Gravity Field Recovery Research Articles

HY-2A Altimeter Data Initial Assessment and Corresponding Two-Pass Waveform Retracker

The accuracy and resolution of the marine gravity field derived from multisatellite altimeter data sets mainly depend on the corresponding range precision and spatial distribution. Here, we preliminarily investigate the performance of HY-2A altimeter data by analyzing cross-mission sea surface height discrepancies with SARAL/AltiKa and calculating correlation coefficients with respect to tide gauge measurements. We also explore the improved range precision that can be achieved using a two-pass weighted least squares retracker which was proposed for the purpose of optimal gravity field recovery. Firstly, both the exact repetitive mission and the geodetic mission for HY-2A provide new track orientations and different data coverage for recovering the marine gravity field, and these dense geographical distributions are more greatly attributed to the geodetic mission in recent years. Secondly, HY-2A provides reliable sea surface height measurements based on exterior verifications by SARAL/AltiKa geophysical data records and tide gauge measurements, although the accuracy level is slightly lower than SARAL/AltiKa. Another more exciting finding is that the statistics of along-track sea surface heights in one-second intervals show that the two-pass retracking does further improve the range precision by a factor of 1.6 with respect to 20 Hz retracked results in sensor data records. In conclusion, the HY-2A mission can substantially improve the global accuracy and resolution of the marine gravity field and will reveal new tectonic features such as microplates, abyssal hill fabric, and new uncharted seamounts on the ocean floor.

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

Influence of laser ranging on the accuracy of static gravity field recovery

Influence of laser ranging on the accuracy of static gravity field recovery

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

The prospects of future satellite gravimetry missions to sustain a continuous and improved observation of the gravitational field have stimulated studies of new concepts of space inertial sensors with potentially improved precision and stability. This is in particular the case for cold-atom interferometry (CAI) gradiometry which is the object of this paper. The performance of a specific CAI gradiometer design is studied here in terms of quality of the recovered gravity field through a closed-loop numerical simulation of the measurement and processing workflow. First we show that mapping the time-variable field on a monthly basis would require a noise level below 5mE/Hz. The mission scenarios are therefore focused on the static field, like GOCE. Second, the stringent requirement on the angular velocity of a one-arm gradiometer, which must not exceed 10-6 rad/s, leads to two possible modes of operation of the CAI gradiometer: the nadir and the quasi-inertial mode. In the nadir mode, which corresponds to the usual Earth-pointing satellite attitude, only the gradient Vyy, along the cross-track direction, is measured. In the quasi-inertial mode, the satellite attitude is approximately constant in the inertial reference frame and the 3 diagonal gradients Vxx,Vyy and Vzz are measured. Both modes are successively simulated for a 239 km altitude orbit and the error on the recovered gravity models eventually compared to GOCE solutions. We conclude that for the specific CAI gradiometer design assumed in this paper, only the quasi-inertial mode scenario would be able to significantly outperform GOCE results at the cost of technically challenging requirements on the orbit and attitude control.

Instrument data simulations for GRACE Follow-on: observation and noise models

Abstract. The Gravity Recovery and Climate Experiment (GRACE) mission has yielded data on the Earth's gravity field to monitor temporal changes for more than 15 years. The GRACE twin satellites use microwave ranging with micrometre precision to measure the distance variations between two satellites caused by the Earth's global gravitational field. GRACE Follow-on (GRACE-FO) will be the first satellite mission to use inter-satellite laser interferometry in space. The laser ranging instrument (LRI) will provide two additional measurements compared to the GRACE mission: interferometric inter-satellite ranging with nanometre precision and inter-satellite pointing information. We have designed a set of simulated GRACE-FO data, which include LRI measurements, apart from all other GRACE instrument data needed for the Earth's gravity field recovery. The simulated data files are publicly available via https://doi.org/10.22027/AMDC2 and can be used to derive gravity field solutions like from GRACE data. This paper describes the scientific basis and technical approaches used to simulate the GRACE-FO instrument data.

