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In this study, we consider methods of spectral analysis and deep learning to improve accuracy and quality of GNSS satellite orbit predictions. The quality of predictions decreases when satellite’s orbit is fixed with maneuvers, which causes satellite orbit predictions to fail. In our previous research orbit accuracy has been improved using analytical and data-driven models. The goal of this study is to improve quality of BeiDou satellite predictions with spectral analysis and to improve accuracy of GNSS satellite orbit predictions with deep learning. Both methods are used to improve the existing model for satellite orbit predictions. The improvement in quality is done by predicting unhealthy time periods of BeiDou’s GEO and IGSO satellites. Periodogram was used to estimate a period of health parameter from broadcast. The improvement in accuracy was done with convolutional neural networks. The convolutional neural network was used to predict RTN errors of existing models orbit predictions. The errors were predited from RTN errors from the beginning of the orbit prediction. With these error predictions the predicted orbit can be corrected. The main results of this study were that unhealthy periods can be predicted from the broadcast data and even a simple convolutional neural network can improve orbit prediction accuracy significantly. Health prediction algorithm could be created from the estimated periods to predict health successfully. Health prediction worked with BeiDou’s GEO and IGSO satellites and predicted over 70% of unhealthy periods in testing. Two different methods for error correction with convolutional neural networks were created and tested with GPS satellites. The better method was also tested with BeiDou satellites of all orbit types. The method improves two week orbit prediction accuracy over 40% on average for all GPS and BeiDou satellites. The best improvements in accuracy were achieved with GEO and IGSO satellites.

In this study, we consider the problem of predicting the orbit of a GNSS satellite with a force model that can be adjusted based on data. In autonomous prediction, the goal is to use the positioning device in a completely or mostly autonomous mode. For this, the usable time of broadcast ephemeris need to be extended and to this end, predicting the orbit of a satellite is necessary. This is done by creating a force model for the satellite. In our previous research, the force model was based on four largest forces acting on a satellite: the gravitation of the Earth, the Sun and the Moon and solar radiation pressure. The position of the satellite in the future can then be computed by integrating the equation of motion with certain initial conditions. The goal of this study was to improve the existing model by adding forces that can be estimated on the positioning device based on received data. This is done with latent force models, where additional forces have some prior model and need to be more accurately estimated with machine learning techniques. We create a state- space model for the latent forces, which is combined with the state-space model of the analytical motion of the satellite. Received broadcast ephemerides can then be used to estimate these forces in addition to position and velocity of a satellite. This is done as statistical inference with filtering and smoothing methods. The main result of this study was that even a relatively simple model can improve prediction accuracy by a significant amount. After the largest forces have been taken into account, the largest improvement comes from a data-driven approach rather than adding more analytical terms to the force model. We created an adaptive algorithm, where data from a new broadcast can be used to update the estimates for the latent forces, which can then be used to predict the position of the satellite more accurately. Our model worked with all tested constellations: GPS, GLONASS and Beidou. The improvement was biggest with GPS and Beidou MEO satellites, while GLONASS satellites did not show as much improvement.