# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
In addition, the vehicle typically travels at a low speed during the U-turn, which reduces the complexity of the model's prediction. This is another reason for the decrease in the horizontal positioning error. Figure 14a shows the horizontal position error distribution for each method in the form of a box plot. The error distribution of the method proposed in this paper is more concentrated, with most errors and the median falling below 5 m, indicating greater stability and accuracy compared to other methods. Figure 14b presents the RMSE and MAX Error of the horizontal absolute position for each method in the form of a bar chart. The proposed method demonstrates strong performance, achieving an RMSE of 4.1 m and a MAX Error of 7.0 m after 200 s of GNSS outage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Method** & **East Error (m)** & **North Error (m)** & **Horizontal Error (m)** \\ \hline \multirow{8}{*}{MAX Error} & Our method & **1.9959** & **2.4495** & **2.6581** \\  & iTransformer & 4.4082 & 4.1171 & 5.0657 \\  & LSTM & 2.9022 & 3.3230 & 4.1863 \\  & GRU & 3.6161 & 5.1970 & 6.0572 \\  & INS & 106.6452 & 13.5499 & 107.5026 \\ \hline \multirow{8}{*}{RMSE} & Our method & **0.9880** & **1.4085** & **1.7205** \\  & iTransformer & 2.0331 & 2.3087 & 3.0763 \\ \cline{1-1}  & LSTM & 1.9485 & 1.5821 & 2.5099 \\ \cline{1-1}  & GRU & 3.1849 & 2.1873 & 3.8636 \\ \cline{1-1}  & INS & 48.9940 & 7.1497 & 49.5129 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MAX Error and RMSE of different methods on Path #1. Table 4 provides a detailed comparison of the RMSE and MAX Error for the east, north, and horizontal position errors of each method on Path #2. The reductions in position errors in the east, north, and horizontal directions are as follows:

* Compared to INS: The RMSE decreased by 98.5%, 97.2%, and 98.3%, and the MAX Error decreased by 98.9%, 97.1%, and 98.6%, respectively;
* Compared to iTransformer: The RMSE is reduced by 61.1%, 46.4%, and 57.8%, and the MAX Error decreased by 64.2%, 47.1%, and 49%, respectively;
* Compared to LSTM: The RMSE decreased by 73.8%, 36.2%, and 69.6%, and the MAX Error decreased by 77.5%, 46.7%, and 68%, respectively;
* Compared to GRU: The RMSE is reduced by 79.6%, 55.6%, and 76.5%, and the MAX Error decreased by 82.6%, 59.7%, and 75.3%, respectively. Figure 12: Trajectory diagram and horizontal position errors diagram on Path #2: (**a**) the trajectory of each method on Path #2; (**b**) the horizontal position errors of each method on Path #2. Figure 13: Position errors of north, east, and altitude on Path #2. Experiments on public datasets demonstrate that the proposed model effectively addresses the rapid accumulation of positioning errors caused by the GNSS outage in professional strapdown inertial navigation systems, outperforming existing methods such as the LSTM and GRU. The model will also be further tested on a low-cost INS/GNSS integrated navigation system and a mobile robot. ### Experiment on Private Dataset

A low-cost INS/GNSS integrated navigation system and a small mobile robot platform were used to collect the private dataset at 13:03 on 11 July 2024, at a university located in Pudong New Area, Shanghai, China. The robot's moving speed was about 0-1.5 m/s, compared to the 3 m/s speed used for the public dataset. Furthermore, the robot's size is \(726\times 617\times 273\)mm, and its net weight is 40 kg. The IMU sensor is the JY901B, and the GNSS module is the ATGM336H-5N-71. The sensors' and mobile robot's parameters are detailed in Table 5. The total duration of the dataset is 2800 s, with 80% (2240 s) used as training data and the remaining 20% (560 s) as test data. Within the test data, a 250 s route is selected as the test track, as shown in Figure 15, in which yellow represents the training part, green represents the testing part, and red indicates the testing path named Path #3. The longitude, latitude, and altitude measurements obtained from the GNSS receiver are used as ground truth values for testing.