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The Combination Service for Time-variable Gravity fields (COST-G) provides models of the time-variable Earth gravity field that may be used for precise orbit determination (POD). While the monthly snapshot solutions based on GRACE or GRACE-FO GPS and microwave ranging interferometer data are the best available information on the time-variable gravity field, their latency of about 2-3 months prevents their use in operational POD. COST-G also provides a signal model fitted to the monthly GRACE-FO gravity fields that is updated quarterly and allows for the prediction of time-variable gravity, e.g. for use in applications that rely on short latency like operational POD.We present POD results for LEO and MEO satellites based on the COST-G fitted signal model (FSM), where we put special attention on the impact of the C20 gravity field coefficient, which is poorly defined from the GRACE/GRACE-FO observations, but may be replaced by SLR-only or SLR+GRACE/GRACE-FO combined solutions. We moreover present an extension of the COST-G FSM, also covering the GRACE-period and therefore suited for reprocessing campaigns that rely on a consistent model of time-variable gravity.

Precise orbit determination (POD) of low earth orbiters (LEO) using data of the Global Positioning System (GPS) and the computation of GPS network solutions are usually performed in separate processes. Typically, orbits and clock corrections of GPS satellites, which have been previously determined as part of a network solution, are introduced as fixed in a LEO POD. However, various studies have shown that the inclusion of GPS observations of LEOs in a global network solution can be advantageous, particularly in terms of the quality of resulting GPS products and certain geodetic parameters, such as the Earth’s center of mass coordinates. Since a few years more and more GPS data from LEO CubeSats are available, such as from the SPIRE satellites which are equipped with dual-frequency GPS receivers and may be used as part of specific scientific investigations. The SPIRE satellite constellation is a group of remote sensing satellites that are used to measure and map the earth's surface and atmosphere.In the present study, we aim to determine the impact of GPS observation data from specific SPIRE satellites when they are included in the computation of a global network solution. Code and phase observations received by GPS receivers on board of selected SPIRE satellites, along with those from ground stations of the International GNSS Service (IGS), are processed together in a joint least-squares adjustment process to obtain a combined GPS-LEO solution. This determines orbit parameters of the SPIRE satellites together with GPS orbit parameters and geodetic parameters, such as station coordinates, Earth rotation parameters, and the Earth's center of mass coordinates. To assess the influence of the SPIRE LEOs more closely, various solutions are analyzed in which GPS observations from different SPIRE satellites and from scientific LEO missions are included. Given the different orbit characteristics of the selected SPIRE satellites, specifically the orbital inclinations, it is also possible to examine the impact of this on the resulting solution. The global solutions are compared to each other and to a solution using only data from terrestrial GPS stations. Quality characteristics are analyzed to assess the quality of the combined GPS-LEO solution, which are the resulting GPS orbit solutions in terms of orbit overlaps at arc boundaries, the quality of geodetic parameters, and the determined formal errors of the estimated parameters. The resulting SPIRE orbits of the combined solutions are also compared to those of a separate POD.

A global Terrestrial Reference Frame (TRF) is realized today by four space geodetic techniques, i.e., Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). The current goals for the TRF realization are specified with an accuracy of 1 mm and long-term stability of 0.1 mm/year according to the Global Geodetic Observing System requirements.Differences in the characteristics of each space geodetic technique might introduce systematic effects into TRF realization. Among the crucial systematics, we can distinguish modeling and calibration deficiencies, i.e., direct solar radiation pressure (SRP) modeling for GNSS and DORIS, GNSS antenna calibration uncertainties, South Atlantic Anomaly handling for DORIS, and time and range bias handling for SLR. The current realization of the TRF is based on independent solutions for each of the four contributing space geodetic techniques that are just connected on the ground via local ties and the Earth Rotation Parameters. A new opportunity to challenge the systematic errors is to co-locate space techniques onboard one satellite, as it is planned for the Genesis-1 mission. The Genesis-1 satellite is the first ever satellite co-locating sensors related to GNSS, SLR, DORIS, and VLBI.In this study, we present preliminary results for orbit reconstruction using simulated GNSS observations for the Genesis-1 satellite. We use the Bernese GNSS Software for different orbital altitudes, including the currently planned altitude of 6000 km. We assess the quality of the orbit reconstruction using simulated GNSS data from observations of the zenith-, nadir-, and both zenith and nadir-looking antennas. Additionally, we assess the visibility from the ground tracking network of VLBI, SLR, and DORIS, for the different satellite altitudes.

Numerous non-gravitational accelerations (NGAs) – due to radiation or gas-surface interactions – act on a typical satellite in low Earth orbit. The modeling of these accelerations is a key aspect of (reduced-)dynamic satellite precise orbit determination. Opposed to a purely empirical estimation of NGAs, especially orbit solutions with a high dynamical stiffness require an explicit NGA forward modelling. This is most important, e.g., for altimetry satellites which require utmost orbit accuracy especially in radial direction.For explicit NGA modelling, a commonly employed strategy is to describe the satellite body in terms of a relatively simple macro model, i.e., a geometry composed of a number of elementary shapes like flat plates, spheres or cylinders, each of which with a specific size, orientation and surface property. During orbit integration, for each individual elementary surface NGAs are then computed based on analytical expressions and the sum over all surfaces yields the total NGA of the satellite at integration epoch. Often each of the elementary surface of the satellite macro model is treated fully independent from the other surfaces and interactions, in particular the (partial) occultation or shadowing of one surface by other surfaces is neglected. In case of satellites with significant non-convex shapes (like the altimetry satellite Sentinel-6A) this can lead to a marked degradation of NGA modeling. On the other hand, very detailed satellite geometry models together with techniques like ray tracing can provide highly accurate NGAs, however, at the price of significantly increased processing times.In this contribution we assess the performance of a relatively simple self-shadowing algorithm for satellites described by a collection of flat convex polygons. Based on the relative plate locations, for each plate we analytically determine the amount of shadow cast by the other plates. We quantify the cost in terms of processing time and the impact on dynamic orbit solutions for the Copernicus Sentinel satellites in terms of empirical orbit parameters, observation residuals as well as other orbit quality metrics. We compare the so-derived NGAs and orbit solutions to results obtained with different other macro models and alternative approaches to take self-shadowing into account.

