Epochwise prediction of GPS single differenced ionospheric delays of formation flying spacecraft

Both single and dual frequency GPS relative navigation filters may benefit from proper predictions of single differenced ionospheric delays. In this article, the single differenced ionospheric delays of GPS observations are predicted for the GRACE formation during the switch manoeuvre.Two prediction methods are considered. The first is based on a Taylor expansion to first order of a mapping function that maps slant total electron content measurements to vertical total electron content estimates. The second method fits a shape profile through undifferenced ionospheric data available. It then raytraces through this profile to estimate the difference in total electron content along the path of the GPS signals.Continuously changing ionospheric conditions hamper the assessment of the quality of the predictions. Comparison of both methods shows that the raytracing method performs better. The difference of predictions and measurements generally shows a smaller RMS than the measurements alone. However, both methods suffer from a number of systematically unpredicted observations, which arise from small unaccounted differential variations in electron densities along the path of the GPS signals. These prediction methods perform better when spacecraft separation is small. Baselines considered here range from tens of kilometres down to several hundred metres. When smallest spacecraft separation occurs (0.4 km), the single differenced ionospheric delays exhibit RMS values of 0.0089 m. The first method shows a difference between measurements and predictions with an RMS of 0.0081 m. For the second method the difference RMS is found to be 0.0067 m.     

Performance of GPS-based accelerometry: A simulation experiment

Recent studies have shown that with the availability of high-quality CHAMP and GRACE gravity field models, it is feasible to determine accurate non-gravitational accelerations for low Earth orbiting satellites indirectly from precise GPS satellite-to-satellite observations. Possible applications of this so-called GPS-based accelerometry approach consist of accelerometer calibration and atmospheric density and wind computations. With the growing number of high-quality space-borne GPS receivers, this method could be applied to a large range of satellites. In this paper an extensive simulation study has been carried out, based on real accelerometer data from the GRACE mission, in order to determine the optimal processing strategy and the resulting accuracy of the estimated non-gravitational accelerations. It is shown that the optimal processing strategy consists of a piecewise linear parameterization of the estimated empirical accelerations, together with short 6-h orbit arcs. The GPS-based accelerometry approach makes use of triple-differenced GPS observations and the impact of considering the correlated observation noise was found to be marginal in the presence of other error sources such as GPS ephemeris errors. Using a priori non-gravitational force models improves the recovery of low temporal resolution accelerations, except during huge geomagnetic storms. With this strategy, non-gravitational accelerations can be recovered during high solar activity with an accuracy of better than 10% of the total signal in along-track direction and around 25–40% in cross-track direction, at time resolutions of around 8–20 min. During solar minimum conditions, the relative recovery error will increase to approximately 50% in along-track direction and around 60–70% in cross-track direction, due to the reduced atmospheric drag signal. Unfortunately, GPS-based accelerometry is hardly sensitive in the radial direction.     

Horizontal and vertical thermospheric cross-wind from GOCE linear and angular accelerations

Thermospheric wind measurements obtained from linear non-gravitational accelerations of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite show discrepancies when compared to ground-based measurements. In this paper the cross-wind is derived from both the linear and the angular accelerations using a newly developed iterative algorithm. The two resulting data sets are compared to test the validity of wind derived from angular accelerations and quantify the uncertainty in accelerometer-derived wind data. In general the difference is found to be less than 50?m/s vertically after high-pass filtering, and 100?m/s horizontally. A sensitivity analysis reveals that continuous thrusting is a major source of uncertainty in the torque-derived wind, as are the magnetic properties of the satellite. The energy accommodation coefficient is identified as a particularly promising parameter for improving the consistency of thermospheric cross-wind data sets in the future. The algorithm may be applied to obtain density and cross-wind from other satellite missions that lack accelerometer data, provided the attitude and orbit are known with sufficient accuracy.     

