution of each method; (**b**) The bar chart shows the RMSE and MAX Error of each method. FECAM-iTransformer shows a smaller overall error than the iTransformer, consistently maintaining its horizontal positioning error below 5 m. This is because the attention mechanism of the iTransformer and FECAM-iTransformer filters out invalid information in the time series, and some noise that causes error accumulation is no longer considered. The FECAM-iTransformer further enhances the effective frequency channel from the frequency domain and weakens the adverse effects brought by the invalid frequencies, so its performance is better than the iTransformer. Figure 18 shows the error values of each method in three different directions on Path #3. ## 5 Discussion

In this paper, an INS/FECAM-iTransformer integrated navigation system is proposed to address the rapid accumulation of INS errors during GNSS outages. Experimental results demonstrate that the FECAM-iTransformer offers higher accuracy and stability compared

Figure 17: Trajectory diagram and horizontal position errors diagram on Path #3: (**a**) the trajectory of each method on Path #3; (**b**) the horizontal position errors of each method on Path #3. Figure 18: Position errors of north, east, and altitude on Path #3.

to existing neural network solutions. The main advantages of the FECAM-iTransformer are as follows:

1. The iTransformer can model the entire input sequence in the time domain across multiple tokens, effectively capturing the variable correlations between the multi-channel data from the IMU. 2. The FECAM enables the FECAM-iTransformer to model in the frequency domain. By using an SE-Block, the FECAM enhances the effective frequency information of the IMU, allowing the model to capture rich frequency-domain features from the IMU data. In this experiment, two datasets were used: a public dataset and a private dataset.