An experimental combination of IGS repro3 campaign’s orbit products using a variance component estimation strategy

Over the past years, the International GNSS Service (IGS) has put efforts into reprocessing campaigns reanalyzing the full data collected by the IGS network since 1994. The goal is to provide a consistent set of orbits, station coordinates, and earth rotation parameters using state-of-the-art models. Different from the previous campaigns - namely: repro1 and repro2 - the repro3 includes not only GPS and GLONASS but also the Galileo constellation. The main repro3 objective is the contribution to the next realization of the International Terrestrial Reference Frame (ITRF2020). To achieve this goal, several Analysis Centers (AC) submitted their specific products, which are combined to provide the final solutions for each product type. In this contribution, we focus on the combination of the orbit products.We will present a consistent orbit solution based on a newly developed combination strategy where the weights are determined by a Least-Squares Variance Component Estimation (LSVCE). The orbits are combined in an iterative processing, first aligning all the products via a Helmert transformation, second defining which satellites will be used in the LSVCE, and finally normalizing the inverse of the variances as weights that are used to compute a weighted mean. Moreover, we will discuss the weight factors and their stability in the time evolution for each AC depending on the constellations. In addition, an external validation using a Satellite Laser Ranging (SLR) procedure will be shown for the combined solution.

An experimental combination of IGS repro3 campaign’s orbit products using a variance component estimation strategy

Over the past years, the International GNSS Service (IGS) has put efforts into reprocessing campaigns reanalyzing the full data collected by the IGS network since 1994. The goal is to provide a consistent set of orbits, station coordinates, and earth rotation parameters using state-of-the-art models. Different from the previous campaigns - namely: repro1 and repro2 - the repro3 includes not only GPS and GLONASS but also the Galileo constellation. The main repro3 objective is the contribution to the next realization of the International Terrestrial Reference Frame (ITRF2020). To achieve this goal, several Analysis Centers (AC) submitted their specific products, which are combined to provide the final solutions for each product type. In this contribution, we focus on the combination of the orbit products.We will present a consistent orbit solution based on a newly developed combination strategy where the weights are determined by a Least-Squares Variance Component Estimation (LSVCE). The orbits are combined in an iterative processing, first aligning all the products via a Helmert transformation, second defining which satellites will be used in the LSVCE, and finally normalizing the inverse of the variances as weights that are used to compute a weighted mean. Moreover, we will discuss the weight factors and their stability in the time evolution for each AC depending on the constellations. In addition, an external validation using a Satellite Laser Ranging (SLR) procedure will be shown for the combined solution.

Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites

Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth orbit (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global Positioning System (GPS) observations of the current seven LEO satellites (Swarm-A/B/C, Gravity Recovery and Climate Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP estimation using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite solutions, the quality of ERP and station coordinates can be improved gradually with the increase in the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are jointly determined, based on SLR and GPS observations, and present a detailed comparison between the one-step solution and two-step solution.

Combination of GNSS and VLBI data for consistent estimation of Earth Rotation Parameters

<p>We present the current activities of the Federal Agency for Cartography and Geodesy (BKG) towards a combined processing of VLBI and GNSS data.  The main goal of the combined analyses of the two different space-geodetic techniques is the improvement of the consistency between the techniques through common parameters, i.e., mainly Earth Rotation Parameters (ERPs), but also station coordinates and tropospheric parameters through local ties and atmospheric ties, respectively.</p><p>Based on our previous combination studies using GNSS data and VLBI Intensive sessions on a daily and multi-day level, we generate a consistent, low-latency ERP time series with a regular daily resolution for polar motion and dUT1. We achieved in this way a significant accuracy improvement of the dUT1 time series and a slight improvement of the pole coordinates time series, comparing ERPs from the combined processing with the individual technique-specific ERPs.</p><p>In our recent studies, we extend the combination of GNSS and VLBI Intensive sessions by adding VLBI 24-hour sessions in order to exploit the benefit of the combination to its maximum extend. We analyse the impact of the combination on the global parameters of interest, i.e., mainly dUT1, polar motion and LOD, but also on station coordinates.</p><p>BKG’s primary interest is the combination of GNSS and VLBI data on the observation level. However, the current combination efforts are based on the normal equation level using technique-specific SINEX files as a starting point.</p>

On the potential of single-satellite space ties to achieve the Global Geodetic Observing System goals

