The estimation of satellite orbits and clocks plays a central role in different Global Navigation Satellite System (GNSS) domains, e.g. precise positioning or time transfer. Such products can be computed in the process of Orbit Determination and Time Synchronization (ODTS), which relies on a network of ground-based stations, well distributed around the globe. The mm-level precision of carrier-phase measurements is exploited in this network estimation following a correct resolution of their ambiguities. For several stations, satellites and/or signals, thousands of ambiguities have to be processed, which means having to deal with high-dimensional ambiguity resolution (HDAR) problems. In this research work, we firstly account for the impact of ambiguity resolution in a varying network size, based on GPS-only, Galileo-only and GPS+Galileo configurations. Using 25 or more stations, the accuracy (1D RMS orbital errors) of fixed solutions reaches a plateau at 1-2 cm. Hence, we focus on a small global network of 14 stations, where the model strength decreases, so does the reliability of the ambiguity fixing process and advantages over a float solution might become less evident. In order to allow reliable HDAR, two implementations of the Vectorial Integer Bootstrapping estimator are presented and evaluated with respect to their scalar counterpart. Finally, it is shown how the proposed fixing processes are more robust, still very efficient, and on certain days they provide a large improvement to satellite products. The orbital results are ultimately validated by considering the satellite midnight discontinuity errors over a 3-month period in 2019.@en

The Swarm satellite mission provides important information regarding the temporal changes of Earth’s gravity field. Several European institutes routinely process Swarm GPS data to produce kinematic orbits, which forms the basis for the estimation of monthly gravity fields. Each institute follows a different gravity field estimation approach and all together they provide complementary advantages. As a result, the combined gravity field model is superior to any individual contribution, improving the accuracy of the measurement of mass transport processes. These models are an integral part of the European Gravity Service for Improved Emergency Management project (http://egsiem.eu), thus providing independent input, in additional to dedicated geodetic data. We illustrate the agreement of the Swarm models with the much more accurate GRACE solutions, at 1666km wavelength and over most of the Swarm mission lifetime. We additionally highlight large surface mass transport processes represented by the Swarm GPS data. @en

It is of great interest to numerous geophysical studies that the time series of global gravity field models derived from Gravity Recovery and Climate Experiment (GRACE) data remains uninterrupted after the end of this mission. With this in mind, some institutes have been spending efforts to estimate gravity field models from alternative sources of gravimetric data. This study focuses on the gravity field solutions estimated from Swarm global positioning system (GPS) data, produced by the Astronomical Institute of the University of Bern, the Astronomical Institute (ASU, Czech Academy of Sciences) and Institute of Geodesy (IfG, Graz University of Technology). The three sets of solutions are based on different approaches, namely the celestial mechanics approach, the acceleration approach and the short-arc approach, respectively. We derive the maximum spatial resolution of the time-varying gravity signal in the Swarm gravity field models to be degree 12, in comparison with the more accurate models obtained from K-band ranging data of GRACE. We demonstrate that the combination of the GPS-driven models produced with the three different approaches improves the accuracy in all analysed monthly solutions, with respect to any of them. In other words, the combined gravity field model consistently benefits from the individual strengths of each separate solution. The improved accuracy of the combined model is expected to bring benefits to the geophysical studies during the period when no dedicated gravimetric mission is operational.

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Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 %; in the absence of the polar data gap, SLR residuals agree by ≈96 %. From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

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