Temporal gravity field modelling from GRACE Follow-On data is usually performed by computing monthly snapshots of spherical harmonic coefficients representing the state of the Earth’s gravity field. Associated to this, the spherical harmonic series has to be truncated at a certain point, commonly atdegree/order 96. Higher degrees and orders are fixed to the a priori used background gravity field model.We present an investigation on the influence of the high degrees and orders of different a priori background gravity field models on monthly gravity field model computations from GRACE Follow-On data. Furthermore, we extend the temporal gravity field modelling to additionally co-estimate a static gravity field for the GRACE Follow-On satellite mission along with the monthly snapshots to provide for a consistent handling of correlations between temporal and static gravity field coefficients.Moreover, we model the stochastic noise of the data with an empirical description of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals, to further study the influence of the high degrees and orders of the a priori background gravity field model on such noise models.We compare and validate the monthly solutions with the models from the operational GRACE Follow-On processing at AIUB by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence in a combination of monthly gravity fields based on other approaches as it is done by the Combination Service for Time-variable Gravity fields (COST-G) and make use of noise and signal assessment applying the quality control tools routinely used in the frame of COST-G.

Dual-frequency GNSS receivers can be utilized to estimate the slant total electron content (TEC). Since slant TEC is integrated quantity it depends on the three-dimensional electron density distribution. Nowadays a large number of LEO satellites can provide slant TEC from altitudes between 400 and 1300 km. If occultation measurements are available, the observed altitude regimes can be extended below the F2 peak.From GNSS slant TEC measurements a global three-dimensional model of the electron density is constructed. This model relies on cubic B-splines in magnetic latitude, magnetic local time and altitude to model the logarithmic electron density. A good coverage in all three dimensions is vital for the reconstruction. The modeled electron density is validated against insitu measurements provided by Swarm and DMSP Langmuir probe measurement. The modeled vertical TEC (vTEC) is validated using Global Ionospheric Maps provided by different processing centers and vTEC observations made by Jason-3.The satellites included in the estimation are Swarm (A/B/C), GRACE-FO (1/2), COSMIC-2 (1-6), Sentinel (1/3), Jason-3, but also cube-sats, such as the SPIRE satellites. Special emphasis will be put on benefits gained if cube-sat missions are included to investigate the potential of constellations., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

The Center for Orbit Determination in Europe (CODE) is contributing to the most recent reprocessing effort of the International GNSS Service (IGS) with a triple-system solution including GPS (since 1994), GLONASS (since 2002) and Galileo (since 2013). Several model improvements with respect to the operational processing scheme have been implemented and applied for the reprocessing effort: The first group of improvements is related to the update of IERS-related models (mean pole and high-frequency pole models). The second group is related to the inclusion of Galileo with calibrated receiver and satellite antennas. The consistency of the scale for the ground station coordinates was verified based on the estimation of GNSS-specific coordinate biases. It turned out that currently widely used GPS-based receiver antenna calibrations do compensate (just by chance) a discrepancy in the scale when using the pre-launch satellite antenna calibrations for Galileo. Furthermore and third, a long-arc solution over three days is introduced where in particular empirical velocity changes are rescheduled with respect to the operational processing chain at CODE. Instead of simply estimating them every 12 h they are now setup at orbit midnight. This rescheduling reduces the size of orbit misclosures by 10% for GPS and 15% for Galileo; no improvement for GLONASS was observed because there the orbit misclosures are dominated by other effects. Another feature applied for the first time in this reprocessing series is to downweight the observations of a number of GPS satellites with a reduced stability in the attitude control around the year 2000. This change in the analysis strategy reduces the noise level of GNSS-derived products, e.g., of the Earth rotation series. Even if the article is focusing on the reprocessing series as provided by the CODE analysis center many of the conclusions may also be applied to other GNSS series in future.

An inherent problem of satellite gravimetry is the limited spatial resolution of space-borne sensors observing various functionals of the Earth's gravity field. Due to the limited amount of sensor data available to calculate monthly gravity fields and the typically applied global mathematical basis functions, the problem is particularly severe for mass change applications from GRACE and GRACE-FO. That leads to apparent mass loss or gain in regions by mass signals from neighbouring regions and is called the spatial leakage effect. The spatial leakage problem was identified well before GRACE's launch (see Wahr et al., 1998), and numerous methods have been proposed to assess and mitigate the adverse effects of spatial leakage. Available approaches can be grouped into estimates obtained from numerical models of the most prominent surface mass processes; data-driven approaches that only rely on the geodetic data themselves; methodologies based on (non-geodetic) satellite remote sensing data; and forward-modelling approaches, where a certain (time-invariant) geometry of surface mass change is assumed a priori and a limited set of (time-variable) parameters are estimated to fit the (spatially much smoother) gravity field data in a least-squares sense. Despite the various approaches available, we note that spatial leakage is treated very differently for individual surface mass change applications and across the various international research institutions. Sometimes, leakage is readily corrected before providing mass anomalies to non-geodetic users. Other groups only provide some leakage approximation to inform users about this systematic error source. And in (increasingly rare) cases, leakage is not even treated at all. In order to consolidate approaches across the geodetic community, we propose to establish an IAG Working Group aiming to collect different leakage mitigation methods; develop a common and independent validation approach; and recommend best practices in communicating spatial leakage to non-geodetic users of surface mass change data derived from satellite gravimetry. This contribution will summarize the current status of our ideas in order to invite all interested colleagues to contribute to this initiative.

