# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sensor** & **Bias Drift** & **Noise** & **Frequency** & **Position Error** \\ \hline Gyroscope & \(10^{\circ}\)/h & \(0.01/\mathrm{s}/\sqrt{\mathrm{Hz}}\) & 100 Hz & \\ Accelerometer & 15 ug & \(60\) ug/\(\sqrt{\mathrm{Hz}}\) & 100 Hz & \\ GNSS & \(\backslash\) & \(\backslash\) & 5 Hz & \(0\sim 2\) m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of MTI710. Figure 9: Trajectory diagram and horizontal position errors diagram: (**a**) the trajectory of each method on Path #1; (**b**) the horizontal position errors of each method on Path #1.

perform well, but on routes with more drastic changes in a motion state, the effectiveness of each method needs further verification. This will be explored in experiments on Path #2. Table 3 provides a detailed comparison of the RMSE and MAX Error for the east, north, and horizontal position errors of each method on Path #1. The proposed method, the FECAM-iTransformer, demonstrates superior performance across all directions, with significant reductions in absolute position errors in the east, north, and horizontal directions:

* Compared to INS: The RMSE decreased by 98%, 80.3%, and 96.5%, and the MAX Error decreased by 98.1%, 81.9%, and 97.5%, respectively;
* Compared to iTransformer: The RMSE is reduced by 51.4%, 39%, and 44.1%, and the MAX Error decreased by 54.7%, 40.5%, and 47.5%, respectively;

Figure 11: The box plot and bar chart of position error on Path #1: (**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. Figure 10: Position errors of north, east, and altitude on Path #1. * Compared to LSTM: The RMSE decreased by 49.3%, 11%, and 31.5%, and the MAX Error decreased by 31.2%, 26.3%, and 36.4%, respectively;
* Compared to GRU: The RMSE is reduced by 69%, 35.6%, and 55.5%, and the MAX Error decreased by 44.8%, 52.9%, and 56.1%, respectively. Path #2 has a duration of 200 s and involves straight lines, right-angle turns, and U-shaped bends, making the vehicle's motion state more complex than that of Path #1. Figure 12 presents the comparison of test tracks and horizontal errors for each method on Path #2. As shown in Figure 12a, the INS trajectory deviates completely from the true path, with an error exceeding 400 m. In contrast, the other methods remain much closer to the true trajectory. The specific horizontal error values are depicted in Figure 12b with a line chart (excluding the INS error, as it is too large and would interfere with the normal display of the other methods). After the first right-angle turn at 60 s, all methods experience some error amplification. However, the iTransformer and our proposed method do not continue to accumulate errors, while the errors for the LSTM and GRU begin to increase further, likely due to the significant impact of the maneuver on the vehicle's state. A second change in positioning error occurs at 165 s when the vehicle navigates a U-turn. Among all the methods, the proposed method exhibits the smallest horizontal error, demonstrating its ability to maintain high positioning accuracy during complex vehicle maneuvers. The comparison of positioning errors in the east, north, and vertical directions is shown in Figure 13, where our method consistently outperforms the others in all directions. It is worth noting that at the U-turn point, the horizontal positioning error briefly decreases before increasing again. This occurs because the northbound and eastbound prediction results of the neural network fluctuate at the vehicle's turning point. As shown in Figure 13, the northbound prediction error increases, while the eastbound prediction error decreases around the 165 s mark. This leads to a temporary reduction in the accumulation of horizontal errors at that point. Subsequently, both the northbound and eastbound prediction errors stabilize, causing the overall horizontal error to increase again.