# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
#### 3.3.3 FECAM: Frequency-Enhanced Channel Attention Mechanism

FECAM [32] learns the frequency-domain representation of a time series by modeling it in the frequency domain, assigning weights to different channels, and determining the importance of each channel at various frequencies. The most notable feature of FECAM is its use of the discrete cosine transform (DCT) to address the high-frequency noise caused by the Gibbs phenomenon [32], which often arises when using Fourier transform in time-series prediction. This approach allows the model to adaptively capture frequency dependencies between channels, effectively reducing prediction errors. The framework of FECAM is shown in Figure 2:4

First, FECAM divides the input feature maps into \(n\) groups along the channel dimension, effectively separating each token. Subsequently, a DCT operation is performed on each token to obtain the frequency representation of the response [32]:

Figure 2:5

where \(V\) represents each input token, \(L_{S}\) is the length of the input token, \(B^{j}_{l}\) is the function of one-dimensional DCT, which can be expressed as [32]:

Figure 2:6

Next, the attention weights for these frequency channel vectors are learned through neural structure as SE-block. The mathematical expression for the frequency channel-enhanced attention mechanism is as follows [32]:

Figure 2:7

where \(att\) is the attention weight learned by the neural structure of SE-block, \(\delta\) and \(\sigma\) are the sigmoid and ReLU activation functions, respectively, \(W_{1}\) and \(W_{2}\) are the linear layer weights learned by the neural structure of SE-block. ## 4 Results and Analyses

The effectiveness of the proposed model is evaluated using both public and private datasets in the experimental section of this paper. Public datasets, obtained with high-precision equipment, are used to assess the model's performance on higher-quality data. In contrast, private datasets, collected using low-cost sensors and mobile robot platforms, are employed to test the model's performance on lower-quality, interference-prone devices. ### Configuration of Model

In addition to INS, the original iTransformer, and the FECAM-iTransformer, two existing deep neural networks, LSTM and GRU, commonly used to address the GNSS loss-of-lock problem, are selected for comparison. The configurations and training parameters of each model are determined using the grid search method and are summarized in Figure 2:8

The computer used for training and testing is configured with a Windows 11 operating system, an Intel i5-12500H CPU, and 16 GB of memory. Additionally, due to the large error associated with INS, it is neither practical nor desirable to display comparisons using images. Therefore, when presenting the test results,

Figure 2:9 The framework of FECAM. the trajectory of the INS should be plotted, but its results will not be included in line charts, box plots, or bar charts. Instead, comparisons between the INS and other methods will be presented in tabular form. ### Experiment on Public Datasets

#### 4.2.1 Description of Public Datasets

The public dataset provided by Dalian University of Technology can be accessed at the following: [[http://www.psins.org.cn/newsinfo/1508278.html](http://www.psins.org.cn/newsinfo/1508278.html)]([http://www.psins.org.cn/newsinfo/1508278.html](http://www.psins.org.cn/newsinfo/1508278.html)) accessed on 29 February 2024. The dataset was uploaded to the open-source website on 24 May 2021. The data collection route was located on an open road with strong GNSS signal reception in Tongzhou District, Beijing, China. The dataset was collected using the MTI710, a high-precision INS/GNSS integrated navigation device, and a vehicle with an average speed of 3.5 m/s. The parameters of MTI710 are detailed in Table 2 below. To avoid repetition of the experimental route, half of the dataset, with a duration of 6000 s, is used in this paper.