The number of satellites equipped with retroreflectors dedicated to Satellite Laser Ranging (SLR) increases simultaneously with the development and invention of the spherical geodetic satellites, low Earth orbiters (LEOs), Galileo and other components of the Global Navigational Satellite System (GNSS). SLR and GNSS techniques onboard LEO and GNSS satellites create the possibility of widening the use of SLR observations for deriving SLR station coordinates, which up to now have been typically based on spherical geodetic satellites. We determine SLR station coordinates based on integrated SLR observations to LEOs, spherical geodetic, and GNSS satellites orbiting the Earth at different altitudes, from 330 to 26,210 km. The combination of eight LEOs, LAGEOS-1/2, LARES, and 13 Galileo satellites increased the number of 7-day SLR solutions from 10–20% to even 50%. We discuss the issues of handling of range biases in multi-satellite combinations and the proper solution constraining and weighting. Weighted combination is characterized by a reduction of formal error medians of estimated station coordinates up to 50%, and the reduction of station coordinate residuals. The combination of all satellites with optimum weighting increases the consistency of station coordinates in terms of interquartile ranges by 10% of horizontal components for non-core stations w.r.t LAGEOS-only solutions.

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20 % improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Besides gravity field information derived from ultra-precise inter-satellite ranging of dedicated missions like GRACE and GRACE-FO, the analysis of GPS tracking data collected by various Low Earth orbiting (LEO) satellites can provide alternative and mostly uninterrupted time series of large-scale time-variable gravity field signals. For this purpose, the GPS data may be used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery.In this study, we focus on the use of the GPS data obtained by the Copernicus Sentinel-1, -2, and -3 missions. Each of these missions consists of a constellation of two LEO satellites operating on sun-synchronous orbits with inclinations of about 98° and at different altitudes ranging from about 700 to 800 km. Besides mission-specific instruments, the Sentinel satellites are equipped with high-quality dual-frequency GPS receivers providing a data sampling rate of 10s (Sentinel-1, -2) or 1s (Sentinel-3). At the Astronomical Institute of the University of Bern (AIUB), GPS-based precise orbit determination is routinely performed for the Sentinel satellites. We make use of the kinematic LEO orbit positions to perform gravity field recovery with the Celestial Mechanics approach. In the presentation, we will provide details on the quality and sensitivity of Sentinel-based gravity field models and analyze their contribution to a combined gravity field time series derived from Swarm and GRACE-FO GPS data.

Benchmark data for verifying background model implementations in orbit and gravity field determination software In the framework of the COmbination Service for Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality and robustness to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (Earth���s gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with auxiliary data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference data set and provides the opportunity to test the implementation of these models at various institutions involved in orbit and gravity field determination from satellite tracking data. In view of the COST-G GRACE and GRACE Follow-On gravity field combinations, we document the outcome of the comparison of the background force models for the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern), the EPOS software of the German Research Centre for Geosciences (GFZ), the GINS software, developed and maintained by the Groupe de Recherche de G��od��sie Spatiale (GRGS), the GRACE-SIGMA software of the Leibniz University of Hannover (LUH) and the GRASP software also developed at LUH. We consider differences in the force modelling for GRACE (-FO) which are one order of magnitude smaller than the accelerometer noise of about 10���10 ms����� to be negligible and formulate this as a benchmark for new analysis centres, which are interested to contribute to the COST-G initiative.

Polar motion (PM) series from various observation methods and sources are analyzed using one and the same simple analysis tool. The maximum time resolution of the Earth Rotation Parameter (ERP) series considered here is one day, which leaves out ERP series with sub-daily time resolution. A longer spacing between subsequent epochs is permissible, a variable spacing between epochs like in the VLBI (Very Long Baseline Interferometry) series as well. The shortest length of the PM time series analyzed, based on GNSS (Global Navigation Satellite Systems), is 26+ years, the longest one, the IERS C01 series, 173+ years. Following the tradition, PM is decomposed into a mean motion, i.e., the motion of the center of the PM curve on the surface of the Earth, a prograde Chandler motion with a nominal period of 432.25 days, and a prograde annual motion with a nominal period of 365.25 days. In our analysis, Secular PM is not assumed as linear, but as piecewise linear and continuous. The defining parameters of the periodic parts of polar motion are not assumed as constant either, but as piecewise linear and continuous functions of time as well. All parameters of the PM model based on one particular ERP series are determined in one and the same linear least squares estimation. Parameters of the same type may be purely deterministic or filtered (smoothed) by constraining the second time differences of the parameters (the second time derivative of the parameter functions) of the same kind. The key results achieved by applying our method to a wide variety of ERP series are visualized and discussed. They include: (a) the description of a sharp bend of mean PM around 1996, (b) strong evidence for a multi-component model for Chandler motion with periods separated by few days, similar to that proposed by Chandler (1901), (c) a reconstruction of mean PM from 1846 to present taking into account the composite nature of the series, and (d) a prediction of Chandler motion for the next decades. A sharp bend of mean PM was found around 1995/96, along the meridian at about 70 ° West to the meridian at about 12–15° West. All PM curves analyzed show a mean motion in this new direction after 1995/95. Smaller excursions w.r.t.d this mean exist, with periods 10 years. A periodic variation with a period of about 180 years was observed in the Chandler signal of PM with an amplitude of more than 200 mas. The variation may be explained approximately by a composite nature of Chandler motion, similar to the model already proposed by Chandler (1901). This simple model was generalized using a Fourier series separated in period by few days. This alternative model of Chandler motion is used to predict the Chandler part of PM, with an amplitude close to zero currently, to reach values of the order of 100 mas around 2028–2030.

Temporal gravity field modelling from GRACE Follow-On has to cope with several noise sources contaminating not only the observations but also the observation equations via mis-modellings in the underlying background force models. One way to deal with such deficiencies is to extend the parameter space by additional quantities, such as pseudo-stochastic parameters, which are co-estimated in the Least-Squares Adjustment (LSA). These parameters are meant to absorb any kind of noise while retaining the signal in the gravity field and orbit parameters. In the Celestial Mechanics Approach (CMA) such pseudo-stochastic parameters are typically set-up as Piece-wise Constant Accelerations (PCA) in regular intervals of e.g., 15 min. The stochastic behaviour of these parameters is unknown because they reflect an accumulation of a variety of noise sources. In the CMA fictitious artificial zero-observations are appended to the vector of observations together with an empirically determined variance to introduce a stochastic model for the PCAs. In order to also co-estimate a stochastic model for the pseudo-stochastic parameters in the LSA we use Variance Component Estimation (VCE) as a well established tool to assign variance components to individual groups of observation. In the simplest case the magnitude of the constraints of the pseudo-stochastic parameters can be determined fully automatically. We present results for GRACE Follow-On gravity field recovery when extending the CMA by stochastic models for the piece-wise constant accelerations computed with VCE and provide noise and signal assessment applying the quality control tools routinely used in the frame of the Combination Service for Time-variable gravity fields (COST-G).