Gravity field recovery from orbit information using the Lagrange formalism

Gravity field reconstruction via the analysis of kinematic orbit positions has been proven to provide essential information for Earth system research purposes. For this aim, various approaches have been developed and applied to exploit kinematic orbits. In addition to those existing methods, in this paper we present a new technique. By means of a series of simulation studies we demonstrate that the novel method is comparable with the hitherto proposed techniques. As the main difference with existing methods, our approach is based on the so-called Lagrange coefficients, i.e., a semi-analytical description of the satellite motion. For this reason, we denote the technique to as the Lagrange formalism. The low sensitivity to the priori information about the gravity field, and less influence of the polar gap are of its characteristics. The investigations demonstrate that the idea of the Lagrange method in determining the Earth's gravity field could represent comparable results in term of quality with other approaches.

Research and Development of Electrostatic Accelerometers for Space Science Missions at HUST

High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.

Regional gravity field recovery using the GOCE gravity gradient tensor and heterogeneous gravimetry and altimetry data

AbstractA regional approach using Poisson wavelets is applied for gravity field recovery using the GOCE (Gravity Field and Steady‐State Ocean Circulation Explorer) gravity gradient tensor, heterogeneous gravimetry data, and altimetry measurements. The added value to the regional model introduced by GOCE data is validated and quantified. The performances of the solutions modeled with different diagonal components of GOCE data and their combinations are investigated. Numerical experiments in a region in Europe show that the effects introduced by GOCE data demonstrate long‐wavelength patterns on the centimeter scale in terms of quasi‐geoid heights, which may allow reducing the remaining long‐wavelength errors in ground‐based data, and improve the regional model. The accuracy of the gravimetric quasi‐geoid computed with a combination of three diagonal components is improved by 0.6 cm (0.5 cm) in the Netherlands (Belgium) compared to that derived from gravimetry and altimetry data alone, when GOCO05s is used as the reference model. Moreover, the added value from GOCE data reduces the mean values of the misfit between the gravimetric solution and GPS/leveling data. Performances of different components and their combinations are not identical, and the solution with vertical gradients is best when a single component is used. The incorporation of multiple components shows further improvements, and the combination of three components best fits the local GPS/leveling data. Further comparison shows that our solution is the highest quality and may be substituted for existing models for engineering purposes and geophysical investigations over the target area.

Independent Mars spacecraft precise orbit determination software development and its applications

In this paper, we present an independent software for Mars spacecraft precise orbit determination and gravity field recovery we call the Mars Gravity Recovery and Analysis Software (MAGREAS), which is aimed to analyze tracking data from the Chinese Mars exploration mission and similar NASA and ESA Mars-related projects. The design structure, module distribution, and functions of the software are described in this manuscript. A detailed cross validation with the mature precise orbit determination platform Geodyn-II was done. Additionally, we use MAGREAS to process the MEX orbital tracking data with two-way and three-way tracking modes separately. Measurement residuals and the difference from the reconstructed ephemeris provided by Royal Observatory of Belgium indicate that our software is reliable. In addition to describe of our software and validate with Geodyn-II, we give a simulation case close to Chinese Mars exploration mission to indicate the application of our software. We present a simulation of a four-way tracking mode between Earth tracking station, Mars orbiter, and Mars lander to validate the effectiveness of our MAGREAS-based approach for Mars orbiter determination and lander positioning. Experimental results show that our proposed tracking mode significantly improves positioning accuracy. This work will provide a reference for the design of the Chinese Mars exploration mission as well as for the processing of Chinese Mars mission orbital tracking data.

Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses

Swarm is a European Space Agency (ESA) project that was launched on 22 November 2013, which consists of three Swarm satellites. Swarm precise orbits are essential to the success of the above project. This study investigates how well Swarm zero-differenced (ZD) reduced-dynamic orbit solutions can be determined using space-borne GPS data and optimized pseudo-stochastic pulses under high ionospheric activity. We choose Swarm space-borne GPS data from 1–25 October 2014, and Swarm reduced-dynamic orbits are obtained. Orbit quality is assessed by GPS phase observation residuals and compared with Precise Science Orbits (PSOs) released by ESA. Results show that pseudo-stochastic pulses with a time interval of 6 min and a priori standard deviation (STD) of 10−2 mm/s in radial (R), along-track (T) and cross-track (N) directions are optimized to Swarm ZD reduced-dynamic precise orbit determination (POD). During high ionospheric activity, the mean Root Mean Square (RMS) of Swarm GPS phase residuals is at 9–11 mm, Swarm orbit solutions are also compared with Swarm PSOs released by ESA and the accuracy of Swarm orbits can reach 2–4 cm in R, T and N directions. Independent Satellite Laser Ranging (SLR) validation indicates that Swarm reduced-dynamic orbits have an accuracy of 2–4 cm. Swarm-B orbit quality is better than those of Swarm-A and Swarm-C. The Swarm orbits can be applied to the geomagnetic, geoelectric and gravity field recovery.

Impact of tracking loop settings of the Swarm GPS receiver on gravity field recovery

The Swarm mission consists of three identical satellites equipped with GPS receivers and orbiting in near-polar low Earth orbits. Thus, they can be used to determine the Earth’s gravity field by means of high-low satellite-to-satellite tracking (hl-SST). However, first results by several groups have revealed systematic errors both in precise science orbits and resulting gravity field solutions which are caused by ionospheric disturbances affecting the quality of Swarm GPS observations. Looking at gravity field solutions, the errors lead to systematic artefacts located in two bands north and south of the geomagnetic equator. In order to reduce these artefacts, erroneous GPS observations can be identified and rejected before orbit and gravity field processing, but this may also lead to slight degradations of orbit and low degree gravity field coefficient quality. Since the problems were believed to be receiver-specific, the GPS tracking loop bandwidths onboard Swarm have been widened several times starting in May 2015. The influence of these tracking loop updates on Swarm orbits and, particularly, gravity field solutions is investigated in this work. The main findings are that the first updates increasing the bandwidth from 0.25 Hz to 0.5Hz help to significantly improve the quality of Swarm gravity fields and that the improvements are even larger than those achieved by GPS data rejection. It is also shown that these improvements are indeed due to an improved quality of GPS observations around the geomagnetic equator, and not due to missing observations in these regions. As the ionospheric activity is rather low in the most recent months, the effect of the tracking loop updates in summer 2016 cannot be properly assessed yet. Nevertheless, the quality of Swarm gravity field solutions has already improved after the first updates which is especially beneficial in view of filling the upcoming gap between the GRACE and GRACE Follow-on missions with hl-SST gravity products.

High-resolution regional gravity field recovery from Poisson wavelets using heterogeneous observational techniques

We adopt Poisson wavelets for regional gravity field recovery using data acquired from various observational techniques; the method combines data of different spatial resolutions and coverage, and various spectral contents and noise levels. For managing the ill-conditioned system, the performances of the zero- and first-order Tikhonov regularization approaches are investigated. Moreover, a direct approach is proposed to properly combine Global Positioning System (GPS)/leveling data with the gravimetric quasi-geoid/geoid, where GPS/leveling data are treated as an additional observation group to form a new functional model. In this manner, the quasi-geoid/geoid that fits the local leveling system can be computed in one step, and no post-processing (e.g., corrector surface or least squares collocation) procedures are needed. As a case study, we model a new reference surface over Hong Kong. The results show solutions with first-order regularization are better than those obtained from zero-order regularization, which indicates the former may be more preferable for regional gravity field modeling. The numerical results also demonstrate the gravimetric quasi-geoid/geoid and GPS/leveling data can be combined properly using this direct approach, where no systematic errors exist between these two data sets. A comparison with 61 independent GPS/leveling points shows the accuracy of the new geoid, HKGEOID-2016, is around 1.1 cm. Further evaluation demonstrates the new geoid has improved significantly compared to the original model, HKGEOID-2000, and the standard deviation for the differences between the observed and computed geoidal heights at all GPS/leveling points is reduced from 2.4 to 0.6 cm. Finally, we conclude HKGEOID-2016 can be substituted for HKGEOID-2000 for engineering purposes and geophysical investigations in Hong Kong.Graphical abstract.