High-fidelity geometry models for improving the consistency of CHAMP,GRACE, GOCE and Swarm thermospheric density data sets

During the last two decades, accelerometers on board of the CHAMP, GRACE, GOCE and Swarm satellites have provided high-resolution thermosphere density data to improve our knowledge on atmospheric dynamics and coupling processes in the thermosphere-ionosphere region. Most users of the data have focused on relative density variations. Scale differences between datasets and models have been largely neglected or removed using ad hoc scale factors. The origin of these scale differences arises from errors in the aerodynamic modelling, specifically in the modelling of the satellite outer surface geometry and of the gas-surface interactions. Therefore, the first step to remove the scale differences is to enhance the geometry modelling. This work forms the foundation for the future improvement of characterization of satellite aerodynamics and gas-surface interactions models at TU Delft, as well as for extending the use of sideways and angular accelerations in the aerodynamic analysis of accelerations and derivation of thermosphere datasets. Although work to improve geometry and aerodynamic force models by other authors has focused on CHAMP and GRACE, this paper includes the GOCE and Swarm satellites as well. In addition, it uses a density determination algorithm that is valid for arbitrary attitude orientations, enabling a validation making use of attitude manoeuvres. The results show an improvement in the consistency of density data between these four missions, and of data obtained before, during and after attitude manoeuvres of CHAMP and Swarm. The new models result in larger densities, compared to the previously used panel method. The largest average rescaling of density, by switching to the new geometry models is reached for Swarm at 32%, the smallest for GRACE at 5%. For CHAMP and GOCE, mean differences of 11% and 9% are obtained respectively. In this paper, an overview of the improvements and comparisons of data sets is provided together with an introduction to the next research phase on the gas-surface interactions.     

The IGY and beyond: A brief history of ground-based cosmic-ray detectors

The state of art of ground-based cosmic-ray research from its discovery to present is reviewed. After discovery of cosmic rays by Hess in 1912, the nature of the primary and secondary radiation was established from recordings by a variety of instruments, sensitive to various components of cosmic rays and operated at different latitudes, longitudes and altitudes, including instruments carried by balloons. The IGY formalized international co-operation and coordinated study of cosmic rays, which is vital for meaningful interpretation of cosmic-ray data. Data collected at different geographic locations require an effective cutoff rigidity as a data ordering parameter. This parameter is obtained from tracing trajectories of primary cosmic rays in the Earth’s magnetic field. After 50 years the world’s neutron monitor network remains still the backbone for studying intensity variations of primary cosmic rays in the rigidity ranges between 1 and 15 GV, associated with transport and with transient events. Also the penetrating muon and neutrino components of secondary cosmic rays have a long history of recording and fundamental problem investigations. Valuable data about composition and spectrum of primary cosmic rays in ever increasing high-energy regions have been obtained during the years of investigations with various configurations and types of extensive air shower detectors. The culture of personal involvement of the physicist in carrying out experiments and data acquisition characterized the continued vitality of cosmic-ray investigations ranging from its atmospheric, geomagnetic and heliospheric transport through to its solar and astrophysical origins.     

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.     

Dynamic and non-dynamic ERS-1 radial orbit improvement from ERS-1/TOPEX dual-satellite altimetry

Dual-satellite altimeter crossover differences between ERS-1 and TOPEX/Poseidon have been included as supplementary tracking data in ERS-1 orbit computations from SLR and single-satellite crossover differences. It was found that including the dual-satellite crossover differences slightly improves the ERS-1 radial orbit accuracy of about 12 cm for orbits computed with the JGM-2 gravity field and also leads to a better ‘centering’ of the ERS-1 orbit in the terrestrial reference frame defined for TOPEX/Poseidon. In addition to this dynamic orbit improvement technique, a non-dynamic technique has been investigated that removes the larger part of the ERS-1 radial orbit error from the dual-satellite crossover difference residuals. For ERS-1 orbits computed with the GEM-T2 gravity field, it was found that the non-dynamic technique could improve the radial orbit accuracy from 140 cm to the same level of accuracy as the ERS-1 JGM-2 orbits.