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.

GRACE and GRACE-Follow On gravity field solutions form an unprecedented time series of time-variable gravity field which is indispensable for geosciences, water and climate monitoring. However, the GRACE and GRACE-Follow On time series suffer from a data gap of about one year. Thus, there is a need for an intermediate technique that will bridge the gap between the two missions and will allow 1) for a continued and uninterrupted time series of mass observations and 2) to compare, cross-validate and link the two time series. The most promising method for the long-wavelength part of the gravity field is a combination of high-low satellite-to-satellite tracking (hlSST) of low-Earth orbiting satellites by GNSS in combination with satellite laser ranging (SLR), where SLR is known to provide the highest quality time-variable gravity for the very low degrees (2-5) and hlSST is able to provide a higher spatial resolution at a lower precision in the very low degrees. In this contribution, we discuss the importance of the SLR contribution to the combined solution showing that a hlSST solution is underperforming and a considerable improvement and stabilization for the low degrees can be achieved by the inclusion of SLR for the very low degrees. We also shed light on different combination techniques on the normal equation level with and without variance component estimation and discuss their advantages and difficulties in the implementation.

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.

GRACE has been undoubtedly one of the most important sources to observe mass transport at global and regional scales. Within the COST-G project, GRACE and GRACE-Follow On gravity field solutions from various processing centers are being combined to further increase the spatial and temporal resolution. However, the GRACE and GRACE-Follow On time series suffer from a data gap of about one year. Thus, there is a need for an intermediate technique that will bridge the gap between the two missions and will allow 1) for a continued and uninterrupted time series of mass observations and 2) to compare, cross-validate and link the two time series. Here, we present a complete series that covers the gap period between the end of the GRACE mission in 2017 and the first available solutions of GRACE-Follow On in 2018. We will focus on the combination of high-low satellite-to-satellite tracking (hlSST) of low-Earth orbiting satellites by GNSS in combination with SLR. SLR is known to provide highest quality time-variable gravity for the very low degrees (2-5) and hlSST is able to provide a higher spatial resolution at a lower precision in the very low degrees. We discuss also the achievable spatial and temporal resolutions and possible applications in GIA and in interseasonal variation analysis.

The combination service for time-variable gravity fields (COST-G) provides the full time-series of monthly GRACE gravity fields: COST-G GRACE RL01, combined in reprocessing mode, and a steadily growing time-series of monthly GRACE-FO gravity fields: COST-G GRACE-FO RL01 OP, combined on an operational basis. Both time-series are currently considered for re-combination. In case of GRACE, new high-quality time-series from Chinese analysis centers are available for combination. In case of GRACE-FO, a revision of the weighting scheme, developed in the frame of the Horizon2020 project Global Gravity-based Groundwater Product (G3P), and the availability of reprocessed GRACE-FO time-series from AIUB, CSR, GFZ, and JPL, lead to a significant improvement of the combined gravity fields. We present the preliminary re-combined GRACE and GRACE-FO time-series and quantify the differences with respect to the COST-G RL01 series in terms of signal and noise content.

The release of the next International Terrestrial Reference Frame (ITRF) 2020 is based on the four geodetic techniques, namely Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Navigation Satellite Systems (GNSS), and Doppler Orbitography and Radio-positioning Integrated by Satellite instrument (DORIS). The upcoming release will presumably define the scale based on the first two techniques.The GNSS scale is mainly driven by the z-component of the satellite antenna phase center offsets. With the disclosure of the Galileo metadata by the European GNSS Agency (GSA) the satellite antenna pattern became available to the public and enabled the GNSS scale determination.We aim to analyze the consistency between the preliminary ITRF 2020 solution and the GNSS based scale. In addition, we will extend our study with all available TRF solutions and compare their consistency with the GNSS derived scale and discuss the resulting comparisons.

Copernicus Sentinel–1 is a C-Band Synthetic Aperture Radar (SAR) satellite mission within the European Copernicus Programme. The two satellites Sentinel-1A and -1B were launched in April 2014 and 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the determination of orbital and auxiliary products required by the Payload Data Ground Segment (PDGS). Precise orbits are determined based on the dual-frequency GPS (Global Positioning System) data delivered by dedicated geodetic-grade GPS receivers on-board the satellites. Several updates in the operational orbit determination were done during the years including an update of the GPS antenna reference point coordinates. The switch to GPS carrier phase ambiguity-fixing was a major improvement. A reprocessing of the entire mission span of both satellites became necessary to provide a consistent orbit time series for the mission based on state-of-the-art models and processing settings. Due to the lack of independent observation techniques, the Sentinel-1 orbit quality has been assessed by analysing processing metrics, orbit overlaps and orbit comparisons. For this purpose, members of the Copernicus POD Quality Working Group (QWG) provided reprocessed Sentinel-1 orbit time series based on their software packages and their orbit determination settings. A weighted average of all five delivered solutions - a combined orbit - serves as reference for the comparisons. The quality and reliability of this reference orbit depends among others on the number of available orbit solutions and whether a manoeuvre has been performed during the processed day or not. The mean orbit consistency between all orbit solutions is below 1 cm in 3D RMS for the entire mission time interval for both satellites. Only few days show inferior quality due to data gaps or orbit manoeuvres. Following this sophisticated validation process, the reprocessed Sentinel-1 orbits from the Copernicus POD Service have been made available to the user community.

We study gravity field determination from GRACE Follow-On satellite-to-satellite tracking using the inter-satellite K-band link and kinematic positions of the satellites as observations and pseudo-observations respectively. A key component of any model is the accurate specification of its quality. In the case of gravity field modelling from satellite data with the Celestial Mechanics Approach (CMA) a least-squares adjustment is performed to obtain a monthly solution of the Earth’s gravity field. However, the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We present gravity field solutions computed with the CMA and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that use empirical modelling with solutions from the operational GRACE Follow-On processing at AIUB by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done by the Combination Service for Time-variable Gravity fields (COST-G) and make use of noise and signal assessment applying the quality control tools routinely used in the frame of COST-G.