Gravity field recovery in the framework of a Geodesy and Time Reference in Space (GETRIS)

The study “Geodesy and Time Reference in Space” (GETRIS), funded by European Space Agency (ESA), evaluates the potential and opportunities coming along with a global space-borne infrastructure for data transfer, clock synchronization and ranging. Gravity field recovery could be one of the first beneficiary applications of such an infrastructure. This paper analyzes and evaluates the two-way high-low satellite-to-satellite-tracking as a novel method and as a long-term perspective for the determination of the Earth’s gravitational field, using it as a synergy of one-way high-low combined with low-low satellite-to-satellite-tracking, in order to generate adequate de-aliasing products. First planned as a constellation of geostationary satellites, it turned out, that an integration of European Union Global Navigation Satellite System (Galileo) satellites (equipped with inter-Galileo links) into a Geostationary Earth Orbit (GEO) constellation would extend the capability of such a mission constellation remarkably. We report about simulations of different Galileo and Low Earth Orbiter (LEO) satellite constellations, computed using time variable geophysical background models, to determine temporal changes in the Earth’s gravitational field. Our work aims at an error analysis of this new satellite/instrument scenario by investigating the impact of different error sources. Compared to a low-low satellite-to-satellite-tracking mission, results show reduced temporal aliasing errors due to a more isotropic error behavior caused by an improved observation geometry, predominantly in near-radial direction within the inter-satellite-links, as well as the potential of an improved gravity recovery with higher spatial and temporal resolution. The major error contributors of temporal gravity retrieval are aliasing errors due to undersampling of high frequency signals (mainly atmosphere, ocean and ocean tides). In this context, we investigate adequate methods to reduce these errors. We vary the number of Galileo and LEO satellites and show reduced errors in the temporal gravity field solutions for this enhanced inter-satellite-links. Based on the GETRIS infrastructure, the multiplicity of satellites enables co-estimating short-period long-wavelength gravity field signals, indicating it as powerful method for non-tidal aliasing reduction.

Retracking of SARAL/AltiKa Radar Altimetry Waveforms for Optimal Gravity Field Recovery

ABSTRACTThe accuracy of the marine gravity field derived from satellite altimetry depends on dense track spacing as well as high range precision. Here, we investigate the range precision that can be achieved using a new shorter wavelength Ka-band altimeter AltiKa aboard the SARAL spacecraft. We agree with a previous study that found that the range precision given in the SARAL/AltiKa Geophysical Data Records is more precise than that of Ku-band altimeter by a factor of two. Moreover, we show that two-pass retracking can further improve the range precision by a factor of 1.7 with respect to the 40 Hz-retracked data (item of range_40 hz) provided in the Geophysical Data Records. The important conclusion is that a dedicated Ka-band altimeter-mapping mission could substantially improve the global accuracy of the marine gravity field with complete coverage and a track spacing of <6 km achievable in ∼1.3 years. This would reveal thousands of uncharted seamounts on the ocean floor as well as important tectonic features such as microplates and abyssal hill fabric.

Self-calibration method of the bias of a space electrostatic accelerometer.

The high precision space electrostatic accelerometer is an instrument to measure the non-gravitational forces acting on a spacecraft. It is one of the key payloads for satellite gravity measurements and space fundamental physics experiments. The measurement error of the accelerometer directly affects the precision of gravity field recovery for the earth. This paper analyzes the sources of the bias according to the operating principle and structural constitution of the space electrostatic accelerometer. Models of bias due to the asymmetry of the displacement sensing system, including the mechanical sensor head and the capacitance sensing circuit, and the asymmetry of the feedback control actuator circuit are described separately. According to the two models, a method of bias self-calibration by using only the accelerometer data is proposed, based on the feedback voltage data of the accelerometer before and after modulating the DC biasing voltage (Vb) applied on its test mass. Two types of accelerometer biases are evaluated separately using in-orbit measurement data of a space electrostatic accelerometer. Based on the preliminary analysis, the bias of the accelerometer onboard of an experiment satellite is evaluated to be around 10-4 m/s2, about 4 orders of magnitude greater than the noise limit. Finally, considering the two asymmetries, a comprehensive bias model is analyzed. A modified method to directly calibrate the accelerometer comprehensive bias is proposed.

