利用GOCE卫星轨道数据恢复地球重力场模型方法的分析

欧空局早期公布的时域法和空域法解算的GOCE模型均采用能量守恒法处理轨道数据, 但恢复的长波重力场信号精度较低, 而且GOCE卫星在两极存在数据空白, 利用其观测数据恢复重力场模型是一个不适定问题, 导致解算的模型带谐项精度较低, 需进行正则化处理。本文分析了基于轨道数据恢复重力场模型的方法用于处理GOCE数据的精度, 对最优正则化方法和参数的选择进行研究。利用GOCE卫星2009-11-01—2010-01-31共92 d的精密轨道数据, 采用不依赖先验信息的能量守恒法、短弧积分法和平均加速度法恢复GOCE重力场模型, 利用Tikhonov正则化技术处理病态问题。结果表明, 平均加速度法恢复模型的精度最高, 能量守恒法的精度最低, 短弧积分法的精度稍差于平均加速度法。未来联合处理轨道和梯度数据时, 建议采用平均加速度法或短弧积分法处理轨道数据, 并且轨道数据可有效恢复120阶次左右的模型。Kaula正则化和SOT处理GOCE病态问题的效果最好, 并且两者对应的最优正则化参数基本一致, 但利用正则化技术不能完全抑制极空白问题的影响, 需要联合GRACE等其他数据才能获得理想的结果。     

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。     

Degradation of Geopotential Recovery from Short Repeat-Cycle Orbits: Application to GRACE Monthly Fields

Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120× 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 × 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution L × L requires the number of orbit-revolutions-to-repeat to be greater than 2L.     

Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions

A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water storage variation by GOCE gradiometer is equivocal even after localization.     

Regularization of geopotential determination from satellite data by variance components

 Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large linear systems. The posterior density function for the variance components, weighting factors and regularization parameters are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach. Received: 5 June 2001 / Accepted: 28 November 2001     

Precise orbit determination for the GRACE mission using only GPS data

The GRACE (gravity recovery and climate experiment) satellites, launched in March 2002, are each equipped with a BlackJack GPS onboard receiver for precise orbit determination and gravity field recovery. Since launch, there have been significant improvements in the background force models used for satellite orbit determination, most notably the model for the geopotential. This has resulted in significant improvements to orbit accuracy for very low altitude satellites. The purpose of this paper is to investigate how well the orbits of the GRACE satellites (about 470 km in altitude) can currently be determined using only GPS data and based on the current models and methods. The orbit accuracy is assessed using a number of tests, which include analysis of orbit fits, orbit overlaps, orbit connecting points, satellite Laser ranging residuals and K-band ranging (KBR) residuals. We show that 1-cm radial orbit accuracy for the GRACE satellites has probably been achieved. These precise GRACE orbits can be used for such purposes as improving gravity recovery from the GRACE KBR data and for atmospheric profiling, and they demonstrate the quality of the background force models being used.     

Geocenter variations derived from GPS tracking of the GRACE satellites

Two 4.5-year sets of daily geocenter variations have been derived from GPS-LEO (Low-Earth Orbiter) tracking of the GRACE (Gravity Recovery And Climate Experiment) satellites. The twin GRACE satellites, launched in March 2002, are each equipped with a BlackJack global positioning system (GPS) receiver for precise orbit determination and gravity recovery. Since launch, there have been significant improvements in the background force models used for satellite orbit determination, most notably the model for the geopotential, which has resulted in significant improvements to the orbit determination accuracy. The purpose of this paper is to investigate the potential for determining seasonal (annual and semiannual) geocenter variations using GPS-LEO tracking data from the GRACE twin satellites. Internal comparison between the GRACE-A and GRACE-B derived geocenter variations shows good agreement. In addition, the annual and semiannual variations of geocenter motions determined from this study have been compared with other space geodetic solutions and predictions from geophysical models. The comparisons show good agreement except for the phase of the z-translation component.     

Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons

Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved.     

First GOCE gravity field models derived by three different approaches

Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analysed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared with combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITG-Grace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-month GOCE gravity field models of 10?cm in terms of geoid heights, and 3?mGal in terms of gravity anomalies, globally at a resolution of 100?km (degree/order 200).     

