G2.1

An accurate model of all the forces acting on a satellite is an essential precondition of achieving high orbit accuracy. Solar radiation pressure (SRP), the largest non-gravitational perturbation for GNSS satellites is typically modeled by an empirical model (i.e., Empirical CODE Orbit Model, ECOM/ECOM2). If satellite metadata information is available, an analytical box-wing model can be formed to reinforce the ECOM models. However, the current GNSS satellite orbits show notable degradation during eclipse seasons in particular for long-arc solutions and orbit predictions. The reason is proven to be mostly due to the ignoring of the thermal imbalanced forces (i.e., radiator emission and thermal radiation of solar panels). The ECOM parameters can compensate these thermal radiation forces fairly well outside eclipse seasons, while this is not true when satellites are inside eclipse seasons, because the Earth’s shadowing of a satellite in orbit causes periodic changes of the thermal environment. On one hand, these thermal imbalanced forces contribute also inside the shadow while inside the shadow all the ECOM parameters are deactivated. On the other hand, satellite attitude could be far from the nominal inside the shadow, making that these thermal imbalanced forces cannot be well absorbed by the ECOM parameters. To capture these thermal forces, we set up physical thermal force models for each Block type of GNSS satellites. In the absence of published thermal properties, we estimate necessary thermal modeling parameters using tracking data over long time period. With the use of the physical thermal force models, satellite orbits inside eclipse seasons are greatly improved. For instance, orbit misclosures are improved by a factor of two for BDS-3 and Galileo satellites when using the 5-parameter ECOM model.

How to cite: Duan, B. and Hugentobler, U.: Impact of thermal imbalanced radiation forces on GNSS satellite orbits, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2832, https://doi.org/10.5194/egusphere-egu22-2832, 2022.

G4S_2.0 is a project funded by the Italian Space Agency aiming to perform a set of Fundamental Physics measurements using the two Galileo FOC satellites GSAT0201 (Doresa) and GSAT0202 (Milena). Indeed, the orbits of these satellites are characterized by a relatively high eccentricity, about 0.16, which represents a good prerequisite for a series of tests and measurements concerning the predictions of different theories of gravitation, as compared with the General Relativity (GR) ones. The main objectives include a new measurement of the gravitational redshift effect of the on-board atomic clocks --- thanks to its modulation with the orbital period due to the high eccentricity of the orbits --- and the measurement of the main precessions of relativistic origin, primarily the Schwarzschild one.

To achieve these significant results, and possibly improve the current constraints of several theories of gravitation with respect to GR, it is of fundamental importance to take a step forward --- compared to the state of the art --- in the reliability of the dynamic model used for the orbits of the satellites and, as a direct consequence of this, in their precise orbit determination (POD). In this context, non-gravitational perturbations (NGPs) are the most subtle and difficult to model because of the complex shape of the Galileo satellites and their attitude law. In this regard, the main challenge is represented by a more refined and reliable model for the direct solar radiation pressure (SRP), the largest NGP on Galileo satellites, as well as on every satellite of every GNSS constellation.

Our final goal is to build a finite element model (FEM) of the Galileo FOC spacecraft, as refined as possible, and apply a dedicated raytracing technique to it to compute the perturbing accelerations due to radiation pressure. In view of this, we have already developed a 3D-CAD model of the spacecraft. As an intermediate step, we have built a Box-Wing (BW) model based on the relatively poor information presently available on the geometrical and physical properties of the spacecraft. This BW model has been used to compute the perturbing accelerations due to the direct SRP and to the Earth's albedo and infrared radiation.

The results obtained for the accelerations, to be included in the POD process, will be presented in various cases. Then, by computing the residuals in the orbital elements, it will be possible to verify the goodness of the POD results and observe the expected progressive improvement starting from the BW model towards the FEM one. The present analyses were made using the nominal attitude law of the Galileo FOC spacecraft; the application of this law will be discussed in the case of satellites in elliptical orbit. We finally highlight that the results of G4S_2.0 in terms of POD improvements are particularly useful for all applications of the Galileo FOC satellites in the fields of space Geodesy and Geophysics.

