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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.

The so-called highly reduced-dynamic (HRD) orbit determination strategy and its use for the determination of the Earth's gravitational field are analyzed. We discuss the functional model for the generation of HRD orbits, which are a compromise of the two extreme cases of dynamic and purely geometrically determined kinematic orbits. For gravity field recovery the energy integral approach is applied, which is based on the law of energy conservation in a closed system. The potential of HRD orbits for gravity field determination is studied in the frame of a simulated test environment based on a realistic GOCE orbit configuration. The results are analyzed, assessed, and compared with the respective reference solutions based on a kinematic orbit scenario. The main advantage of HRD orbits is the fact that they contain orbit velocity information, thus avoiding numerical differentiation on the orbit positions. The error characteristics are usually much smoother, and the computation of gravity field solutions is more efficient, because less densely sampled orbit information is sufficient. On the other hand, the main drawback of HRD orbits is that they contain external gravity field information, and thus yield the danger to obtain gravity field results which are biased towards this prior information

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.

Gravity field parameters are usually determined from observations of the GRACE satellite mission together with arc-specific parameters in a generalized orbit determination process. When separating the estimation of gravity field parameters from the determination of the satellites' orbits, correlations between orbit parameters and gravity field coefficients are ignored and the latter parameters are biased towards the a priori force model. We are thus confronted with a kind of hidden regularization. To decipher the underlying mechanisms, the Celestial Mechanics Approach is complemented by tools to modify the impact of the pseudo-stochastic arc-specific parameters on the normal equations level and to efficiently generate ensembles of solutions. By introducing a time variable a priori model and solving for hourly pseudo-stochastic accelerations, a significant reduction of noisy striping in the monthly solutions can be achieved. Setting up more frequent pseudo-stochastic parameters results in a further reduction of the noise, but also in a notable damping of the observed geophysical signals. To quantify the effect of the a priori model on the monthly solutions, the process of fixing the orbit parameters is replaced by an equivalent introduction of special pseudo-observations, i.e., by explicit regularization. The contribution of the thereby introduced a priori information is determined by a contribution analysis. The presented mechanism is valid universally. It may be used to separate any subset of parameters by pseudo-observations of a special design and to quantify the damage imposed on the solution.

The COSMIC-2 mission is a follow-on mission of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) with an upgraded payload for improved radio occultation (RO) applications. The objective of this paper is to develop a near-real-time (NRT) orbit determination system, called NRT National Chiao Tung University (NCTU) system, to support COSMIC-2 in atmospheric applications and verify the orbit product of COSMIC. The system is capable of automatic determinations of the NRT GPS clocks and LEO orbit and clock. To assess the NRT (NCTU) system, we use eight days of COSMIC data (March 24-31, 2011), which contain a total of 331 GPS observation sessions and 12 393 RO observable files. The parallel scheduling for independent GPS and LEO estimations and automatic time matching improves the computational efficiency by 64% compared to the sequential scheduling. Orbit difference analyses suggest a 10-cm accuracy for the COSMIC orbits from the NRT (NCTU) system, and it is consistent as the NRT University Corporation for Atmospheric Research (URCA) system. The mean velocity accuracy from the NRT orbits of COSMIC is 0.168 mm/s, corresponding to an error of about 0.051 μrad in the bending angle. The rms differences in the NRT COSMIC clock and in GPS clocks between the NRT (NCTU) and the postprocessing products are 3.742 and 1.427 ns. The GPS clocks determined from a partial ground GPS network [from NRT (NCTU)] and a full one [from NRT (UCAR)] result in mean rms frequency stabilities of 6.1E-12 and 2.7E-12, respectively, corresponding to range fluctuations of 5.5 and 2.4 cm and bending angle errors of 3.75 and 1.66 μrad .