Short-arc analysis of intersatellite tracking data in a gravity mapping mission

 A technique for the analysis of low–low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple-data-type solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum by orders of magnitude. Received: 26 June 2001 / Accepted: 21 January 2002     

The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value

We present a global static model of the Earth’s gravity field entitled DGM-1S based on GRACE and GOCE data. The collection of used data sets includes nearly 7 years of GRACE KBR data and 10 months of GOCE gravity gradient data. The KBR data are transformed with a 3-point differentiation into quantities that are approximately inter-satellite accelerations. Gravity gradients are processed in the instrumental frame. Noise is handled with a frequency-dependent data weighting. DGM-1S is complete to spherical harmonic degree 250 with a Kaula regularization being applied above degree 179. Its performance is compared with a number of other satellite-only GRACE/GOCE models by confronting them with (i) an independent model of the oceanic mean dynamic topography, and (ii) independent KBR and gravity gradient data. The tests reveal a competitive quality for DGM-1S. Importantly, we study added value of GOCE data by comparing the performance of satellite-only GRACE/GOCE models with models produced without GOCE data: either ITG-Grace2010s or EGM2008 depending on which of the two performs better in a given region. The test executed based on independent gravity gradients quantifies this added value as 25–38 % in the continental areas poorly covered with terrestrial gravimetry data (Equatorial Africa, Himalayas, and South America), 7–17 % in those with a good coverage with these data (Australia, North America, and North Eurasia), and 14 % in the oceans. This added value is shown to be almost entirely related to coefficients below degree 200. It is shown that this gain must be entirely attributed to gravity gradients acquired by the mission. The test executed based on an independent model of the mean dynamic topography suggests that problems still seem to exist in satellite-only GRACE/GOCE models over the Pacific ocean, where noticeable deviations between these models and EGM2008 are detected, too.     

GPS-derived orbits for the GOCE satellite

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.     

GOCE卫星重力梯度校准与无阻尼控制效果分析

GOCE卫星是首颗搭载高精度梯度仪,通过加速度计差分测量确定地球重力场的现代重力卫星。该卫星设计为无阻尼飞行状态（沿轨方向）,加速度计并未安置在卫星质心,这些特点使得GOCE与标准的卫星跟踪卫星重力测量模式有着显著的区别。本文首先指出GOCE任务中普通模式加速度校准存在不严密性问题,并提出了分别校准6个加速度计,分离偏差参数的方案。利用GOCE任务期内的几何法精密轨道,采用动力法完成校准,并分析了无阻尼控制的效果,发现：①虽然GOCE所在轨道高度的中性大气密度较GRACE高两到三个量级,但GOCE卫星在沿轨方向的残余非保守力比GRACE卫星的对应分量小一个量级,充分显示了无阻尼控制系统的补偿效果;②通过精密轨道内插的轨道速度与动力法轨道速度的比较可以得出,卫星无阻尼控制系统对GOCE卫星速度的显著影响;③计算了GOCE卫星所受的非保守力。获得了GOCE任务期间的加速度计校准参数,并讨论了利用其辅助重力梯度仪数据预处理的可能方法。     

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry,altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.     

Mission design,operation and exploitation of the gravity field and steady-state ocean circulation explorer mission

The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March 2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS) heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter. In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users.     

Numerical study on the mixed model in the GOCE polar gap problem

Gravity gradients acquired by the Gravity field and steady-state Ocean Circulation Explorer(GOCE) do not cover the entire earth because of its sun-synchronous orbit leaving data gaps with a radius of about 6.5° in the polar regions.Previous studies showed that the loss of data in the polar regions deteriorates the accuracy of the low order(or near zonal) coefficients of the earth gravity model,which is the so-called polar gap problem in geodesy.In order to find a stable solution for the earth gravity model from the GOCE gravity gradients,three models,i.e.the Gauss-Markov model,light constraint model and the mixed model,are compared and evaluated numerically with the gravity gradient simulated with the EGM2008.The comparison shows that the Best Linear Uniformly Unbiased Estimation(BLUUE) estimator of the mixed model can solve the polar gap problem as effectively as the light constraint model;furthermore,the mixed model is more rigorous in dealing with the supplementary information and leads to a better accuracy in determining the global geoid.     

GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE

 A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient to support the GOCE gravity mission and in particular its gravity gradiometer. Received: 21 January 2000 / Accepted: 4 July 2000     

现代低轨卫星对地球重力场探测的实践和进展

综述了现代低轨卫星对地球重力场测量的特点和近况，介绍了已经和即将发射的重力卫星CHAMP、GRACE、GOCE和新型测高卫星，讨论了作为现代重力卫星首次实践－－CHAMP卫星的进展和目前尚待解决的问题。     

Efficient gravity field recovery from GOCE gravity gradient observations

 An efficient algorithm is proposed for gravity field recovery from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravity gradient observations. The mathematical model is formulated in the time domain, which allows the inclusion of realistic observational noise models. The algorithm combines the iterative solution of the normal equations, using a Richardson-type iteration scheme, with the fast computation of the right-hand side of the normal equations in each iteration step by a suitable approximation of the design matrix. The convergence of the iteration is investigated, error estimates are provided, and the unbiasedness of the method is proved. It is also shown that the method does not converge to the solution of the normal equations. The performance of the approach for white noise and coloured noise is demonstrated along a simulated GOCE orbit up to spherical harmonic degree and order 180. The results also indicate that the approximation error may be neglected. Received: 30 November 1999 / Accepted: 31 May 2000