**3. CNN-GRU**

The overall architecture of our method is shown in Figure 2. In this paper, we use a loosely coupled integrated navigation scheme that is based on the combination of CKF and CNN-GRU. The CKF module provides highly accurate position, velocity, attitude, and IMU error information. The inputs and outputs of the network are shown in Figure 2, where *WI* and *FI* are the angular velocity and specific force that are provided by the IMU, *AINS* and *VINS* are the attitude and velocity information that is calculated by the INS. The outputs of the network are the position increments *δP* output by the CKF module, which are integrated as the pseudo-GNSS position information. When the GNSS signals are available, the CNN-GRU module operates in learning mode. When the GNSS signals become unavailable, the CNN-GRU module operates in prediction mode, and the pseudo-GNSS position increments are predicted to ensure navigation accuracy. Specifically, three operating modes are included: learning mode when the GNSS signals are available, prediction mode and learning mode during GNSS short-term outage, and prediction mode during GNSS long-term outage. When the GNSS signals are available, the length of each learning sample is 2 min and the learning interval is controlled in 1 min. The reason for choosing – min is that most GNSS interruption scenarios last less than 2 min, and the purpose of the learning interval is to reset the CKF filter. When the GNSS signals are unavailable, the model that was trained in the previous phase is used for prediction, while the previous historical data are used for training the new fine model, and the model is switched to the new fine model to improve the prediction accuracy when the GNSS signals that are interrupted exceed 2 min. In order to ensure that the training of historical data can be completed within 2 min, we consider the differences of the model under different motion states of the vehicle and reduce the length of the training data. The decision is done using the vehicle motion state according to the output data of INS, which are zero speed, zero angular speed, zero lateral speed, and zero vertical speed, and stop saving data when a period of continuous motion state exceeds five minutes, thus improving the training efficiency.

**Figure 2.** The overall architecture of the proposed method (**a**) GNSS is available; (**b**) GNSS ioutage (less than 2 min); (**c**) GNSS outage (more than 2 min).

The CNN-GRU networks consist of a one-dimensional version of CNN, GRU, and a fully connected layer. Since the inputs involve multiple sensors and the coupling of multidimensional motion information, the intake features need to be extracted more accurately, so the CNN is used to quickly extract features from the sensor sequences. Since the vehicle motion and IMU sensor errors are time-dependent, the GRU is adopted to extract deeper hidden information from the sensor history data. Finally, a fully connected layer is used to obtain the final navigation information.

The structure of CNN is shown in Figure 3. CNN is one of the common network models in the field of deep learning, which is a multi-layer feedforward neural network with high generalization ability and robustness by local connectivity, weight sharing, and pooling operation [28]. The pooling layer is used to compress the high-dimensional features of the input after processing in the convolutional layer to reduce the parameter matrix dimension, which reduces the computational workload by reducing the parameters of the network. The fully connected layer can combine all of the local features into global features.

**Figure 3.** The structure of CNN.

The GRU neural network is an improvement on the LSTM neural network. The LSTM neural network provides a new solution to the short-term memory problem and solves the problem of gradient disappearance and gradient explosion when the RNN exists to handle longer sequences. The GRU is simplified for the same estimation accuracy and higher training efficiency compared to the LSTM. The GRU model consists of two gates: the update gate and the reset gate. The update gate determines how much information from the previous state is brought into the current state. The larger the update gate is, the more the previous state is brought into the current state. The reset gate determines how the new input information is combined with the previous memory. The smaller the reset gate is, the more information about the previous state is ignored. The schematic diagram of GRU is shown in Figure 4.

**Figure 4.** The structure of GRU.

GRU undertakes the most important task of sequence analysis, and the time-dependent nature of GRU makes training more difficult. Therefore, the core parameters are the size and structure of the GRU network. The hyperparameters that have the greatest impact on the performance include the number of GRU layers, the number of neurons, and the step size. Too many neurons lead to an overfitting phenomenon and degradation of the generalization performance, while insufficient number of neurons cannot fully extract the relationship between the input and output sequences, and too many GRU layers also lead to instability of the model. Considering the prediction accuracy and computation time, the number of GRU layers, the number of neurons, and the step size are set to 2, 48, and 2, respectively. The training time of the network increases with the above three hyperparameters. Two layers of GRU are sufficient to extract the hidden information, and too many layers can lead to overfitting.
