High-precision orbit and clock information is a basic requirement for precise positioning with Global Navigation Satellite Systems (GNSSs) such as the American GPS or the European Galileo. Satellite orbits and clocks are determined using observation data from a global GNSS network together with other parameters such as station coordinates, earth rotation parameters and troposphere parameters. Operational orbit and clock products for GPS, GLONASS, Galileo, BeiDou and QZSS are generated at GSOC using the NAPEOS software. A near-real-time solution provides orbit predictions every 3 hours, which are used for the real-time estimation of clock parameters with the RETICLE software.
Radiation pressure modeling
GNSS satellites are subject to a large number of disturbing forces that must be taken into account in orbit determination. The greatest uncertainty is currently due to solar radiation pressure.
Fig. 1: Box-wing model for modeling the radiation pressure of the Sun.
This can be taken into account by using empirical parameters or a so-called box-wing model, for example. In this case, the satellite body is modeled as a cuboid and the solar panels as rectangular surfaces. The dimensions and optical properties of these geometric bodies are required to calculate the disturbance acceleration. These are publicly available for the Galileo satellites, for example. For other satellites, these properties must be estimated as parameters or determined empirically.
Fig. 2: Influence of radiation pressure modeling on clock residuals for GPS III satellites as a function of the Sun-Earth-satellite angle epsilon.
Figure 2 illustrates the advantages of such a box-wing model compared to the empirical ECOM-2 model for a satellite of the latest GPS III generation. While the residuals of the satellite clock for this model show a clear dependence on the angle epsilon (Sun-Earth-satellite), this systematics disappears when using a box-wing model.
Antenna Thrust
Fig. 3: The transmission of navigation signals causes GNSS satellites to accelerate in the radial direction aAT.
However, very small effects must also be taken into account for maximum accuracy. These include the so-called antenna thrust. This is caused by the transmission of navigation signals and generates a constant acceleration in the radial direction. The transmission power and the mass of the satellite are required for modeling.
Fig. 4: Transmission power measured with the 30 m antenna in Weilheim for different generations of GPS satellites.
In collaboration with the Institute of Communications and Navigation, the transmission power of selected GNSS satellites was measured using the 30 m antenna at the Weilheim ground station. These are shown in Fig. 4 for the different generations of GPS satellites (Block IIA, IIR, IIR-M and IIF). Depending on the satellite type, the transmission power is 20 - 300 watts and influences the satellite orbit in the range of 2 to 30 mm, see Fig. 5.
Fig. 5: Influence of the antenna thrust on the radial component of the satellite orbit for different types of GPS, GLONASS, Galileo, BeiDou and QZSS satellites.
Steigenberger, P., Thoelert, S., & Montenbruck, O. (2020). GPS III Vespucci: Results of half a year in orbit. Advances in Space Research, 66(12), 2773–2785. https://doi.org/10.1016/j.asr.2020.03.026
Steigenberger, P., Thoelert, S., & Montenbruck, O. (2018). GNSS satellite transmit power and its impact on orbit determination. Journal of Geodesy, 92(6), 609–624. https://doi.org/10.1007/s00190-017-1082-2
Darugna, F., Steigenberger, P., Montenbruck, O., & Casotto, S. (2018). Ray-tracing solar radiation pressure modeling for QZS-1. Advances in Space Research, 62(4), 935–943. https://doi.org/10.1016/j.asr.2018.05.036
Montenbruck, O., Steigenberger, P., & Darugna, F. (2017). Semi-analytical solar radiation pressure modeling for QZS-1 orbit-normal and yaw-steering attitude. Advances in Space Research, 59(8), 2088–2100. https://doi.org/10.1016/j.asr.2017.01.036
Montenbruck, O., Steigenberger, P., & Hugentobler, U. (2015). Enhanced Solar Radiation Pressure Modeling for Galileo Satellites. Journal of Geodesy, 89(3), 283–297. https://doi.org/10.1007/s00190-014-0774-0
Contact
Dr.-Ing. Benjamin Braun
German Aerospace Center (DLR)
Space Operations and Astronaut Training
Spaceflight Technology
Münchener Straße 20, 82234 Oberpfaffenhofen-Weßling
