The use of Global Positioning System (GPS) observables provides the primary and advantageous technique for satellite orbit determination in low earth orbit (LEO), in particular when onboard autonomy is required. A wide range of LEO spacecraft equipped with GPS receivers have been launched into space for different applications. Aiming at determining the position and velocity of the satellite in real-time, a consider Kalman filter (CKF)-based reduced-dynamic orbit determination (RDOD) is introduced in this paper. In the CKF, orbit dynamic model is simplified to meet the space-borne computational limitations. The atmospheric drag and solar radiation pressure coefficients are considered rather than estimated in the conventional RDOD strategy. Only a lower order and degree of an earth gravity model is used in the orbit model. However, the propagation of the covariance of the consider parameters is able to absorb the unmodeled and dismodeled perturbations. Therefore, the filter could become convergent with desirable orbit determination performance. The CKF-RDOD method is implemented with a set of the Gravity Recovery and Climate Experiment flight data. The solutions indicate that this proposed method could achieve satisfactory precision orbit determination with approximately 1.5 m level of three-dimensional root-mean-square error using GPS broadcast messages in real-time scenarios.

GNSS/INS integration is widely used for train positioning, but railways tunnels and mountains can interfere GNSS signals and will lead to performance degradation when the system is operated in the standalone INS mode. This paper proposes a Long Short Term Memory (LSTM)-assisted GNSS/INS integration system using recomputed Inertial Measurement Unit (IMU) error, to suppress the error divergence of an INS in the case of GNSS solution non-availability. The IMU error recomputation method is firstly proposed, where the GNSS/INS-derived position, velocity and attitude (PVA) information is utilized when is GNSS available. The train's attitude computed using the GNSS dual-antenna moving baseline method is used as the heading constraint for GNSS/INS integration so as to provide accurate attitude information. The recomputed IMU sensor error is then used for model training, and the system switches to LSTM-assisted INS mode when GNSS solutions are unavailable. The system predicts the IMU sensor error using the train motion state, and corrects the IMU measurements to suppress the accumulating IMU sensor error.The proposed system was evaluated through a train experiment on the Shuozhou-Huanghua railway. The IMU error Recomputation Method (IMU-RM) was evaluated on four time slots of varying lengths, and the proposed LSTM-assisted GNSS/INS integration system using IMU-RM was evaluated in two “difficult” GNSS signal areas, of curved and straight railtrack segments, were simulated. Results showed significant improvement in horizontal position accuracy compared to conventional methods, with suppression of INS sensor error divergence by 79% and 63% for curved and straight segments, respectively.