# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
The trajectory of the dataset is shown in Figure 8, where the yellow segment represents the training set, with a duration of 4800 s, accounting for 80% of the data. The green segment represents the test set, with a duration of 1200 s, accounting for 20% of the data, as shown in Figure 8a. Within the test set, two representative sections with different durations are selected as test tracks and marked in red, with durations of 100 s and 200 s, called Path #1 and Path #2, respectively, as shown in Figure 8b. The longitude, latitude, and altitude measurements obtained from the GNSS receiver are used as ground truth values for testing. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **FECAM-iTransformer** & **iTransformer** & **LSTM** & **GRU** \\ \hline learning rate & 0.0001 & 0.0001 & 0.001 & 0.001 \\ batch size & 32 & 32 & 64 & 64 \\ training epochs & 10 & 10 & 50 & 50 \\ input length & 8 & 8 & 4 & 4 \\ encoder layers & 2 & 2 & \(\backslash\) & \(\backslash\) \\ number of heads & 8 & 8 & \(\backslash\) & \(\backslash\) \\ number channels & 512 & \(\backslash\) & \(\backslash\) & \(\backslash\) \\ hidden size & \(\backslash\) & \(\backslash\) & 64 & 64 \\ number of layers & \(\backslash\) & \(\backslash\) & 2 & 2 \\ learning rate decay & \(\backslash\) & \(\backslash\) & 0.0001 & 0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The configurations and training parameters of each model. Figure 8: The trajectory of public datasets: (**a**) the trajectory of training part and testing part of public datasets; (**b**) the trajectory of Path #1 and Path #2. #### 4.2.2 The Results of Experiment on Public Dataset

Path #1 has a duration of 100 s and follows a gentle curve, with the movement of the vehicle being relatively stable and smooth. Figure 9 presents a comparison of the test tracks and the horizontal errors for each method on Path #1. It is evident from the trajectory diagram that all integrated navigation methods based on neural networks closely fit the real path, with minimal differences among the various methods. The same path results in similar trajectories and errors for each method. In contrast, the INS approach significantly deviates from the true path, particularly when the vehicle changes direction. Figure 9 shows the comparison of horizontal position errors for the different methods, excluding pure INS (since the INS error is excessively large, making it difficult to display alongside other methods, a graphical comparison would be meaningless here; instead, a quantitative comparison will be provided in tabular form later). From the 8 th second onward, the positioning errors of each method begin to change significantly, though the differences between the methods remain relatively small. Among these, the method proposed in this paper demonstrates the least error. Figure 10 shows the error values of each method in three different directions, showing small differences along the stable route. Since the vehicle is in a horizontal motion, the altitude error is very small. Figure 11 presents the horizontal position error distribution of each method in the form of a box plot. The error distribution of the method proposed in this paper is more concentrated, with most of the errors and the median below 3 m indicating greater stability compared to other methods. Figure 11 shows the root mean square error (RMSE) and maximum error (MAX Error) of the horizontal position for each method, presented in a bar chart. Our method yields strong results, with an RMSE of 1.7 m and a MAX Error of 2.7 m after 100 s of GNSS outage. While the iTransformer's error is slightly higher than that of the LSTM, the difference is minimal. On the more moderate route, both the LSTM and GRU