The official GFZ RL05 monthly GRACE gravity models were processed in a two-step approach. In the first step the orbits were determined. In the second step corrections to the gravity field parameters were estimated, while the orbits were kept fixed. This led to a significant de-noising of the resulting monthly models, but accidentally also to a regularization, i.e., the estimated gravity field coefficients were biased towards the a priori model. We compare the GFZ RL05 models to a revised version RL05a that was determined in a common estimation of orbit and force model parameters. A large number of gravity field coefficients is significantly affected. We relate this effect to the one-hourly stochastic accelerations estimated for orbit determination, and to ignoring the correlations. In the main part of this paper we study the interaction between pseudo-stochastic orbit parameters and gravity field coefficients. To explain this interaction we make use of a time-wise approach to gravity field determination. We apply the linear perturbation theory developed by Hill for circular orbits to compute lumped coefficients of the inter-satellite range-rate observations. We illustrate that the pseudo-stochastic orbit parameters act as a high-pass filter on the lumped coefficients spectra of the range-rates. Because the lumped coefficients are related to the spherical harmonics coefficients via a summation over all degrees, the whole range of gravity field coefficients is affected. This result is of relevance for all approaches to gravity field estimation from orbit observations, where dynamic orbits are introduced a priori and the arc-specific parameters are kept fixed.

The Swarm mission consists of three satellites orbiting the Earth at low orbital altitudes. The onboard GPS receivers, star cameras, and laser retro-reflectors make the Swarm mission an interesting candidate to explore the contribution of Swarm GPS data to the recovery of both the static and time-variable gravity fields. We use 1.5 years of Swarm GPS and attitude data to generate kinematic positions of high quality to perform gravity field determination using the Celestial Mechanics Approach. The generated gravity fields reveal severe systematic errors along the geomagnetic equator. Their size is correlated with the ionospheric density and thus strongly varying over the analyzed time period. Similar to the findings of the GOCE mission, the systematic errors are related to the Swarm GPS carrier phase data and may be reduced by rejecting 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. Long wavelength signatures of the gravity field may then be recovered with a similar quality as achieved with GRACE GPS data, which makes the Swarm mission well suited to bridge a potential gap between the current GRACE and the future GRACE Follow-On mission.

The Gravity Recovery And Interior Laboratory (GRAIL) mission orbiting the Moon and the Gravity Recovery And Climate Experiment (GRACE) mission orbiting the Earth share many conceptual commonalities. Major differences reside, however, in the absolute positioning of the spacecraft, which is accomplished by Doppler tracking from NASA’s Deep Space Network (DSN) for GRAIL and by the Global Positioning System (GPS) for GRACE. Data from GRACE and from the Gravity and steady-state Ocean Circulation Explorer (GOCE) are used to investigate the role of position information. Artificially degrading either the geographical coverage or the accuracy of kinematic positions serving as input data together with continuously available K-Band inter-satellite data is shown not to be a limiting factor for gravity field recovery using the Celestial Mechanics Approach (CMA). Eventually, the CMA is applied to Level-1B data of the GRAIL mission to derive first Bernese lunar gravity field solutions.

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.

Gravity missions such as the Gravity field and steady-state Ocean Circulation Explorer (GOCE) are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD), instrument time-tagging, and the extraction of the long wavelength part of the Earth’s gravity field. The very low orbital altitude of the GOCE satellite and the availability of dense 1 s GPS tracking data are ideal characteristics to exploit the contribution of GPS high-low Satellite-to-Satellite Tracking (hl-SST) to gravity field determination. We present gravity field solutions based on about 8 months of GOCE GPS hl-SST data from 2009 and compare the results with those obtained from the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) missions. The very low orbital altitude of GOCE significantly improves gravity field recovery from GPS hl-SST data above degree 20, but not for the degrees below 20, where the quality of the spherical harmonic coefficients remains essentially unchanged. Despite the limited time span of GOCE data used, the gravity field of the Earth can be resolved up to about degree 115 using GPS data only. Empirically determined phase center variations (PCVs) of the GOCE onboard GPS helix antenna are, however, mandatory to achieve this performance.