The use of zero-difference processing schemes becomes more and more popular within the GNSS (Global Navigation Satellite Systems) community. This change from double- to zero-difference approaches increases the demand of PPP-AR (Ambiguity Resolution for Precise Point Positioning) enabling products. Those products can be created in two ways, either estimate the geometrical part (orbits) based on a double-difference global network solution with a separate zero-difference solution for the clocks and phase biases, or in a combined zero-difference solution. The latter one allows a more flexible approach; however, the challenge lies in the handling of the increased number of parameters and ambiguity resolution.The estimation of combined orbit and clock zero-difference enabling products needs a thought-out design of the processing strategy, where the elimination and back-substitution steps are vital to deal with the large number of parameters. Nonetheless, the amount of ambiguity parameters dramatically grows with an increasing size of the network, posing some computational limitations, since they should not be eliminated for a successful ambiguity resolution. Such a restriction originates from fixing float orbits: their accuracy does not allow to estimate reliable ambiguity parameters. To cope with that, we propose a new algorithm capable to decouple them from the orbits, allowing to fix between-satellite ambiguities in a later station-wise parallelisation.On the poster, we describe selected details on the ambiguity resolution strategy that we have developed. The obtained results are characterized and compared to other solutions using classical ambiguity resolution schemes.

The GOCE satellite was orbiting the Earth in a Sun-synchronous orbit at a very low altitude for more than 4 years. This low orbit and the availability of high-quality data make it worthwhile to assess the contribution of GOCE GPS data to the recovery of both the static and time-variable gravity fields. We use the kinematic positions of the official GOCE precise science orbit (PSO) product to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity field solutions reveal severe systematic errors centered along the geomagnetic equator. Their size is significantly coupled with the ionospheric density and thus generally increasing over the mission period. The systematic errors may be traced back to the kinematic positions of the PSO product and eventually to the ionosphere-free GPS carrier phase observations used for orbit determination. As they cannot be explained by the current higher order ionospheric correction model recommended by the IERS Conventions 2010, an empirical approach is presented by discarding GPS data affected by large ionospheric changes. Such a measure yields a strong reduction of the systematic errors along the geomagnetic equator in the gravity field recovery, and only marginally reduces the set of useable kinematic positions by at maximum 6 % for severe ionosphere conditions. Eventually it is shown that GOCE gravity field solutions based on kinematic positions have a limited sensitivity to the largest annual signal related to land hydrology.

Introduction The exploration of Callisto is part of the extensive interest in the icy moons characterization. As other missions will focus on Ganymede and Europa, mission proposals devoted to the exploration and characterization of Callisto are currently emerging [2][6]. Compared to the other Galilean moons, the outermost moon has kept the best-preserved records of the Jovian system formation, which makes it a candidate of choice to understand how the Jupiter system formed, and how it works. Led by the National Space Science Center (NSSC), Chinese Academy of Science (CAS), the Gan De mission [2] aims to send an orbiter around Callisto in order to map its gravity and magnetic field, and to characterize its exosphere, surface and interior. Callisto’s degree of differentiation will also be investigated as well as the possible existence of an internal ocean, as Galileo measurements suggested. Because the mission is at a very early planning stage, there is no definitive mission plan yet. In this context, we selected a small representative set of potential science orbits around Callisto. These orbits are tested under different assumptions in a detailed simulation environment, to analyse the orbit recovery as well as the recovery of Callisto gravity field and k2 Love number using tracking data. The effect of non-gravitational forces exerting on the orbiter is carefully considered, especially the strategy to handle them through the whole estimation process. Exploring different orbits Flybys of Callisto from the JUICE and the Europa Clipper missions will already provide further information on this moon [4]. However, the global mapping of the outermost Galilean moon will be uniquely improved by means of an orbiter at a high inclination and a low altitude. A specific difficulty in the orbit design in the Jovian system is related to the orbit stability, which is highly impacted by the influence of Jupiter as a third body exerting strong perturbations on a Callisto orbiter. Additionally, the occultations of the Sun by Callisto should be minimized to ensure a maximum solar illumination for power, which is critical this far from the Sun. This implies a minimum angle between the orbital plane w.r.t the direction of the Sun (βSun), which is larger the lower the orbit is. Depending on the position of the Earth at that time, this might have a direct impact on the angle between the orbital plane w.r.t the direction of the Earth (βEarth), which is of importance for orbit determination and gravity field recovery using Doppler tracking data. In this presentation, we selected various low Callisto orbits, which are suitable as science orbits for Gan De. These orbits have different altitudes, Earth beta angles, and injection date into orbit. Although several of them can be used sequentially, they are considered separately. A detailed force model The set of different reference orbits is propagated using the planetary extension of the Bernese Software (BSW) [3]. All the planets of the solar system, as well as the Galilean satellites, are considered as point masses. In the case of Jupiter, the zonal harmonics of the gravity field are also part of the force model. Because our knowledge of Callisto’s gravity field is restricted to the results of the Galileo mission (degree 2) [1], we have derived a synthetic gravity field as ground truth for our simulation. The scaled gravity field of the Earth’s Moon is used from degree 3 to 100. An artificial value of k2 Love number is also adopted to provide a ground truth. In order to rely on solar power this far from the Sun, the size of the solar panels is significant, which makes the effect of the solar and planetary radiation pressure on them essential to account for. However, the modelling of these forces can be challenging, particularly because of their dependency on the geometry and the optical properties of the probe. Even with a precise macro model, the optical properties of each plate can evolve with time. Several strategies are tested to handle these non-conservative forces, such as the use of pseudo-stochastics parameters and the possibility of an on-board accelerometer. Orbit determination and gravity field recovery Using a detailed noise model [5] and a realistic tracking station schedule, realistic Doppler tracking data (2-way Ka-band Doppler range rate) is simulated as measurements from the Deep Space Network. The non-gravitational accelerations in action during the orbit propagation are used to generate realistic accelerometer measurements. These observations are then used to reconstruct the orbit along with dynamical parameters in a global least-squares adjustment. Within this closed-loop simulation, we investigate the impact of the non-gravitational accelerations and orbit geometry on the orbit determination and the recovery of the geodetic parameters. The focus of this presentation is on the quality of the retrieved gravity field parameters and tidal Love number k2. Acknowledgements This study has been funded with the support of the Swiss National Foundation (SNF). References [1] Anderson, J. D., et al. "Shape, mean radius, gravity field, and interior structure of Callisto." Icarus 153.1 (2001): 157-161. [2] Blanc, Michel, et al. "Gan De: Science Objectives and Mission Scenarios for China's Mission to the Jupiter System." EGU General Assembly Conference Abstracts. 2020. [3] Dach, R. et al. "Bernese GNSS software version 5.2." (2015). [4] Di Benedetto, Mauro, et al. "Analysis of 3GM Callisto Gravity Experiment of the JUICE Mission." arXiv preprint arXiv:2101.03401 (2021). [5] Iess, Luciano, et al. "Astra: Interdisciplinary study on enhancement of the end-to-end accuracy for spacecraft tracking techniques." Acta Astronautica 94.2 (2014): 699-707. [6] Smith, David E., et al. "MAGIC, A Discovery Proposal to the Icy Moon Callisto." AGU Fall Meeting Abstracts. Vol. 2019. 2019.