Innovative optical power detection array system for relative positioning of inner-formation flying system

The Inner-formation flying system (IFFS) is conceived to feature a spherical proof mass falling freely within a large cavity for space gravity detection, of which first application focuses on the Earth’s gravity field recovery. For the IFFS, it is the relative position of the proof mass to its surrounding cavity that is feedback into thrusters for tracking control, even as part of data to detect gravity. Since the demonstration and verification of demanding technologies using small satellite platforms is a very sensible choice prior to detection mission, an optical power detection array system (OPDAS) is proposed to measure the relative position with advantages of low cost and high adaptability. Besides that, its large dynamic range can reduce the requirement for satellite platform and releasing mechanism, which is also an attracting trait for small satellite application. The concept of the OPDAS is firstly presented, followed by the algorithm to position the proof mass. Then the radiation pressure caused by the measuring beam is modeled, and its disturbance on the proof mass is simulated. The experimental system to test the performance of a prototype of the OPDAS is established, and the preliminary results show that a precision of less than 0.4 mm across a dynamic range of several centimeters can be reached by the prototype of the OPDAS.

The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016

For more than 14years, the Gravity Recovery and Climate Experiment (GRACE) mission has provided information about Earth’s gravity field with unprecedented accuracy. The twin satellites GRACE-A and GRACE-B are both equipped with a three-axis electrostatic accelerometer, measuring the non-gravitational forces acting on the spacecraft. In order to make use of the uncalibrated Level-1B accelerometer (ACC1B) data during gravity field recovery, bias and scale parameters have to be estimated.The proposed calibration method is a two-step approach and makes use of modeled non-conservative accelerations. The simulated non-conservative accelerations serve as reference for the a priori accelerometer calibration, i.e. for the ACC1B data. During gravity field recovery the calibration parameters are re-estimated. Several calibration parameters for the GRACE accelerometers using different methods have already been published. The aim of our study was primarily to analyze the temperature-dependent behavior of the accelerometer scale factors and biases, and the impact of the parametrization of scale factors and biases on the recovered gravity field solutions; but not to obtain calibrated accelerometer data.Within the ITSG-Grace2016 release, the accelerometer biases are estimated daily using uniform cubic basis splines (UCBS), the scale factors are also estimated daily using a fully-populated scale factor matrix. Therefore, not only the scale factors in along-track, cross-track, and radial direction are estimated, but also the non-orthogonality of the accelerometer axes (cross-talk) and the misalignment between the Accelerometer Frame (AF) and Science Reference Frame (SRF) are taken into account.The time evolution of the estimated calibration parameters over the whole GRACE period (2002-04 to 2016-01) shows a clear temperature-dependency for both scale factors and biases. Using this new approach, the estimates of the C20 coefficient significantly improve, with results now comparable to Satellite Laser Ranging (SLR) solutions. Based on the achieved results, we suggest the presence of a clear temperature-dependent behavior and the presence of off-diagonal elements in the accelerometer scale factor matrix.

