# 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  & **Method** & **East Error (m)** & **North Error (m)** & **Horizontal Error (m)** \\ \hline \multirow{4}{*}{MAX Error} & Our method & **4.8879** & **6.0308** & **6.9790** \\  & iTransformer & 13.6634 & 11.3954 & 13.6902 \\ \cline{1-1}  & LSTM & 21.7570 & 11.3180 & 21.8038 \\ \cline{1-1}  & GRU & 28.0816 & 14.9659 & 28.2057 \\ \cline{1-1}  & INS & 444.8387 & 207.2744 & 490.7587 \\ \hline \multirow{4}{*}{RMSE} & Our method & **3.3980** & **2.3024** & **4.1046** \\ \cline{1-1}  & iTransformer & 8.7338 & 4.2948 & 9.7326 \\ \cline{1-1}  & LSTM & 12.9937 & 3.6071 & 13.4851 \\ \cline{1-1}  & GRU & 16.6707 & 5.1831 & 17.4579 \\ \cline{1-1}  & INS & 226.1042 & 83.2790 & 240.9533 \\ \hline \end{tabular}
\end{table} 
Table 4: MAX Error and RMSE of different methods on Path #2. Figure 14: The box plot and bar chart of position error on Path #2: (**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. For the test on the private dataset, we first compare the RMSE and MAX Errors. An intuitive comparison of RMSE and MAX Errors is shown in Figure 16. Table 6 provides a detailed comparison of the RMSE and MAX Error for each method in the east, north, and horizontal directions. It can be seen that the method proposed in this paper achieved excellent results in all directions, with the reduction in absolute position error in the east, north, and horizontal directions as follows:

* Compared to INS: The RMSE and MAX Error decreased by 99.9% in all directions, respectively;
* Compared to iTransformer: The RMSE is reduced by 55%, \(-\)32.4%, and 37.2%, and the MAX Error decreased by 51.6%, \(-\)13.6%, and 37.4%, respectively;
* Compared to LSTM: The RMSE decreased by 85.9%, 74.3%, and 82.4%, and the MAX Error decreased by 86.1%, 78.4%, and 82%, respectively;
* Compared to GRU: The RMSE is reduced by 55.5%, 83.4%, and 78.2%, and the MAX Error decreased by 53.3%, 87.9%, and 81.7%, respectively. Among these, the iTransformer achieved the best performance in the north direction, slightly outperforming the method proposed in this paper. However, its performance in the east direction was weaker, leading to a lower overall score in horizontal positioning. Our method achieved the best overall performance. Additionally, due to the high noise and low stability of the low-cost sensors, the error in pure INS inertial navigation was so large that its trajectory and error values could not be properly displayed alongside the other methods. Therefore, the INS is excluded from further comparisons. Figure 15: Data acquisition platform and trajectory of datasets: (**a**) The appearance and electrical connection diagram of the data acquisition platform are provided; (**b**) The data acquisition path covers the entire route with a strong GNSS signal throughout, lasting a total of 2800 s. Of this, 2240 s are used for the training set, 560 s for the test set, and a 25 s segment is designated as the test path called Path #3. \begin{table}
\begin{tabular}{c c c c} \hline
**Sensor** & **Bias Drift** & **RMS Noise** & **Frequency** & **Position Error** \\ \hline Gyroscope & 2.24\({}^{\text{o}}\)/h & 0.028 \(\sim\) 0.07\({}^{\text{o}}\)/s & 100 Hz & \\ Accelerometer & \(\pm\)20 \(\sim\) 40 mg & 0.75 \(\sim\) 1 mg & 100 Hz & \\ ATGM336H-5N-71 & \(\backslash\) & \(\backslash\) & 1 Hz & 0 \(\sim\) 2.5 m \\ \hline \end{tabular}
\end{table} 
Table 5: The parameters of JY901B, ATGM336H-5N-71, and mobile robot. It is worth noting that on Path #3, the neural network performs better than on Path #2 due to differences in the operating environments of the public and private datasets, as well as the speeds of the acquisition vehicles and robots. The faster the vehicle and the more complex the operating environment, there will be more pronounced changes in motion during acceleration, deceleration, and turning. The neural network must adapt to these rapid changes, which can introduce fluctuations.