# A Novel FECAM-iTransformer Algorithm for Assisting INS/GNSS Navigation System during GNSS Outages
## 1 Introduction  
Highly accurate and reliable positioning, navigation, and timing technologies are essential for the safe operation of mobile smart devices [1]. Inertial navigation systems (INS) are characterized by short-term high accuracy and independence from environmental influences. However, standalone INS solutions degrade over time due to the significant errors inherent in the raw measurements of inertial measurement units (IMUs) [2]. This degradation is especially pronounced and drastic in INS systems that use small, low-cost IMU devices, which many mobile devices are compelled to use due to space constraints. The integration of global navigation satellite systems (GNSSs) and INS has been widely used to improve the accuracy and reliability of positioning [3, 4], because GNSSs can provide long-term accurate and continuous positioning signals under decent visibility conditions [5], compensating for the defect of low-cost INS. However, the GNSS has one almost inevitable drawback: it relies heavily on stable signals for high-precision positioning. In areas with ambiguous signals, such as cities, forests, and tunnels, GNSS signals can become unstable or even lost [6, 7]. If the GNSS signal is interrupted for a prolonged period, the GNSS/INS integrated navigation system will inevitably revert to a pure INS, leading tothe rapid accumulation of positioning errors and compromising the safety and efficiency of vehicle operation [8]. There are many solutions to this problem, typically involving the addition of extra sensors such as barometers, odometers, cameras, LIDAR, etc., to collect richer environmental data [9; 10; 11]. However, this approach results in higher hardware costs and a more complicated data fusion process, making it less economical for general application scenarios [12]. In recent years, machine learning algorithms have been shown to improve the performance of GNSS/INS integrated navigation systems by modeling the mathematical relationship between navigation parameters and vehicle dynamic data during GNSS outages [13]. [PERSON] et al. used a radial basis function neural network to model INS positions and the mathematical relationship between INS and GNSS for stable and reliable navigation performance [14; 15]. [PERSON] et al. employed support vector machines (SVM) optimized by genetic algorithms (GAs) to address neural network overfitting and local minimum problems [16]. Static neural networks have limited navigation performance due to their inability to remember long-term time features, leading to the application of more advanced deep learning models. Long short-term memory (LSTM), as a dynamic neural network, uses past and present information to predict future states and was applied to obtain stable GNSS navigation data during interruptions [17]. [PERSON] et al. proposed a convolutional neural networks-gated recurrent unit (CNNs-GRU) hybrid model combined with an improved robust adaptive Kalman filter to enhance navigation accuracy during GNSS failures [18]. Despite solving the basic degradation problem, these deep neural networks still face accuracy and long-term stability issues. To further explore artificial intelligence in this field, large-scale deep learning models have been integrated into INS/GNSS systems. For example, the Transformer [19] was used to improve navigation reliability during GNSS outages [20], and the time convolutional network (TCN) was applied for its feature extraction and time modeling capabilities, achieving multi-task learning when combined with other neural networks like GRU [21]. It is worth noting that the models mentioned above are significant research advancements in time-series prediction, which raises the question of whether other models could also improve navigation stability. In time-series prediction, recurrent neural networks such as LSTM [22] and GRU [23] are well suited for capturing long-term dependencies due to their gating mechanisms and memory units. However, they lack specialized feature extraction units.