How to cite: Lucchesi, D., Cinelli, M., Di Marco, A., Fiorenza, E., Lefevre, C., Loffredo, P., Lucente, M., Magnafico, C., Peron, R., Santoli, F., Sapio, F., and Visco, M.: The Galileo for Science (G4S_2.0) project: Precise Orbit Determination for Fundamental Physics and Space Geodesy, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5884, https://doi.org/10.5194/egusphere-egu22-5884, 2022.

The constellation of China’s BeiDou navigation satellite system (BDS) has been fully constructed since July 2020 and provides open services for worldwide users. Due to the natural sensitivity of satellite technique to geocenter motion, BDS has the capability to determine the time series of geocenter coordinates (GCCs). The purpose of this study is to assess the impact of solar radiation pressure (SRP) modeling on the BDS-derived geocenter motion. To that end, 3-year sets of daily GCCs have been determined with data of BDS. The data was recorded over the period 2019-2021 by a global network of 93 iGMAS stations. Different SRP models including the empirical CODE orbit model (ECOM/ECOM2) and the a prior box-wing model have been applied for BDS geocenter estimation, respectively. We find that under the purely empirical SRP model, the peak-to-peak amplitude of geocenter z-coordinates (GCC-Zs) can reach to 10 cm. In additional, IGSOs would bring obvious jumps to GCC-Zs during earth eclipse periods. The introduction of an a priori box-wing model can largely mitigate the spurious signals in the spectra of GCC-Zs, presenting (13.0, 4.5, 2.1, 2.4) mm for the amplitude of the 1, 3, 5, 7 cpy signals, compared to (26.2, 5.9, 1.2, 2.0) mm in the ECOM case. However, the jumps brought by IGSOs still remains, which could be caused by distortion of optical properties. Therefore, we simultaneously estimate the optical properties together with other parameters in the processing. This model, known as a prior adjustable bow-wing model (ABW), appears to improve the orbit modeling in the eclipsing season and eliminate the negative influence of IGSOs on GCC-Zs, which is reflected in the decrease of spurious signal at periods other than annual one and the amplitude of the 1, 3, 5, 7 cpy signals for GCC-Zs are (16.2, 3.8, 1.4, 0.3) mm. The ABW solution is thus closer to the geocenter motions determined with other space-geodetic techniques.

How to cite: Huang, S., Yuan, Y., Zhang, K., and Li, X.: Geocenter motions derived from BDS: The impact of solar radiation force model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6796, https://doi.org/10.5194/egusphere-egu22-6796, 2022.

Global Navigation Satellite Systems (GNSS) play a critical role for providing real-time positioning and navigation services, and the precise satellite orbit and clock products are essential for the high-precision GNSS applications. The International GNSS Service (IGS) and its Analysis Centers (ACs) have been working on the study on precise GNSS data processing and provision of the precise products. The German Research Center for Geosciences (GFZ), as one of the ACs, also provides the multi-GNSS rapid products: the GBM product. We introduce the GBM data processing strategy, analyze the precision of GBM multi-GNSS orbits from 2015 to 2021, and present the impact of applying the undifferenced ambiguity resolution on satellite orbits. The GPS orbits of GBM products agree with the IGS final orbits at the level of 11-13 mm in the three directions, and the GPS orbit 6-hour prediction precision is around 6 cm. The 6-hour prediction precision of GLONASS is around 12 cm, slightly worse than that of GALILEO, which hold an average value of 10 cm in the same period but shows a significant improvement to around 5 cm after end of 2016. The prediction precision of BDS MEO satellites are around 10 cm, and that of the BDS GEO satellites and QZSS satellites are at the level of 1 to 3 meter. The Satellite Laser Ranging (SLR) residuals show that the orbit precision of GALILEO, GLONASS, and BD3-MEO is 23 mm, 41 mm, and 47 mm, respectively. Moreover, comparing the double-differenced ambiguity resolution, adopting the undifferenced ambiguity resolution improves the 6-hour orbit prediction precision by 9-15%，15-18%，11-13%，6-17%和14-25% for the GPS, GLONASS, GALILEO, BDS-2 and BDS-3 MEO satellites, respectively.

How to cite: Deng, Z., Wang, J., and Ge, M.: The GBM Rapid Product and the Improvement from Undifferenced Ambiguity Resolution, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-794, https://doi.org/10.5194/egusphere-egu22-794, 2022.