A large number of time-series of monthly gravity fields derived from GRACE data provide users with a wealth of information on mass transport processes in the system Earth. The users are, however, left alone with the decision which time-series to analyze. Following the example of other well-known combination services provided by the geodetic community, the prototype of a combination service has been developed within the frame of the project EGSIEM (2015–2017) to combine the different time-series with the goal to provide a unique and superior product to the user community. Four associated analysis centers (ACs) of EGSIEM, namely AIUB, GFZ, GRGS and IfG, generated monthly gravity fields which were then combined using the different normal equations (NEQs). But the relative weights determined by variance component estimation (VCE) on the NEQ level do not lead to an optimal combined product due to the different processing strategies applied by the individual ACs. We therefore resort to VCE on the solution level to derive relative weights that are representative of the noise levels of the individual solutions. These weights are then applied in the combination on the NEQ level. Prior to combination, empirical scaling factors that are based on pairwise combinations of NEQs are derived to balance the impact of the NEQs on the combined solution. We compare the processing approaches of the different ACs and introduce quality measures derived either from the differences w.r.t. the monthly means of the individual gravity fields or w.r.t. a deterministic signal model. After combination, the gravity fields are validated by comparison to the official GRACE SDS RL05 time-series and the individual contributions of the associated ACs in the spectral and the spatial domain. While the combined gravity fields are comparable in signal strength to the individual time-series, they stand out by their low noise level. In terms of noise, they are in 90% of all months as good or better than the best individual contribution from IfG and significantly less noisy than the official GRACE SDS RL05 time-series.

Earth observation satellites yield a wealth of data for scientific, operational and commercial exploitation. However, the redistribution of mass in the system Earth is not yet part of the standard inventory of Earth Observation (EO) data products to date. It is derived from the Gravity Recovery and Climate Experiment (GRACE) mission and its Follow-On mission (GRACE-FO). Among many other applications, mass redistribution provides fundamental insights into the global water cycle. Changes in continental water storage impact the regional water budget and can, in extreme cases, result in floods and droughts that often claim a high toll on infrastructure, economy and human lives. The initiative for a European Gravity Service for Improved Emergency Management (EGSIEM) established three different prototype services to promote the unique value of mass redistribution products for Earth Observation in general and for early-warning systems in particular. The first prototype service is a scientific combination service to derive improved mass redistribution products from the combined knowledge of the European GRACE analysis centres. Secondly, the timeliness and reliability of such products is a primary concern for any early-warning system and therefore EGSIEM established a prototype for a near real-time service that provides dedicated gravity field information with a maximum latency of five days . Third, EGSIEM established a prototype of a hydrological / early warning service that derives wetness indices as indicators of hydrological extremes and assessed their potential for timely scheduling of high-resolution optical/radar satellites for follow-up observations in case of evolving hydrological extreme events.

Even though ESA's three-satellite low-earth orbit (LEO) mission Swarm is primarily a magnetic field mission, it can also serve as a gravity field mission. Located in a near-polar orbit with initial altitudes of 480 km for Swarm A and Swarm C and 530 km for Swarm B and equipped with geodetic-type dual frequency Global Positioning System (GPS) receivers, it is suitable for gravity field computation. Of course, the Swarm GPS-only gravity fields cannot compete with the gravity fields derived from the ultra-precise Gravity Recovery And Climate Experiment (GRACE) K-band measurements. But for various reasons like the end of the GRACE mission in October 2017, data gaps in the previous months due to battery aging, and the gap between GRACE and the recently launched GRACE Follow-On mission, Swarm gravity fields became important to maintain a continuous time series and to bridge the gap between the two dedicated gravity missions. By comparing the gravity fields derived from Swarm kinematic positions to the GRACE gravity fields, systematic errors have been observed in the Swarm results, especially around the geomagnetic equator. These errors are already visible in the kinematic positions as spikes up to a few centimeters, from where they propagate into the gravity field solutions. We investigate these systematic errors by analyzing the geometry-free linear combination of the GPS carrier-phase observations and its time derivatives using a combination of a Gaussian filter and a Savitzky–Golay filter and the Rate of Total Electron Content (TEC) Index (ROTI). Based on this, we present different weighting schemes and investigate their impact on the gravity field solutions in order to assess the success of different mitigation strategies. We will show that a combination of a derivative-based weighting approach with a ROTI-based weighting approach is capable of reducing the geoid rms from 21.6 to 12.0 mm for a heavily affected month and that almost 10 % more kinematic positions can be preserved compared to a derivative-based screening.

