GOCE orbit predictions for SLR tracking

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 50m 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

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth's non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30

Highly-reduced dynamic orbits and their use for global gravity field recovery: A simulation study for GOCE

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 informatio

Propagation of atmospheric model errors to gravity potential harmonics—impact on GRACE de-aliasing

High-frequency, time-varying mass redistributions in the ocean and atmosphere have an impact on GRACE gravity field solutions due to the space-time sampling characteristics of signal and orbit. Consequently, aliasing of these signals into the GRACE observations is present and needs to be taken into account during data analysis by applying atmospheric and oceanic model data (de-aliasing). As the accuracy predicted prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties are regarded as a potential error source in GRACE gravity field determination. Therefore, this study aims to improve the de-aliasing process in order to obtain a more accurate GRACE gravity field time-series. As these time-series provide estimates for the integrated mass transport in the Earth system, like the global water cycle and solid Earth geophysical processes, any increase in accuracy will lead to improvements in the geophysical interpretation of the results. So in conclusion, improving the de-aliasing is of relevance for a better understanding of geophysical processes. By no longer regarding the atmosphere and ocean model output as error-free, deeper insight into the impact of such uncertainties on the de-aliasing and on the resulting GRACE gravity field models can be obtained. For this purpose, in a first step, a full error propagation of the atmospheric and oceanic model parameters up to the de-aliasing gravity field coefficients is performed and the GRACE K-Band-Satellite-to-Satellite Tracking (KBR-SST) residuals, as an intermediate gravity field result, are analysed. The paper reviews the standard GRACE de-aliasing process and presents the mathematical model applied for the error propagation. Specifically, the effect of uncertainties in the atmospheric input parameters (temperature, surface pressure, specific humidity, geopotential) on the gravity field potential coefficients used for de-aliasing is shown in several scenarios. Finally, the impact of de-aliasing products (with and without error propagation) on a GRACE gravity field solution is investigated on the level of observation residuals. From the results obtained in this study it can be concluded that with respect to the current GRACE error budget, atmospheric model uncertainties do not play a prominent role in the error budget of current GRACE gravity field solutions. Nevertheless, in order to fully exploit the GRACE measurements towards the baseline accuracy, an optimized de-aliasing is needed. In this case, GRACE gravity field solutions are sensitive to uncertainties in atmospheric and oceanic models. Thus, the associated geophysical model errors shall be taken into account in the de-aliasing proces

High-rate GPS clock corrections from CODE: support of 1Hz applications

GPS zero-difference applications with a sampling rate up to 1Hz 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 (<2h) 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 1Hz 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 5s may be linearly interpolated resulting in less than 2% degradation of accurac