The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler etal. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CM

The new COST-G deterministic signal model

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

On the co-estimation of static and monthly gravity field solutions from GRACE Follow-On data

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 Earthâ?Ts gravity field. Associated to this, the spherical harmonic series has to be truncated at a certain point, commonly at degree/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