The generation and use of GNSS analysis products that allow—particularly for the needs of single-receiver applications—precise point positioning with ambiguity resolution (PPP-AR) are becoming more and more popular. A general uncertainty concerns the question on how the necessary phase bias information should be provided to the PPP-AR user. Until now, each AR-enabling clock/bias representation method had its own practice to provide the necessary bias information. We have generalized the observable-specific signal bias (OSB) representation, as introduced in Villiger (J Geod 93:1487–1500, 2019) originally exclusively for pseudorange measurements, to carrier phase measurements. The existing common clock (CC) approach has been extended in a way that OSBs allowing for flexible signal and frequency handling between multiple GNSS become possible. Advantages of the proposed OSB-based PPP-AR approach are: GNSS biases can be provided in a consistent way for phase and code measurements and it is capable of multi-GNSS and suitable for standardization. This new, extended PPP-AR approach has been implemented by the Center for Orbit Determination in Europe (CODE). CODE clock products that adhere to the integer-cycle property have been submitted to the International GNSS Service (IGS) since mid of 2018 for three analysis lines: Rapid, Final, and MGEX (Multi-GNSS Extension). Ambiguity fixing is performed not only for GPS but also for Galileo. The integer-cycle property of between-satellite clock differences is of fundamental importance when comparing satellite clock estimates among various analysis lines, or at day boundaries. Both kinds of comparisons could be exploited at a very high level of consistency. Any retrieved comparison essentially indicated a standard deviation for between-satellite clocks from CODE of the order of 5 ps (1.5 mm in range). Finally, the integer-cycle property that may be recovered between the CODE Final clock and the accompanying bias product of consecutive daily sessions (using clock estimates additionally provided for the second midnight epoch) allows us to deduce GPS satellite clock and phase bias information that is consistent and continuous with respect to carrier phase observation data over two, three, or, in principle, yet more days. Phase-based clock densification from initially estimated integer-cycle-conform clock corrections at intervals of 300 s to 30 s (5 s in case of our Final clock product) is a matter of particular interest. Based on direct product comparisons and GRACE K-band ranging (KBR) data analysis, the quality of accordingly densified clock corrections could be confirmed to be on a level similar to that of “anchor” (300 s) clock corrections.

For the monitoring of mass transport and mass distribution in the Earth’s system, the gravity field and its temporal variations provide an important source of information. Dedicated satellite missions like GRACE and GRACE-FO allow to resolve the Earth’s time-variable gravity field based on ultra-precise inter-satellite ranging. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite equipped with an on-board GNSS receiver may also serve as a gravity field sensor. For this purpose, the collected GNSS data is used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery. Although this technique is less sensitive and restricted to the long wavelength part of the gravity field, it provides valuable information, particularly for those months where no inter-satellite ranging measurements are available from GRACE or GRACE-FO. Furthermore, the increasing number of operational LEO satellites makes it attractive to produce combined Multi-LEO gravity field solutions that will take advantage of the variety of complementary orbital configurations and can offer additional sensitivities to selected coefficients of solutions based on inter-satellite ranging.At the Astronomical Institute of the University of Bern (AIUB) GPS-based kinematic orbits are routinely processed for various LEO satellites like missions dedicated to gravity (GOCE, GRACE/-FO), altimetry (Jason, Sentinel), or further constellations of Earth-observing satellites like SWARM. Beside conventional ambiguity-float orbits, also ambiguity-fixed orbits are recently being computed based on new phase bias and clock products of the Center for Orbit Determination in Europe (CODE). The kinematic orbit positions offer the opportunity to derive time series of monthly gravity field solutions for the different LEO satellites that are eventually combined on the level of normal equations.In this contribution, we will present first results of our effort to generate a combined time series of monthly gravity field solutions based on the kinematic orbits of multiple LEO satellites. In a first step, the focus is laid on the GRACE/-FO missions that provide the longest time series in terms of collected GNSS data and that will therefore serve as a backbone for future combinations. We analyze the impact of accelerometer data on the recovery of time-variable mass variations. This will be particularly important for the handling of non-dedicated gravity missions, for which accelerometer measurements are usually not available. Furthermore, we study and compare the performance of gravity field recoveries based on ambiguity-float and ambiguity-fixed kinematic orbit solutions. We assess our results with respect to superior gravity field models based on inter-satellite ranging for selected areas with strong mass change signals like in Greenland, West-Antarctica or the Amazon river basin.

A key component of any model is the accurate specification of its quality. In gravity field modelling from satellite data, as it is done with the observation collected by GRACE Follow-On, usually least-squares adjustments are performed to obtain a monthly solution of the Earth’s gravity field. However,the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We take the Celestial Mechanics Approach (CMA), developed at the Astronomical Institute, University of Bern (AIUB), and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that employ empirical modelling with solutions that do not contain sophisticated noise modelling by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done in the COST-G framework.

Satellite Laser Ranging (SLR), i.e., the optical distance measurement to satellites equipped with laser retro-reflectors, has become an invaluable core technique in numerous geodetic applications. For instance, SLR measurements to spherical geodetic satellites, such as LAGEOS-1/2 or Etalon-1/2, form an essential contribution for the determination of geocenter coordinates and global scale in the International Terrestrial Reference Frame (ITRF) realizations.SLR measurements to active satellites in Low Earth Orbit (LEO) are, on the other hand, up to now mostly used for an independent validation of orbit solutions, usually derived by microwave tracking techniques based on Global Navigation Satellite Systems (GNSS) or Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). This allows for the analysis of systematic orbit errors (e.g., originating from poorly known satellite center of mass locations or sensor offsets) not only in radial direction, but in three dimensions. A high level of radial orbit reliability is, e.g., key to satellite altimetry applications.For many of these geodetic SLR applications a mm accuracy and 0.1 mm/year stability is required or at least desired. Unavoidable SLR station biases are a major error source and obstacle to reach the aforementioned accuracy and stability goals. Among the stations of the International Laser Ranging Service (ILRS) there is a large diversity of biases and measurement qualities, and the calibration of these biases for all stations is key to further exploit SLR data for present and future geodetic applications.In this presentation we demonstrate that the analysis of SLR data to active LEO satellites equipped with GNSS or DORIS receivers is a promising means to analyze SLR biases and their stability. Using three independent selections of Earth observation missions in LEOs with three different SLR analysis software packages (Bernese GNSS Software, Zoom, Napeos), we estimate SLR range biases for all involved tracking stations on a yearly basis. We find that for many of the stations the three independently estimated sets of biases agree on a few-mm level and that the inclusion of satellites from multiple missions allows to render the bias estimation more robust and in particular less prone to geographically correlated orbit errors. This shows that microwave-derived orbits of active LEO satellites, nowadays of very high quality due to numerous advances in modeling and analysis techniques, can serve as interesting sources for SLR station calibration in demanding geodetic applications like, e.g., future ITRF realizations.