The gravity field model AIUB-CHAMP02S, which is based on six years of CHAMP GPS data, is presented here. The gravity field parameters were derived using a two step procedure: In a first step a kinematic trajectory of a low Earth orbiting (LEO) satellite is computed using the GPS data from the on-board receiver. In this step the orbits and clock corrections of the GPS satellites as well as the Earth rotation parameters (ERPs) are introduced as known. In the second step this kinematic orbit is represented by a gravitational force model and orbit parameters. In order to ensure full model consistency the GPS satellite orbits and clock corrections, which have been used for the generation of the kinematic LEO trajectories, were taken from the Center for Orbit Determination in Europe (CODE), located at AIUB ( Dach et al., 2009 ). In recent years many changes have taken place in the processing chain of global navigation satellite system (GNSS) data, e.g., the implementation of absolute antenna phase center modeling. Therefore a reprocessing of the GPS data to obtain state-of-the-art GPS satellite orbits and clock corrections was performed. From these updated GPS products new kinematic orbits of the CHAMP satellite were derived for the years 2002–2007. From the updated CHAMP trajectories spherical harmonic (SH) coefficients of the Earth’s gravity field were determined in exactly the same way as from the original LEO orbit. This allowed us to study the impact of the improved LEO orbits on the derived gravity field parameters and the generation of the multi-year gravity field model AIUB-CHAMP02S. The change of the IGS standards creates an inconsistency to existing global gravity field models, which mainly affects the zonal coefficients of low even degrees. The inconsistency is caused by the change to the absolute antenna phase center model and can be reduced by estimating the phase center variation of the CHAMP GPS antenna.

GPS zero-difference applications with a sampling rate up to 1 Hz require corresponding high-rate GPS clock corrections. The determination of the clock corrections in a full network solution is a time-consuming task. The Center for Orbit Determination in Europe (CODE) has developed an efficient algorithm based on epoch-differenced phase observations, which allows to generate high-rate clock corrections within reasonably short time (< 2 h) and with sufficient accuracy (on the same level as the CODE rapid or final clock corrections, respectively). The clock determination procedure at CODE and the new algorithm is described in detail. It is shown that the simplifications to speed up the processing are not causing a significant loss of accuracy for the clock corrections. The high-rate clock corrections have in essence the same quality as clock corrections determined in a full network solution. In order to support 1 Hz applications 1-s clock corrections would be needed. The computation time, even for the efficient algorithm, is not negligible, however. Therefore, we studied whether a reduced sampling is sufficient for the GPS satellite clock corrections to reach the same or only slightly inferior level of accuracy as for the full 1-s clock correction set. We show that high-rate satellite clock corrections with a spacing of 5 s may be linearly interpolated resulting in less than 2% degradation of accuracy.

The determination of high-precision orbits for Low Earth Orbiting (LEO) satellites (e.g., CHAMP, GRACE, MetOp-A) is based on dual-frequency tracking data from on-board GPS (Global Positioning System) receivers. The two frequencies allow it to eliminate the first order ionosphere effects. Data screening and precise orbit determination (POD) procedures are optimized under the assumption of the availability of two frequencies. If only single-frequency data is available, the algorithms have to be modified to consider the ionospheric effect. We develop and study different approaches for POD with single-frequency data. Reduced-dynamic as well as kinematic POD techniques using pseudorange and carrier phase GPS data are considered. One week of data in the year 2007 is used to assess the potential of single-frequency POD in different environments by comparing the results with dual-frequency POD for LEOs orbiting the Earth in different heights. Data from the two GRACE and the MetOp-A satellites is processed for this purpose. Moreover, the impact of different data sampling rates on single-frequency POD is considered. For this period with low solar activity a 3D orbit accuracy of 1 dm could be reached for one of the GRACE satellites. It could be shown that it is necessary to have a high data sampling of 10 s or more available when the impact of the ionosphere is high due to low altitude of the satellite or high solar activity. Our study helps to define requirements for GNSS (Global Navigation Satellite System) receivers and POD algorithms for future LEO missions for which only moderate orbit accuracy of about one to few decimeter is needed.

