China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing (bw) model based on the estimated optical properties is introduced. Various physical effects, such as yaw bias, self-shadowing, radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model, 5 parameters), ECOM+along-track and ECOM2 (both 7 and 9 parameters) models are employed on top of the a priori box-wing model in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. The STD (standard deviation) of daily LOD estimates with respect to IERS-C04-14 series increases from 40 s (ECOM) to 85 s (ECOM+along-track). After the consideration of the a priori box-wing model, satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons; dependencies of SLR (satellite laser ranging) residuals on the sun elongation angle almost vanish for BDS-3 satellites. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters. In particular, the total amplitude of the 1, 3, 5, 7 cpy signals for the geocenter Z component has been reduced by a factor of 4.5 for the ECOM model. In general, the combination of the introduced physical a priori box-wing model and the ECOM model is preferred for BDS satellites.

In this simulation study we analyze the benefit of ground-space optical two-way links (OTWL) for Galileo precise orbit determination (POD). OTWL is a concept based on continuous wave laser ranging and time transfer with modulated signals from and to ground stations. The measurements are in addition to Global Navigation Satellite System (GNSS) observations. We simulate the measurements with regard to 16 Galileo Sensor Stations. In the simulation study we assume that the whole Galileo satellite constellation is equipped with terminals for OTWL. Using OTWL together with Galileo L-band, in comparison with an orbit solution calculated with L-band-only, demonstrates the advantage of combining two ranging techniques with different influences of systematic errors. The two-way link allows a station and satellite clock synchronization. Furthermore, we compare the ground-space concept with the satellite-to-satellite counterpart known as optical two-way inter-satellite links (OISL). The advantage of OTWL is the connection between the satellite system and the solid Earth as well as the possibility to synchronize the satellite clocks and the ground station clocks. The full network, using all three observation types in combination is simulated as well. The possibility to estimate additional solar radiation pressure (SRP) parameters within these combinations is a clear benefit of these additional links. We paid great attention to simulate systematic effects of all observation techniques as realistically as possible. For L-band these are measurement noise, tropospheric delays, phase center variation of receiver and transmitter antennas, constant and variable biases as well as multipath. For optical links we simulated colored and distance-dependent noise, offsets due to the link repeatability and offsets related to the equipment calibration quality. In addition, we added a troposphere error for the OTWL measurements. We discuss the influence on the formal orbit uncertainties and the effects of the systematic errors. Restrictions due to weather conditions are addressed as well. OTWL is synergetic with the other measurement techniques like OISL and can be used for data transfer and communication, respectively.

Today, concepts within the Global Geodetic Observing System (GGOS) aim a Terrestrial Reference System (TRS) with 1 mm accuracy and long-term stability of 0.1 mm/year. GETRIS (Geodesy and Time Reference In Space) is a concept that aims to realize a relativistic reference system based on satellites as an extension to the TRS. This helps with another goal of the GGOS, namely, the connection of different satellite layers with the TRS. For a valuable contribution to the GGOS’s goals, we would expect to achieve precise determined satellite orbits at the level of 1–3 mm and satellite clocks with a picosecond accuracy. The use of increasingly precise links helps to improve the satellite precise orbit determination (POD) and is necessary to synchronize the clocks in the satellite/station network. We analyze a complementary use of high-precision optical dual one-way links at the level of 1 mm precision together with the L-band. In previous studies, we analyzed the benefit for satellite POD, achieving Medium Earth Orbit (MEO) as well as geosynchronous orbit (GSO) accuracies at the low-millimeter level. In this work, we analyze the capabilities for clock synchronization. We compare two different clock types for estimation and prediction. We analyze different satellite constellations and different combinations of measurement links.

Progress in precise satellite orbit determination (POD) and navigation depends on the future ranging and time transfer capabilities. This leads to the need for high-precision links as well as high-precision clocks. However, not only a higher accuracy is required, but also the use of combination of complementary observation techniques to reduce systematic errors within an observation network. In a simulation study, we show our first concept of a GEodesy and Time Reference In Space (GETRIS). The initial GETRIS concept is based on the idea to have the reference in space build on geosynchronous orbit (GSO) satellites, but using Medium Earth Orbit (MEO) satellites is also possible. The goal is to achieve orbit accuracies of the GETRIS satellites at the same level as for ground stations – a few millimeters. Using high-precision optical links, the GETRIS shall establish connections to satellites in the near Earth environment and in deep space. When creating our GETRIS concept, we focus on three key pillars of a simulation study: Instrumentation, geometry and modelling. In terms of instrumentation, we performed scenarios using the synergy between L-band observations as well as high-precision dual one-way Optical Inter-Satellite Links (OISL) and ground-space based dual one-way links, called Optical Two-Way Links (OTWL), in different combinations. The geometry changes depending on the used observations network and the satellite constellation. Thereby, we analyze scenarios using a MEO-only and MEO+GSO constellations. To finally achieve mm-level orbit accuracies, an advanced modelling of non-gravitational forces is essential. A GETRIS can not only help with the connection of near Earth and deep space satellites, but also support the Global Geodetic Observing System (GGOS) and satellite missions such as GENESIS, which aim to realize a precise terrestrial reference frame with 1 mm accuracy and a stability of 0.1 mm/year.