The joint project ADVANTAGE (Advanced Technology for Navigation and Geodesy) by the German Aerospace Agency (DLR) and the German Research Centre for Geosciences (GFZ) aims at studying the potential of optical ranging and time transfer technology for future satellite navigation systems and its impact on scientific applications. Within the project a constellation, named Kepler, of 24 Galileo-like Medium Earth Orbit (MEO) navigation satellites and 6 Low Earth Orbit (LEO) satellites, is proposed. In this concept the neighboring MEOs as well as LEOs and MEOs are connected by two-way optical links enabling data communication, constellation-wide clock synchronization and precise ranging. Using GFZ's EPOS-OC software for precise orbit determination (POD) and parameter estimation, the Kepler space-borne and ground GNSS data as well as inter-satellite ranges are simulated with models and standards taken from processing of real data. In a batch estimation step (recovery), the orbits of MEO and LEO satellites are simultaneously computed using an integrated approach. In a close to real-world scenario, a number of modeling errors are introduced, affecting solar radiation pressure, LEO air drag, gravity field models etc. It is shown, that the availability of precise inter-satellite links and fully synchronized clocks enables mitigation of the dynamic modeling errors by e.g. additional estimation of empirical accelerations. The orbit recovery results for the Kepler system are compared with the Galileo constellation. It is demonstrated, that only one ground station is sufficient for POD of the Kepler system with radial accuracies below 1 cm. One of the scientific applications which can benefit from the proposed future GNSS architecture is the provision of global terrestrial reference frames (TRFs) being the metrological basis for almost all geodetic measurements associated with the Earth. To study the impact of the Kepler constellation on the determination of TRFs, simulations similar to those used for POD are performed but including a large network of globally distributed observing stations. In the recovery step performed on the normal equation level, station coordinates, Earth rotation parameters as well as geocentre coordinates are estimated and compared to the results from the Galileo constellation. It is shown, how the inclusion of the LEO satellites, the inter-satellites links and the synchronized clocks contribute to the improvement of the reference frame.

Laser technology for satellites has reached the level of maturity that is required for multi-year service-driven missions. Examples are the four Sentinel-1 and Sentinel-2 satellites which have employed more than 20,000 laser communication links via ESA’s EDRS geo-stationary data relay system. Looking at Galileo system benefits from having this enabling tool now available, we analyzed the capability of a two-way data transfer link for ranging and time transfer from ground to the Galileo satellites. For the two-way measurement we propose an active retroreflector on all Galileo satellites, which can act as a synchronous or asynchronous transponder. The synchronous transponder on the satellite receives a signal and sends it back with constant delay by the active element. In the case of an asynchronous transponder the active element on the satellite sends a signal according to its clock value independent from the signal it receives from ground.
The presentation discusses the technical feasibility and the necessary requirements, like calibration capability for ranging and clock synchronization and the use of adaptive optics for the compensation of atmospheric turbulences and compares it to normal SLR ranging. We discuss the advantages for individual ground stations and individual satellites equipped with such a link, where the systematic effects of GNSS measurements, like multipath, can be studied and present a simulation study where the whole Galileo constellation is equipped with such a link. The restrictions due to weather conditions is addressed as well as systematic effects on the orbit, clock synchronization and the prediction. Especially the consistency between orbits and clocks are evaluated.

Numerous active low Earth orbiters (LEOs) and Global Navigation Satellite System (GNSS) satellites, including the Galileo constellation, are equipped with laser retroreflectors used for Satellite Laser Ranging (SLR). Moreover, most LEOs are equipped with GNSS receivers for precise orbit determination. SLR measurements to LEOs, GNSS, and geodetic satellites vary in terms of registered numbers of the normal points (NPs) or registered satellite passes. In 2016-2018, SLR measurements to LEOs constituted 81% of all NPs and 59% of all registered satellite passes, whereas 10% of NPs and 30% of satellite passes, respectively, were assigned to GNSS. The remaining SLR measurements, 9% of NPs and 11% of passes, were completed by geodetic satellites, including LAGEOS-1 and LAGEOS-2.
SLR-GNSS co-location onboard LEOs and GNSS satellites, as well as the remarkable improvement of GNSS and LEO orbits, allow for new applications of SLR observations to active satellites at different orbital altitudes. Despite a large number of SLR observations to new GNSS satellites and to active LEOs, these observations are typically only used for the GNSS and LEO orbit quality assessment and the validation of the employed orbit models. No SLR observations to active GNSS and LEO satellites are used for the realization of the International Terrestrial Reference Frame (ITRF).
In this study, we show that the SLR observations to Galileo, LAGEOS, and active LEO satellites together with precise GNSS-based orbits of LEOs can be used for the determination of SLR station coordinates, global geodetic parameters including Earth rotation parameters (ERPs) and geocenter coordinates. Station coordinates, as well as the realization of the ITRF, are typically determined using SLR observations to passive geodetic satellites, such as LAGEOS-1/2. Here, we use SLR observations to Galileo, LAGEOS-1/2, Sentinel-3A/B satellites to investigate whether they can be applied for the reference frame realization and for deriving high-quality station and geocenter coordinates and ERPs.
We present various types of solutions based on different solution lengths, different SLR ground network constraining, and the combination of different sets of satellites to investigate the best solution set-up and the relative weights for the variance scaling factors of normal equations. We compare our results with the standard LAGEOS-based solutions and show the consistency level of the results with respect to the classical SLR solutions. We found that the combination of SLR observations improves the station coordinates especially for those stations which are dedicated to tracking specific constellations, i.e., providing more SLR observations to LEOs (e.g. Arequipa) or Galileo satellites (e.g. Grasse, Wettzell) than to LAGEOS.