Since May 2003, the Center for Orbit Determination in Europe (CODE), one of the analysis centers of the International GNSS Service, has generated GPS and GLONASS products in a rigorous combined multi-system processing scheme, which promises the best possible consistency of the orbits of both systems. The resulting products, in particular the satellite orbits and clocks, are easily accessible by the user community. In the first part of this article, we focus on the generation of the combined global products at CODE, where we put emphasis not only on accuracy, but also on completeness. We study the impact of GLONASS on the CODE products, and the benefit of using them. Last, but not least, we introduce AGNES (Automated GNSS Network for Switzerland), a regional tracking network of small extensions (roughly 400 km East–West, 200 km North–South), which consequently tracks all GNSS satellites and analyzes their measurements using the CODE products.

The global navigation satellite system receiver for atmospheric sounding (GRAS) on MetOp-A is the first European GPS receiver providing dual-frequency navigation and occultation measurements from a spaceborne platform on a routine basis. The receiver is based on ESA’s AGGA-2 correlator chip, which implements a high-quality tracking scheme for semi-codeless P(Y) code tracking on the L1 and L2 frequency. Data collected with the zenith antenna on MetOp-A have been used to perform an in-flight characterization of the GRAS instrument with focus on the tracking and navigation performance. Besides an assessment of the receiver noise and systematic measurement errors, the study addresses the precise orbit determination accuracy achievable with the GRAS receiver. A consistency on the 5 cm level is demonstrated for reduced dynamics orbit solutions computed independently by four different agencies and software packages. With purely kinematic solutions, 10 cm accuracy is obtained. As a part of the analysis, an empirical antenna offset correction and preliminary phase center correction map are derived, which notably reduce the carrier phase residuals and improve the consistency of kinematic orbit determination results.

The two GRACE satellites provide the ideal platform to study the performance of different strategies for precise orbit determination using undifferenced or doubly differenced GPS data. We use pseudo-stochastic orbit modeling techniques in a batch least-squares environment for the two GRACE satellites to outline the mutual benefits of processing doubly differenced instead of undifferenced GPS data. We either process the space baseline only, the space-ground baselines only, or both types of baselines together, and show that the fixing of the GPS double difference carrier phase ambiguities has a significant impact on the space baseline, but also on the space-ground baselines. The validation of the relative orbit positions by inter-satellite K-band observations shows precisions of better than 1 mm in the case of fixed space baseline ambiguities, precisions of a few millimeter in the case of fixed space-ground baseline ambiguities, and precisions of about 1 cm in the case of float ambiguities. We discuss the differences between the various GRACE orbit solutions in order to formulate well suited orbit determination strategies tailored to the GRACE configuration. Satellite laser ranging observations indicate that accuracies between 2 cm and 2.5 cm are achieved.

Efficient precise orbit determination of LEO satellites plays an important role for near real-time studies of GPS satellite occultations for meteorological purposes. Precise point positioning for each epoch is one approach to achieve this goal. Using IGS orbits and precise clocks for the GPS satellites the positions are generated by the combination of code derived positions and phase derived position differences. Fitting an orbit based on a physical model to the positions promises to complement a procedure that meets the requirements regarding precision and processing speed. This efficient procedure is tested with data of TOPEX/POSEIDON.

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 $${\approx }10~\%$$ ; in the absence of the polar data gap, SLR residuals agree by $${\approx }96~\%$$ . 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.

Preprocessing is an essential aspect for zero- and double-difference GPS software packages. In the first case we have to produce “clean” code and phase observations on the single receiver and single satellite level, in the second case solely double-difference observations have to be checked. The checks usually are performed on the “minimum constellation” level, i.e., the single receiver level for zero-, the single baseline level for double-difference packages. When analyzing the code observations stemming from a permanent array, this step may be performed in a much more efficient and robust way because the known geometry and, if available, the known atmospheric delays may be removed from the original observations. In an array of n receivers observing m satellites this leaves us with n · m observations and n+m − 1 unknowns (the clock parameters relative to a reference clock). The degree of freedom of f=n · m − ( n +m − 1 ) (for, e.g., n= 10 and m= 10, we have f= 81) allows for a very robust detection of outliers and enables generating a satellite clock file based on code measurements (with very much reduced multipath and noise characteristics). A similar step may be performed with the differences of phase observations between subsequent epochs. Using an analogous procedure as in the case of code observations we may generate phase files with all cycle slips flagged or, in the case of “small-area” arrays, even with cycle slips repaired. Both steps, phase and code cleaning, are performed in the same program unit. We discuss this new development and present first results and applications using data from the AGNES (Automated GPS Network Switzerland) and the IGS (International GPS Service) Networks.