Observing Earth-orbiting satellites additionally to natural extra-galactic radio sources with Very Long Baseline Interferometry (VLBI) radio telescopes offers a variety of new possibilities and allows expanding the research activities of this highly accurate technique. The combination of observations to satellites and quasars permit the determination of the satellite orbit from VLBI observations in the terrestrial as well as in the International Celestial Reference Frame. The latter is enabled by the unique capability of VLBI to determine Universal Time UT1.

In this contribution for the first time, the precision of short satellite orbital arcs determined with simulated VLBI observations to Galileo satellites for different observation geometries using various VLBI networks and arc lengths is investigated. For this purpose, schedules including both, observations to quasars and satellites, are created using the scheduling software VieSched++. The simulations of the scheduled observations and the estimation of the satellite arcs are carried out using the Vienna VLBI and Satellite Software (VieVS). The quality of the estimated orbits is investigated and assessed based on the mean formal errors and the repeatabilities of the individual components of the satellite positions based on Monte Carlo simulations. 

How to cite: Wolf, H., Böhm, J., Nothnagel, A., Hugentobler, U., and Schartner, M.: Precision of Galileo satellite orbits obtained from simulated VLBI observations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4834, https://doi.org/10.5194/egusphere-egu22-4834, 2022.

Low Earth orbiting (LEO) satellites require routine maneuvers to maintain the predefined trajectories. However, spaceborne scientific instruments might suffer from data discontinuities or even anomalies due to instantaneous orbit changes caused by the performed maneuvers. With the advances of spaceborne Global Navigation Satellite System (GNSS) technique, the high-low satellite-to-satellite tracking observations enable us to generate high precision satellite orbits for the nominal orbit operation periods, and more importantly, also for the maneuver periods. This research will outline the recent developments of Precise Orbit Determination (POD) for  maneuvering LEO satellites at the Astronomical Institute of the University of Bern (AIUB). The Sentinel-3 mission, an European Space Agency (ESA) Earth observation satellite formation devoted to oceanography and land-vegetation monitoring, is used as test example.

A prerequisite input for this research is the maneuver information collected by the telemetry measures which clarify the maneuver time span and accelerations. Due to unavoidable in-flight software delays and hardware performance accuracy, the maneuver information may not be perfect and needs to be improved  in the POD process. Essentially two solutions are made in this research: a. estimating the full accelerations or corrections to the known maneuver accelerations, b. estimating instantaneous velocity pulses at the requested epochs. Both algorithms are tested using the Bernese GNSS Software and POD performances for the maneuver days during 2018-2020 will be assessed. Results reveal that the post-fit carrier phase residuals can be significantly reduced, ensuring better internal consistency between the reduced-dynamic and kinematic orbit solutions. Besides, a few institution members from the Copernicus POD Quality Working Group (QWG) have been routinely generating orbit products for the maneuver days, allowing for the direct cross-validations with our new AIUB products. This research implies promising benefits to the Sentinel-3 POD and scientific research community.

How to cite: Mao, X., Arnold, D., and Jäggi, A.: Precise orbit determination for the maneuvering Sentinel-3 satellites, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7335, https://doi.org/10.5194/egusphere-egu22-7335, 2022.

The precise orbit determination (POD) of Low Earth Orbiters (LEO), e.g. the Copernicus Sentinel Earth observation satellites, relies on the precise knowledge of the Earth gravity field and its variations with time. The most precise observation of time-variable gravity on a global scale is currently provided by the GRACE-FO satellites. But the monthly gravity field solutions are released with a latency of approx. 2 months, therefore they cannot be used for operational POD.

We present a deterministic signal model (DSM) that is fitted to the time-series of COST-G combined monthly gravity fields and describe the differences with respect to the available long-term gravity models including seasonal and secular time-variations. To validate the DSM, dynamic POD of the Sentinel-2B, -3B and -6A satellites is performed based on long-term or monthly gravity field models, and on the COST-G DSM. We evaluate the model quality on the basis of carrier phase residuals, orbit overlap analysis and independent satellite laser ranging observations, and study the limitation on orbit altitude posed by the reduced spherical harmonic resolution of the monthly models and the DSM.

The COST-G DSM is updated quarterly with the most recent GRACE-FO combined monthly gravity fields. It is foreseen to apply a sliding window approach with flexible window length to allow for an optimal adjustment in case of singular events like major earthquakes.

