# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 2 Theory of INS/GNSS Integrated Navigation System
Therefore, we require a neural network that can model the correlations between these multi-channel input sequences, rather than simply focusing on the temporal progression of the inputs. After various attempts, we selected the iTransformer for this task, which is thoroughly explained in Section 3.3.2. Additionally, we suggest addressing the noise in IMU measurements and exploring potential kinematic features from a frequency-domain perspective. Treating time series as signals allows it to be decomposed into a linear combination of sinusoidal components without losing any information. Each component has a unique frequency, initial phase, and amplitude, as shown in Figure 2b. Thus, the frequency domain provides another view of the IMU signal. Each IMU signal in the time domain can be transformed into the frequency domain using a Fourier transform. This conversion provides a more compact and elegant representation, typically expressed in a complex number, and can be mathematically represented by the following formula [31]:

\[X(f)=|X(f)|e^{i\theta(f)}=|X(f)|(\cos\theta(f)+j\sin\theta(f)) \tag{8}\]

where \(X(f)\) is the complex number associated with the frequency component at frequency \(f\), \(|X(f)|\) is the amplitude of the frequency component, and \(\theta(f)\) is the phase of the frequency component. In the frequency domain of IMU signals, the high-frequency components tend to be noisier, while the low-frequency components contain more valuable information. However, these two elements are often intertwined across all frequencies, making it challenging to separate them. To amplify the impact of useful information within the frequency components, we propose utilizing neural networks, specifically incorporating FECAM. By integrating FECAM into the iTransformer, we aim to strengthen its ability to capture and express frequency-domain features. Subsequent experiments have demonstrated the effectiveness of this approach, with notable improvements observed. The detailed workings of FECAM are outlined in Section 3.3.3. Figure 2: Relationship and features of IMU signal and GNSS. (**a**) IMU measurements correspond to changes in the vehicle’s GNSS position, \(f_{\text{h}x}^{b}\), \(f_{\text{h}y}^{b}\), \(f_{\text{h}z}^{b}\) are the measurement from accelerometer of IMU, \(\omega_{\text{h}x}^{b}\), \(\omega_{\text{h}y}^{b}\), \(\omega_{\text{h}z}^{b}\) are the measurement from gyroscope of IMU, \(p_{GNSS}(t)\) and \(p_{GNSS}(t-1)\) are the GNSS position at time \(t\) and \(t-1\), \(\delta p_{GNSS}=\{\delta Longitude,\delta Latitude,\delta Altitude\}\) is the GNSS position increment from time \(t-1\) to \(t\); (**b**) The IMU signal can be represented as the superposition of several sine waves, each characterized by its amplitude, frequency, and phase. ### The Overall Architecture of INS/FECAM-iTransformer Integrated Navigation System

The overall architecture of our approach is illustrated in Figure 3, which corresponds to the training model and the prediction model of the system, respectively. This paper presents a loosely integrated navigation scheme that combines artificial intelligence with an extended Kalman filter (EKF). In this scheme, the EKF module provides high-precision error information to the system, which is then used to correct the attitude, speed, and position. The AI module, the FECAM-iTransformer, temporarily supplies the EKF with essential GNSS positioning data during GNSS outages. The principle and framework of the FECAM-iTransformer will be described in detail in Section 3.3. The training mode of the system is shown in Figure 3a. When the GNSS works, the FECAM-iTransformer model is trained. Data memory store IMU measurements, GNSS position measurements, and GNSS position increments at each moment. The features and labels required for model training are \(f_{ib}^{b}\), \(\omega_{ib}^{b}\), and \(\delta p_{GNSS}\) of the past few minutes.