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission using close formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model (DEM) with 2 m height precision and 10 m ground resolution from the configurable SAR interferometer with space baselines of a few hundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the two satellites must be determined with an accuracy of 1 mm (1D RMS) from GPS measurements collected by the onboard receivers. The operational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences (GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysis strategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Institute of the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW). Dual-frequency baseline solutions are compared for a 1-month test period in January 2011. Differences of reduced-dynamic baseline solutions exhibit a representative standard deviation (STD) of 1 mm outside maneuver periods, while biases are below 1 mm in all directions. The achieved baseline determination performance is close to the mission specification, but independent SAR calibration data takes acquired over areas with a well known DEM from previous missions will be required to fully meet the 1 mm 1D RMS target. Besides the operational solutions, single-frequency baseline solutions are tested. They benefit from a more robust ambiguity fixing and show a slightly better agreement of below 1 mm STD, but are potentially affected by errors caused by an incomplete compensation of differential ionospheric path delays.

The first ESA (European Space Agency) Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched on 17 March 2009 into a sun-synchronous dusk–dawn orbit with an exceptionally low initial altitude of about 280 km. The onboard 12-channel dual-frequency GPS (Global Positioning System) receiver delivers 1 Hz data, which provides the basis for precise orbit determination (POD) for such a very low orbiting satellite. As part of the European GOCE Gravity Consortium the Astronomical Institute of the University of Bern and the Department of Earth Observation and Space Systems are responsible for the orbit determination of the GOCE satellite within the GOCE High-level Processing Facility. Both quick-look (rapid) and very precise orbit solutions are produced with typical latencies of 1 day and 2 weeks, respectively. This article summarizes the special characteristics of the GOCE GPS data, presents POD results for about 2 months of data, and shows that both latency and accuracy requirements are met. Satellite Laser Ranging validation shows that an accuracy of 4 and 7 cm is achieved for the reduced-dynamic and kinematic Rapid Science Orbit solutions, respectively. The validation of the reduced-dynamic and kinematic Precise Science Orbit solutions is at a level of about 2 cm.

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).

Precise orbit determination for low Earth orbiting (LEO) satellites using the global positioning system (GPS) is usually done in a post-processing mode introducing GPS satellite orbits and clock corrections. Depending on the mission objectives, the latency and required accuracy of precise LEO orbit information can vary significantly. Near real-time (NRT) orbits for certain geodetic missions (e.g. atmospheric sounding or altimetry) may require accuracy down to 10 cm (radial) or 0.1 mm s − 1 (along-track) and with a latency of less than 2–3 hours after the GPS measurements have been taken on the satellite. In order to fulfill such a demand in NRT, it is crucial that GPS orbit and clock products are available within the desired time frame and with adequate accuracy. In response to the demanding NRT processing for future geodetic satellite missions (i.e. ESA's Sentinel series), the Astronomical Institute of the University of Bern (AIUB) and Deutsches Zentrum fur Luft- und Raumfahrt (DLR) have made an effort in finding an alternative approach to obtain high-rate NRT GPS orbit and clock solutions by way of GPS clock corrections estimation. A realistic NRT orbit determination (OD) scenario has been simulated in this joint-study assuming a radial orbit accuracy of 10 cm and of 3 hours latency for the orbit product. A summary of all currently available NRT GPS orbit and clock products and a description of the generation of NRT GPS clock corrections are given in detail in this paper. The estimated GPS clock corrections are validated with a kinematic precise point positioning (PPP) for static ground stations. For direct evaluation of this innovative approach on the LEO orbits, the resultant merged high-rate NRT GPS product was tested using GPS data from the GRACE (Gravity Recover And Climate Experiment) mission. The results from the NRT simulation show promising aspect of such a concept to achieve unprecedented LEO orbit accuracy in NRT.