The Copernicus Sentinel-1 SAR (Synthetic Aperture Radar) mission consists of two satellites A and B launched in April 2014 and April 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the generation of precise orbital products of the mission requiring a high orbit accuracy of 5 cm in 3D RMS in the comparison to external processing facilities.The operational POD setup at the Copernicus POD Service has passed through several updates during the last years. For instance the ITRF update from ITRF08 to ITRF14 at the end of January 2017, the fundamental background model update in May 2020, and the switch to updated GPS antenna reference point coordinates together with the introduction of carrier phase ambiguity fixing at the end of July 2020 have been done to mention just the major changes in the processing. To provide a homogeneous and up-to-date orbit time series for the two satellites a reprocessing of the full mission period is done. The quality control of the reprocessed Copernicus Sentinel-1 orbits is done by analysing processing metrics and by comparing the results to orbits, which were independently reprocessed by members of the Copernicus POD Quality Working Group (QWG).Results from the full Copernicus Sentinel-1 POD reprocessing campaign are presented together with the accuracy and quality assessment of the orbits.

The exploration of Callisto is part of the extensive interest in the icy moons characterization. Indeed, Callisto is the Galilean moon with the best-preserved records of the Jovian system formation. Led by the National Space Science Center (NSSC), Chinese Academy of Science (CAS), the planned Gan De mission aims to send an orbiter around Callisto in order to characterize its surface and interior. Potential orbit configurations are currently under study for the Gan De mission proposal.As part of a global characterization of Callisto, its gravity field can be inferred using radio tracking data from an orbiter. Mission characteristics such as orbit type, Earth beta angle and solar elongation will have a direct influence on the recoverability of its gravity field parameters. In this study, we will analyse this influence from closed-loop simulations using the planetary extension of the Bernese GNSS Softwareai.A number of reference orbits with different orbital characteristics will be selected for the Gan De mission and, using an extended force model, will be propagated from different starting dates and different initial Earth beta angles. Realistic Doppler tracking data (2-way X-band Doppler range rate) will be simulated as measurements from ground stations, with a dedicated noise model. These observations will then be used to reconstruct the orbit along with dynamical parameters. The focus of this presentation will be on the quality of the retrieved gravity field parameters and tidal Love number k2.

Global Navigation Satellite Systems such as the Global Positioning System (GPS) are a unique tool for deriving very precise orbits of Low Earth orbiting (LEO) satellites equipped with onboard GPS receivers. LEO precise orbit determination (POD) requires the proper modeling of antenna phase center variations (PCVs) for both the GPS transmitter and the LEO receiver antennas. While for the GPS antennas the nadir-dependent values from the official absolute antenna phase center model igs14.atx of the International GNSS Service (IGS), consistent with the underlying GPS orbit and clock products, are used, official PCV maps are usually not available for the LEO receiver antennas. If these variations are not considered, however, this may result in systematic errors in the derived LEO orbits. LEO PCV maps can be determined and exploited in different ways. One possibility is to use the PCV maps from ground calibrations provided by the manufacturer, which usually do not reflect, however, the influence of error sources which are additionally encountered in the actual spacecraft environment, e.g., near-field multipath. Alternatively, one can make use of GPS measurements and POD results to estimate the PCV map empirically, as it is done in this study.In this study, the influence of different attitude modes on Jason-3 POD using GPS observations and PCV map estimation is investigated. As Jason-3 in an altimetry satellite, its main objective is to measure global sea-level rise. Therefore, it is of particular importance to precisely determine the radial component of the orbit and proper PCV modeling is of high importance. As Jason-3 is experiencing different attitude modes, yaw-steering and fixed-yaw attitude with either the positive or negative x-axis pointing in the direction of flight, PCV maps are expected to be better disentangled from other error sources. In this study, we are analyzing PCV maps determined from residual stacking using GPS data from the different attitude modes and from different orbit parametrizations. First results indicate that PCV maps estimated from time spans of different attitude modes differ and systematic orbit differences are occurring in a reduced-dynamic POD.

The Astronomical Institute of the University of Bern (AIUB) collaborates with the Federal Agency for Cartography and Geodesy (BKG) in Germany to develop new procedures to generate products for the International Laser Ranging Service (ILRS). In this framework the SLR processing of the standard ILRS weekly solutions of spherical geodetic satellites at AIUB, where the orbits are determined in 7-day arcs together with station coordinates and other geodetic parameters, is extended from LAGEOS-1/2 and the Etalon-1/2 satellites to also include the LARES satellite orbiting the Earth at much lower altitude. Since a lower orbit experiences a more variable enviroment, e.g. it is more sensitive to time-variable Earth's gravity field, the orbit parametrization has to be adapted and also the low degree spherical harmonic coefficients of Earth's gravity field have to be co-estimated. The impact of the gravity field estimation is studied by validating the quality of other geodetic parameters such as geocenter coordinates, Earth Rotation Parameters (ERPs) and station coordinates. The analysis of the influence of LARES on the SLR solution shows that a good datum definition is important.

We examine how inequality and openness interact in shaping the long-run growth prospects of developing countries. To this end, we develop a Schumpeterian growth model with heterogeneous households and non-homothetic preferences for quality. We show that inequality affects growth very differently in an open economy as opposed to a closed economy: If the economy is close to the technological frontier, the positive demand effect of inequality on growth found in closed-economy models may be amplified by international competition. In countries with a larger distance to the technology frontier, however, rich households satisfy their demand for high quality via importing, and the effect of inequality on growth is smaller than in a closed economy and may even be negative. We show that this theoretical prediction holds up in the data, both when considering growth in export quality at the industry level and when considering growth in GDP per capita.