Impact of Swarm GPS receiver updates on POD performance

The Swarm satellites are equipped with state-of-the-art Global Positioning System (GPS) receivers, which are used for the precise geolocation of the magnetic and electric field instruments, as well as for the determination of the Earth’s gravity field, the total electron content and low-frequency thermospheric neutral densities. The onboard GPS receivers deliver high-quality data with an almost continuous data rate. However, the receivers show a slightly degraded performance when flying over the geomagnetic poles and the geomagnetic equator, due to ionospheric scintillation. Furthermore, with only eight channels available for dual-frequency tracking, the amount of collected GPS tracking data is relatively low compared with various other missions. Therefore, several modifications have been implemented to the Swarm GPS receivers. To optimise the amount of collected GPS data, the GPS antenna elevation mask has slowly been reduced from 10° to 2°. To improve the robustness against ionospheric scintillation, the bandwidths of the GPS receiver tracking loops have been widened. Because these modifications were first implemented on Swarm-C, their impact can be assessed by a comparison with the close flying Swarm-A satellite. This shows that both modifications have a positive impact on the GPS receiver performance. The reduced elevation mask increases the amount of GPS tracking data by more than 3 %, while the updated tracking loops lead to around 1.3 % more observations and a significant reduction in tracking losses due to severe equatorial scintillation. The additional observations at low elevation angles increase the average noise of the carrier phase observations, but nonetheless slightly improve the resulting reduced-dynamic and kinematic orbit accuracy as shown by independent satellite laser ranging (SLR) validation. The more robust tracking loops significantly reduce the large carrier phase observation errors at the geomagnetic poles and along the geomagnetic equator and do not degrade the observations at midlatitudes. SLR validation indicates that the updated tracking loops also improve the reduced-dynamic and kinematic orbit accuracy. It is expected that the Swarm gravity field recovery will benefit from the improved kinematic orbit quality and potentially also from the expected improvement of the kinematic baseline determination and the anticipated reduction in the systematic gravity field errors along the geomagnetic equator. Finally, other satellites that carry GPS receivers that encounter similar disturbances might also benefit from this analysis.

A simulation of the Four-way lunar Lander–Orbiter tracking mode for the Chang’E-5 mission

The Chang’E-5 mission is the third phase of the Chinese Lunar Exploration Program and will collect and return lunar samples. After sampling, the Orbiter and the ascent vehicle will rendezvous and dock, and both spacecraft will require high precision orbit navigation. In this paper, we present a novel tracking mode—Four-way lunar Lander–Orbiter tracking that possibly can be employed during the Chang’E-5 mission. The mathematical formulas for the Four-way lunar Lander–Orbiter tracking mode are given and implemented in our newly-designed lunar spacecraft orbit determination and gravity field recovery software, the LUnar Gravity REcovery and Analysis Software/System (LUGREAS). The simulated observables permit analysis of the potential contribution Four-way lunar Lander–Orbiter tracking could make to precision orbit determination for the Orbiter. Our results show that the Four-way lunar Lander–Orbiter Range Rate has better geometric constraint on the orbit, and is more sensitive than the traditional two-way range rate that only tracks data between the Earth station and lunar Orbiter. After combining the Four-way lunar Lander–Orbiter Range Rate data with the traditional two-way range rate data and considering the Lander position error and lunar gravity field error, the accuracy of precision orbit determination for the Orbiter in the simulation was improved significantly, with the biggest improvement being one order of magnitude, and the Lander position could be constrained to sub-meter level. This new tracking mode could provide a reference for the Chang’E-5 mission and have enormous potential for the positioning of future lunar farside Lander due to its relay characteristic.

Orbit determination and gravity field recovery from Doppler tracking data to the Lunar Reconnaissance Orbiter

We present results for Precise Orbit Determination (POD) of the Lunar Reconnaissance Orbiter (LRO) based on two-way Doppler range-rates over a time span of ~13 months (January 3, 2011 to February 9, 2012). Different orbital arc lengths and various sets of empirical parameters were tested to seek optimal parametrization. An overlap analysis covering three months of Doppler data shows that the most precise orbits are obtained using an arc length of 2.5 days and estimating arc-wise constant empirical accelerations in along track direction. The overlap analysis over the entire investigated time span of 13 months indicates an orbital precision of 13.79m, 14.17m, and 1.28m in along track, cross track, and radial direction, respectively, with 21.32m in total position. We compare our orbits to the official science orbits released by the US National Aeronautics and Space Administration (NASA). The differences amount to 9.50m, 6.98m, and 1.50m in along track, cross track, and radial direction, respectively, as well as 12.71m in total position. Based on the reconstructed LRO orbits, we estimated lunar gravity field coefficients up to spherical harmonic degree and order 60. The results are compared to gravity field solutions derived from data collected by other lunar missions.