Apart from the gradiometer as the core instrument, the first ESA Earth Explorer Core Mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) will carry a 12-channel GPS receiver dedicated for precise orbit determination (POD) of the satellite. The EGG-C (European GOCE Gravity-Consortium), led by the Technical University in Munich, is building the GOCE HPF (High-level Processing Facility) dedicated to the Level 1b to Level 2 data processing. One of the tasks of this facility is the computation of the Precise Science Orbit (PSO) for GOCE. The PSO includes a reduced-dynamic and a kinematic orbit solution. The baseline for the PSO is a zero-difference procedure using GPS satellite orbits, clocks, and Earth Rotation Parameters (ERPs) from CODE (Center for Orbit Determination in Europe), one of the IGS (International GNSS Service) Analysis Centers. The scheme for reduced-dynamic and kinematic orbit determination is based on experiences gained from CHAMP and GRACE POD and is realized in one processing flow. Particular emphasis is put on maximum consistency in the analysis of day boundary overlapping orbital arcs, as well as on the higher data sampling rate with respect to CHAMP and GRACE and on differences originating from different GPS antenna configurations. We focus on the description of the procedure used for the two different orbit determinations and on the validation of the procedure using real data from the two GRACE satellites as well as simulated GOCE data.

The classic theory of secularization of the industrialized West refers to two dimensions: First, it means the institutional and juridical separation of state and church, which led to a decline of the impact the institution Church has in modern societies. Second, it means a decrease of religion as a category of orientation for the individual as well as the collective conduct of life. While the first aspect of this thesis is hardly being disputed today, criticism basically focuses on the assertion that the conduct of life of modern people has been secularized. The Anglo-Saxon scene has become the centre of this debate: while the British tradition defends the secularization thesis, the contemporary American Sociology of Religion finds so much empirical evidence against secularization that it wants to abolish the concept altogether.

Reduced-dynamic orbit determination for spaceborne GPS receivers is a method promising highest accuracy of the estimated LEO trajectories. We compare the performance of different pseudo-stochastic orbit parametrizations (instantaneous velocity changes and piecewise constant accelerations) and probe the range between dynamic and heavily reduced dynamic orbits. Internal indicators like formal accuracies of orbit positions, comparisons with orbits computed at the Technical University of Munich (TUM), and validations with SLR measurements are used to assess the quality of the estimated orbits. For piecewise constant accelerations comparisons between the estimated and the measured accelerations from the STAR accelerometer allow for an additional and independent validation of the estimated orbits.

Using an efficient and robust combination of a kinematic and reduced-dynamic orbit determination procedure CHAMP GPS data spanning about eleven months are processed and different aspects are addressed. Kinematic solutions are generated with and without elevation-dependent weighting of the observations in order to study the impact on the solution. GPS clock corrections with a sampling rate of 30 seconds and of 5 minutes, both interpolated to 10 seconds, are used. The orbit results are compared with the Post-processed Science Orbits from the GeoForschungsZentrum Potsdam, Germany, with orbit solutions from the Technical University of Munich, Germany, and they are validated with SLR measurements.

With an increasing number of satellites carrying reliable GPS receivers orbit determination using the high precision and uninterrupted GPS tracking technique gains increasing attention. Different from other approaches for generating kinematic satellite trajectories based on zero- or double-differenced GPS observations the procedure developed at our institute uses zero-differences with differences from epoch to epoch for the phase observable. The approach is very efficient due to the elimination of the phase ambiguities. In addition it includes a sophisticated data cleaning procedure. It may also be applied to objects moving on other than Earth-orbiting trajectories.

Kinematic point positioning of a Low Earth Orbiter (LEO) using GPS data is one possibility to get precise orbit information. This approach is followed at the Astronomical Institute of the University of Bern (AIUB) as an alternative to the dynamical orbit determination. Kinematic point positioning allows to recover the trajectory of the LEO without making use of any a priori gravity field information. This may be very useful for gravity field recovery, in particular in view of present and upcoming satellite missions like CHAMP, GRACE and GOCE which all have an accelerometer on board.