<p>GGOS-SIM-2, funded by the German Research Foundation (DFG), is a research collaboration project between the German Research Center for Geosciences (GFZ) and the Technische Universität Berlin (TUB). Simulations are utilized to examine the potential of co-location in space, called space ties, of the four main space geodetic techniques, i.e. DORIS, GNSS, SLR and VLBI to achieve the requirements of the Global Geodetic Observing System (GGOS) for a global terrestrial reference frame (TRF), 1 mm accuracy and 1 mm / decade long-term stability. The simulations are performed for six fictional orbit scenarios, including proposed missions GRASP (USA) and E-GRASP (EU), and expanded by a variation of the E-GRASP orbit with lower eccentricity as well as three higher orbiting circular orbits with different inclination over a time span of seven years. For most realistic simulations, we first evaluated real DORIS, GPS and SLR observations to the satellites LAGEOS 1 und 2, Ajisai, LARES, Starlette, Stella, ENVISAT, Jason 1 und 2, Sentinel 3A and B using Precise Orbit Determination (POD), to get detailed information about the individual station and receiver accuracy, availability and further technique-specific effects. Then, we generate simulated single-technique TRF solutions based on existing missions and add the co-location-in-space satellite in the six orbit scenarios. In order to quantify the effects of the different scenarios, we examine the added value w.r.t. the existing missions in terms of origin and scale and of formal errors of the station coordinates and Earth rotation parameters. We also investigate the impact of systematic errors on the derived orbits on the final TRF. The different techniques show individual advantages regarding the respective orbit parameters. For instance, a higher eccentricity of the orbit seems to lead to improved accuracy of length-of-day (LOD) from SLR. The results will help to find the best trade-off for a satellite that co-locates all four techniques in space towards a GGOS-compliant TRF and Earth rotation parameters.</p>

Propagation of satellite orbit modelling deficiencies into the global GNSS solutions – simulation-based study

<p>The Non-Gravitational Perturbations (NGP), out of which the Solar Radiation Pressure (SRP) is the largest, have a significant impact on GNSS satellite orbits. In addition to the SRP, other relevant perturbations should also be taken into account, as this may result in substantial modelling errors if underestimated. Particularly, the force model should also consider Earth’s albedo in terms of the emitted and reflected radiation, as well as a physical satellite model (box-wing) with its optical and thermal properties.<br>GNSS satellite orbit modelling may suffer from deficiencies for various reasons (simplification of the complexity of the used model or uncertainty of the input information). The impact of such model errors on global GNSS data analyses is assessed in an error propagation study based on simulated observations. The influence of artificially introduced orbit errors on estimated parameters, e.g. Earth rotation parameters, orbit parameters (initial conditions and dynamical orbit parameters), station coordinates, station-wise troposphere parameters, as well as receiver and satellite clock corrections is investigated. In this study a dedicated simulation environment is used to analyse the relation between results and certain individual shortcomings in the NGP models. In addition, apart from a commonly used epoch-wise clock estimation, the analytical models for satellite clock corrections are introduced in order to exploit the high stability of the passive H-masers on-board the Galileo satellites. The simulation environment also allows to assess how the impact of float- versus fixed-ambiguities.<br>Finally, simulation-based analyses offer an excellent framework for more detailed validations and further refinements of the physical satellite models, which will consequently stabilize the global solution.</p>

Impact of low-degree gravity field estimation in the SLR data processing of spherical satellites at AIUB

<p>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.</p>

Earth rotation parameters estimation using satellite laser ranging measurements to multiple LEO satellites

<p>Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). Currently, the ERP products from International Laser Ranging Service (ILRS) are generated based on SLR observations to LAGEOS and Etalon satellites, which account for only about 9% of total SLR observations to Earth satellites. A large amount of SLR observations for the geodetic and oceanographic LEOs are neglected due to relatively degraded orbit caused by imperfect orbit models. However, thanks to the recent refinement of both dynamic and observation models, the quality of LEO orbits has been improved significantly, which makes it worthwhile to investigate the potential of these LEOs in the ERP estimation. In this study, we focus on the contribution of SLR observations from multiple LEO satellites to ERP estimation. The SLR observations of current seven LEO satellites (Swarm-A/B, GRACE-C/D, Sentinel-3A/B and Jason-3) as well as LAGEOS are used. Several strategies are designed to investigate the impact of the LEO orbit altitude, inclination and the number of LEO satellites. We also discuss the contribution of the application of ambiguity-fixed orbits and consider the simultaneous processing of SLR and GPS observations. The three-day solutions are selected and all the results are evaluated by the comparison with IERS Bulletin A.</p><p>The results show that for the single-LEO solutions, there is no evident relationship between the accuracy of ERP and the LEO orbit altitude and inclination. The best consistency with the IERS products is achieved by the Jason-3 solutions, with RMS values of 1.9mas, 1.8mas and 93us for X pole, Y pole and length of day (LOD) respectively. The multi-LEO solution results indicate that the accuracy of ERP can be improved gradually with the increase of LEO satellites. Compared with the single-LEO solution, the accuracy of X pole and Y pole of the 7-LEO solution is improved by 39.27% and 53.84% respectively. This result can be easily understood by the evident increase of SLR observations with the increase of LEO satellites. We also find the ERP estimation can benefit from the application of the ambiguity-fixed orbit.</p><p>In addition, apart from the solutions with LEO orbits fixed (two-step method), we also jointly process the onboard GPS observations and SLR measurements to obtain LEO orbits and ERP simultaneously (one-step method). The result indicates that the ERP of the one-step solution present a better accuracy than that of the two-step solution. Moreover, the LEO orbits can also benefit from the integrated processing.</p>

