Data-driven force models in GNSS satellite orbit prediction
Rautalin, Sakari Kalevi
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Dataan perustuvat voimamallit GNSS satelliittien rataennustuksissa
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.