This paper proposes a novel dynamic modeling approach that fuses Empirical Mode Decomposition (EMD) with artificial neural networks for addressing the online calibration of rotational inertial navigation axis errors. Initially, EMD is employed to extract characteristic features from signals containing inertial navigation system axis errors. Subsequently, artificial neural networks are utilized for pattern learning, followed by error prediction using the iteratively trained models. The study implements BPNN, LSTM, and CNN models for experimental validation. Results demonstrate that this methodology exhibits excellent feature extraction and modeling capabilities for axis errors. Furthermore, the neural network incorporating the CNN model achieves superior prediction accuracy compared to other neural networks.

As a dead-reckoning system, an inertial navigation system (INS) always needs an accurate initial position and attitude to calculate a vehicle's position, velocity and attitude accummulatedly. A celestial navigation system (CNS) can be introduced to help the INS determine an initial position, which thus constitutes a CNS/INS integrated navigation system to work as a backup of global navigation satellite system (GNSS). However, owing to its positioning principle limitation, the CNS needs horizontal information (roll and pitch angles) to convert the attitude expressed in inertial frame ($i$-frame) to the navigation frame ($n$-frame). Therefore, this configuration leads to a dilemma: how to use the limited information from the CNS and INS to determine an initial position. Fortunately, the calculation of the horizontal information does not rely on position during the INS alignment process. Thus, in this manuscript, in order to achieve a higher horizon accuracy, a one-axis rotational INS is implemented in the CNS/INS integrated navigation to eliminate the effect of constant accelerometers' biases. The predetermined horizontal information in the INS coarse alignment will be applied in the CNS for a rough position calculation, while the calculated position will be further fed back to the INS fine alignment process to calculate the roll and pitch angles more accurately. A Kalman filter is implemented to estimate the accelerometers' and gyroscopes' biases to achieve higher horizon and position calculation accuracy. Simulation and experiments verify the effectiveness of the proposed method, which can not only calculate an initial position in the case that GNSS cannot work or non-GNSS positioning is required, but also help improve the position reinitialization accuracy for the CNS/INS integrated navigation especially when the stars are retracked at night.