The availability of high-precision GNSS orbit models is an essential prerequisite for accurate positioning applications, and also for orbit prediction. The present orbit products of the IGS analysis centers are based on dynamic orbit models including a variety of perturbation forces. Those perturbations can be system-specific, such as the satellite shape and material or antenna power, or external such as variations in the solar wind and radiation or variations in the Earth's gravity field.
GNSS orbit modelling deficiencies are known to propagate into further products like satellite clock corrections, Earth rotation parameters and station parameters, producing artefacts in the time series at the draconitic period of about 352 days.

Kinematic orbit determination is a powerful tool to observe those effects, but its use for high-precision applications has been hampered by the high correlation between the radial orbit component and the satellite clock parameter. The availability of new generation clocks with very high long-term stability (several orbital revolutions), such as the Passive Hydrogen Masers (PHM) flying on-board of the Galileo satellites, allows for a very accurate clock modeling.

In this study, GNSS satellite clock corrections are modeled by two components: (1) a deterministic part consisting of a linear polynomial representing the behavior of the clock over one day and (2) a stochastic model making use of relative constraints between subsequent epochs to account for short-time variations of the clock. This enables the resolution of the radial component of the orbit with an RMS level below 3 cm for Galileo satellites.
The final results cover two 1-month periods in December 2016 and Mai 2017 with a 5 min sampling rate. Observation data from 81 ground stations measuring Galileo and GPS signals was used. The main focus was laid on the 13 Galileo satellites available at the time. For comparison, the 12 GPS Block IIF satellites were also analyzed.

Our kinematic orbits have been compared with the precise orbit products available publicly from 6 different analysis centers: CODE-MGEX, ESOC, GFZ, CNES, TUM and Wuhan University. Periodic variations with frequencies of once and twice per revolution were clearly identified. We can show that some of their amplitude and phase shift are correlated with the angle of the Sun above the orbital plane, and that their behavior differs for the orbit models used by the different IGS analysis centers studied here. We will also show effects appearing during shadow periods and the importance of correct attitude modelling.

The effects visible in GPS when constraining the satellite clock are most probably due to variations of the clock itself, as they are consistent with previous analyses of variations of the GPS Block IIF clock.

Finally, comparison with Satellite Laser Ranging (SLR) residuals show a good agreement with the kinematic solutions, with a reduction in standard deviation as much 47 % compared to the dynamic orbit models. With an increased sampling rate and availability compared to SLR, the kinematic orbit estimation has also the advantage to work for satellites that are not equipped with laser reflectors.

Galileo satellites trajectories are usually numerically simulated in a space-time described by a post-Newtonian treatment. In this work, a metric that takes into account the gravitational influence of Earth, Sun and Moon, including Earth oblateness, is considered. By examining a feasible set of initial conditions, the satellite world-lines are calculated. The time-like geodesics of this metric are solved by numerical integration. A Runge-Kutta method allows solving the geodesics system of ordinary differential equations, with high accuracy for the numerical method (10^{-17}) and with multiple precision (40 significant digits for each number). This method is used in our computations. In a first step, the orbit of one satellite of the Galileo constellation is computed and tested. The procedure presented here increases the accuracy due to the fact that the orbit obtained considers every time more orbit perturbations. This work is presented here. In a second step, these calculated satellites world lines, will allow us to locate (with the so called Relativistic Positioning System, RPS) in a space-time with the metrics proposed. In this way, the numerical algorithm is checked and prepared to compute the position and coordinate time of a test particle using four Galileo satellites as it is done in current RPS. The future study paves the way to determine with more precision the location and coordinate time of a user with a RPS in a considered space-time by using numerical procedures with high accuracy and also computationally fast. This second step is in progress.