## 1 Introduction
In GNSS/INS integrated navigation systems, several solutions have been provided to maintain continuous high-precision navigation capabilities during GNSS signal outages. One method is the zero-velocity update (ZUPT) [15; 16], where the vehicle's speed is zero when stationary, and the calculated speed from the vehicle's inertial system is used as an observation of the system's speed error to correct other error quantities. The application of zero-velocity correction is limited because the vehicle must periodically stop moving, which is challenging in high-dynamic or continuous motion scenarios. Another method is the non-holonomic constraint (NHC) [17; 18], which enhances system performance by using the vehicle's motion restrictions (e.g., the vehicle cannot move laterally), but this method relies on an accurate understanding of the vehicle's dynamic model. In practice, the actual driving state of the vehicle may deviate from the model assumptions, especially in complex road conditions and extreme driving behaviors, making NHC's restrictions and assumptions less effective and reducing the accuracy of the navigation system. Recently, with the development of artificial intelligence and neural network technologies, neural networks have been proposed to address GNSS/INS integrated navigation issues during GNSS outages [19; 20]. By training neural networks and predicting GNSS data, they can cope with various signal interruption scenarios, enhancing integrated navigation accuracy during GNSS outages [21]. [PERSON] et al. [22] used a multilayer perceptron (MLP) to assist GPS/INS positioning, reducing the cumulative positioning error of the independent INS during GNSS interruptions. [PERSON] et al. [23] used a recurrent neural network (RNN) to assist INS/GNSS integrated navigation in GNSS denial environments. However, MLP and RNN tend to overfit on training data and face issues of gradient vanishing or exploding. Toovercome some of the shortcomings of MLP and RNN, [PERSON] et al. [24] and [PERSON] et al. [25] used long short-term memory (LSTM) to predict pseudo GNSS positions during GNSS outages. LSTM reduces the risk of overfitting through regularization and introduces gating mechanisms to mitigate gradient vanishing or exploding. Gated recurrent unit (GRU) maintains LSTM's ability to handle long-term dependencies while reducing model complexity and computational demands. [PERSON] et al. used GRU to bridge GNSS outages [26], with GRU surpassing LSTM in prediction accuracy and training efficiency. In response to the issues with traditional compensation methods, this paper proposes a CNN-GRU-assisted GNSS/INS factor graph integrated navigation method. This unique combination not only enhances the robustness of the integrated navigation system during signal interruptions but also improves the system's adaptability to complex environments. The proposed method demonstrates significant advantages in handling nonlinear dynamics, addressing GNSS signal interruptions, and mitigating error accumulation during long-term operations. Experimental validation shows that this method significantly improves navigation accuracy in special environments such as urban buildings and tunnels, demonstrating superior performance over traditional integrated navigation technologies. The remainder of this paper is organized as follows: Section 2 introduces the integrated system solution and presents the implementation process of the proposed method. Section 3 discusses the model and information fusion theory of factor graph. Section 4 details the CNN-GRU network and the neural network prediction assistance model. Section 5 conducts road tests and result analysis under frequent and sustained GNSS interruptions, with conclusions presented in Section 6.