Estimating variations in Earth rotation using GPS, GLONASS, and Galileo

<p>Variations in the Earth's rotation can be examined in the low-frequency and high-frequency temporal scales. The low-frequency variations are dominated by the annual and Chandler wobbles, while the high-frequency variations are primarily caused by tidal effects and mass redistributions within the system Earth. Depending on the purpose, the Earth Rotation Parameters (ERPs) can be estimated in different time resolutions using space-geodetic techniques, especially using GNSS. However, the residual signals between different space geodetic techniques or satellite constellations indicate system-specific differences, which have to be correctly identified.</p><p>This research provides the daily, and sub-daily series of Earth Rotation Parameters (ERPs) estimated using GPS, GLONASS, and Galileo observations. We test different sampling intervals of estimated ERPs from 1h to 24h. The GNSS-based sub-daily estimates have been compared with the external models of variations in ERPs induced by the ocean tides from the IERS 2010 Conventions, a new model by Desai-Sibois, and the VLBI-based model by Gipson.</p><p>Any system-specific ERPs are affected by the orbital and draconitic signals. The orbital signals are visible in all system-specific ERPs at the periods that arise from the resonance between the Earth's rotation and the satellite revolution period, e.g., 8.87h, 34.22h, 3.4 days, 10 days for Galileo; 7.66h, 21.29h, 3.9 days, 7.9 days for GLONASS; 7.98h (S3 tidal term), 11.97h (S2 tidal term), 23.93h (S1 tidal term) for GPS. In the Galileo and GLONASS solutions, the artificial non-tidal signals' amplitudes can reach up to 30 µas. The GPS-derived sub-daily ERPs suffer from the overlapping periods of the diurnal and semidiurnal tidal terms and the harmonics of the GPS revolution period. After recovery of 38 sub-daily tidal terms, the Galileo-based model is more consistent with the external models than the GPS-based model, especially in the prograde diurnal band. The results confirmed that the Desai–Sibois model is more consistent with GNSS observations than the currently recommended model by the IERS 2010 Conventions. Moreover, GPS-based length-of-day (LoD) is systematically biased with respect to the IERS-C04-14 values with a mean offset of −22.4 µs/day, because of the deep resonance 2:1 between the satellite revolution period and the Earth rotation. The Galileo-based and GLONASS-based solutions are almost entirely free of this issue. Against the individual system-specific solutions, the multi-GNSS solution is not affected by most of the system-specific artifacts. Thus, multi-GNSS solutions are clearly beneficial for the estimation of both daily and sub-daily ERPs.</p>

Consistent Weather-Dependent Corrections for Space Geodesy; Validation via GNSS and VLBI Analysis

<p align="justify"><span>W</span><span>hether utilizing consistent models to describe weather-dependent effects on geodetic observations or a collection of models that yield accurate results individually, has </span><span>remained an unanswered question in space geodesy. </span><span>We study the superimposed effect of atmospheric refraction and environmental loading on GNSS and VLBI data analysis. Variable atmospheric refraction and site displacements induced by non-tidal geophysical loading constitute a large contribution to the modern space geodetic data analysis error budget. State-of-the-art weather models such as ECMWF‘s operational analysis and the atmospheric reanalysis ERA5 have proven to be an accurate forcing data set to drive relevant measurement corrections. Since the effects of these phenomena (refraction and loading) on geodetic observables exhibit non-trivial correlations with each other at a multitude of spatio-temporal scales, employing inconsistent data sets may deteriorate the geodetic results, such as the station coordinates and the Earth rotation parameters. The purpose of this contribution is twofold: (i) present our strategy towards consistent weather-dependent models and explore the merits stemming from the adoption thereof, and (ii) evaluate atmospheric delay and geophysical loading models consistently derived from ERA5 via the reanalysis of GNSS and VLBI data. To identify the extent to which the application of inconsistently forced reduction models causes discrepancies in the geodetic adjustment, we carried out a series of Monte Carlo runs. GNSS and VLBI observations were simulated employing ERA5-driven data (ray-traced delays and loading displacements), but reduced by applying a version thereof subjected to systematic and random noise driven from the performance of state-of-the-art models, at the observation equation level. To evaluate the model coupling with real data, we conduct a GNSS and VLBI repro and compare our new solutions to the GFZ‘s contribution to ITRF2020.</span></p>