How to cite: Meyer, U., Peter, H., Lasser, M., and Jäggi, A.: The new COST-G deterministic signal model, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1614, https://doi.org/10.5194/egusphere-egu22-1614, 2022.

The use of CubeSats is expanding in space and earth science applications due to the low costs of building and the possibility of launching them in a large low-earth orbits (LEO) constellation. Such constellation can serve as an augmentation system for positioning, navigation and timing. However, real-time precise orbit determination (POD) is still one of the challenges for this application. Real-time reduced-dynamic POD requires more processing capability than what is available in current CubeSats, and the kinematic POD highly depends on the number and the quality of the signals from Global Navigation Satellite Systems (GNSS). In this study, an approach is proposed to increase the orbital accuracy by implementing the precise inter-satellite ranges in the Kinematic POD. The precise orbits of a set of CubeSats from the Spire Global constellation that are determined using the reduced-dynamic POD is to be used to generate the precise inter-satellite ranges. These ranges vary from hundreds to thousands of kilometres and are constrained in the relative kinematic POD between the tested CubeSats. The results, which depend on the length of the inter-satellite ranges, show the improvement of the orbital accuracy in all directions. An initial architecture for implementing such a method in a smart CubeSats constellation is proposed and the limitations and remedies are discussed.

How to cite: Allahvirdi-Zadeh, A. and El-Mowafy, A.: The impact of precise inter-satellite ranges on relative precise orbit determination in a smart CubeSats constellation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2215, https://doi.org/10.5194/egusphere-egu22-2215, 2022.

At the last EGU and AGU conferences, we have proposed and demonstrated the feasibility of a laser GNSS receiver in the LEO orbit in order to provide carrier-phase measurements on a CW laser between a LEO satellite and GNSS satellites equipped with SLR arrays. This is a novel approach in space geodesy for precise orbit determination (POD) of LEO satellites and the gravity field mapping from space. Considering that the wet delay in signal propagation is typically 67x smaller for optical than for microwaves, we have extended this laser GNSS receiver to laser occultation for atmosphere sounding where use of a modulation on a CW laser could be applied to combine this method with the GNSS radio-occultation (GNSS-RO). In that case, one could compare in LEO orbit microwave GNSS measurements and CW laser measurements between a LEO and GNSS satellites from the top of the atmosphere down to the clouds and the lower troposphere.

Here we propose to further extend the laser GNSS approach in space geodesy, and to demonstrate the combination of a CW laser and GNSS measurements with a ground parabolic antenna of about 60 cm diameter. The CW laser and the receiving photodiode is to be placed in the optical center and collocated with the phase center of the parabolic GNSS antenna. If the same parabolic mirror is used as an antenna to track laser and microwave GNSS measurements to a single GNSS satellite in the zenith direction, all geometry effects can be removed (geometry-free), ending up with the Galileo satellite clock and GNSS receiver clock parameter being the only parameters of such a geometry-free ground-to-space optical/microwave metrology link for Galileo. Considering that optical frequency of a CW laser, stabilized by an internal cavity, can be provided with the frequency stability of <7×10^-16, it can be transformed into a microwave band (with frequency comb) and with the same level of stability used as a reference frequency of the GNSS receiver. Therefore, one can use optical frequency of a CW laser via microwave Galileo signal to compare frequency of Galileo satellite clocks or optical clocks in the timing labs. Atmosphere effects for optical band (CW laser) can be applied a priori, whereas for microwave GNSS, troposphere zenith delays (TZDs) need to be estimated with the noise level of about a few millimeters in the zenith direction. Therefore, by selecting one Galileo satellite, close to zenith from two optical clocks on the ground, all Galileo satellite-related errors will be removed including Galileo satellite clock parameter, and time and frequency of optical clocks could be compared at the 10^-17 - 10^-18 frequency uncertainty level. This opens up the possibility of using Galileo by the timing labs for the generation of the official time (TAI, UTC) and for metrology in space, along with the laser GNSS applications in LEO orbit for POD and atmosphere sounding that very nicely complement the microwave GNSS.

How to cite: Svehla, D.: Laser GNSS Receiver for LEO POD, Laser Occultation and Time & Frequency Transfer of Optical Clocks in the Timing Labs, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-12288, https://doi.org/10.5194/egusphere-egu22-12288, 2022.