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1.
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 相似文献
2.
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. 相似文献
3.
First GOCE gravity field models derived by three different approaches 总被引：28，自引：10，他引：18
Roland Pail Sean Bruinsma Federica Migliaccio Christoph F?rste Helmut Goiginger Wolf-Dieter Schuh Eduard H?ck Mirko Reguzzoni Jan Martin Brockmann Oleg Abrikosov Martin Veicherts Thomas Fecher Reinhard Mayrhofer Ina Krasbutter Fernando Sans�� Carl Christian Tscherning 《Journal of Geodesy》2011,85(11):819-843
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). 相似文献
4.
Johannes Bouman Sietse Rispens Thomas Gruber Radboud Koop Ernst Schrama Pieter Visser Carl Christian Tscherning Martin Veicherts 《Journal of Geodesy》2009,83(7):659-678
One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the
gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight
using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity
field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate
the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information
and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally
below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute
deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different
methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate
for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results
are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method
uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow
to estimate gravity gradient scale factors down to the 10−3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity
gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10−2 level with this method. 相似文献
5.
从球冠谐理论出发,详细推导了球冠坐标系下扰动重力梯度的无奇异性计算公式。基于Tikhonov正则化方法,利用GOCE卫星实际观测数据解算局部重力场球冠谐模型。数值计算表明,基于扰动重力梯度的球冠谐分析建模方法能够有效地恢复局部重力场中的短波信号,与GO_CONS_GCF_2_DIR_R5模型的差异在±0.3×10~(-5) m/s~2水平。 相似文献
6.
根据经典的球谐函数方法,为满足正交化要求,观测数据需要覆盖整个球面,而对于地表局部测量数据,则无法应用球谐方法解算重力场模型。针对此问题,采用Slepian局部谱分析方法解算中国大陆范围内的实测重力场变化数据,并以GOCE卫星球谐函数解作为已知模型,评估由于实际陆地重力测点的非均匀分布对球谐函数解的误差影响。通过计算多个阶次中国大陆局部范围的Slepian基函数分布;采用GOCE卫星获得重力场模型的前72阶球谐系数作为已知结果,评价实际测点非均匀分布的解算有效性,并针对中国大陆地区采用Slepian基函数进行解算,通过模型对比选择最优截段项数;针对2005—2008年中国大陆地区流动重力测量获得的重力场变化信号进行解算,获得了72阶重力场变化模型。 相似文献
7.
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. 相似文献
8.
GOCE采用的高低卫-卫跟踪和卫星重力梯度测量技术在恢复重力场方面各有所长并互为补充,如何有效利用这两类观测数据最优确定地球重力场是GOCE重力场反演的关键问题。本文研究了联合高低卫-卫跟踪和卫星重力梯度数据恢复地球重力场的最小二乘谱组合法,基于球谐分析方法推导并建立了卫星轨道面扰动位T和径向重力梯度Tzz、以及扰动位T和重力梯度分量组合{Tzz-Txx-Tyy}的谱组合计算模型与误差估计公式。数值模拟结果表明,谱组合计算模型可以有效顾及各类数据的精度和频谱特性进行最优联合求解。采用61天GOCE实测数据反演的两个180阶次地球重力场模型WHU_GOCE_SC01S（扰动位和径向重力梯度数据求解）和WHU_GOCE_SC02S（扰动位和重力梯度分量组合数据求解）,结果显示后者精度优于前者,并且它们的整体精度优于GOCE时域解,而与GOCE空域解的精度接近,验证了谱组合法的可行性与有效性。 相似文献
9.
Evaluation of the first GOCE static gravity field models using terrestrial gravity,vertical deflections and EGM2008 quasigeoid heights 总被引：1，自引：1，他引：0
Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected
by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that
GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data
for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial
gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth
data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their
spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual
terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis
of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different
GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy,
we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows
location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data
sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185
in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The
results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge
of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South
America and Antarctica, in comparison with the pre-GOCE-era. 相似文献
10.
Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons 总被引：6，自引：3，他引：3
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. 相似文献
11.
Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach 总被引：1，自引：0，他引：1
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters. 相似文献
12.
Energy integral method for gravity field determination from satellite orbit coordinates 总被引：22，自引：1，他引：21
A fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully. The method is based on energy conservation and avoids problems related to orbit dynamics and initial state. In addition, the particular geometry of a repeat orbit is exploited by using a very efficient iterative estimation scheme, in which a set of normal equations is approximated by a sparse block-diagonal equivalent. Recovery experiments for spherical harmonic gravity field models up to degree and order 80 and 120 were conducted based on a 29-day simulated data set of orbit coordinates. The method was found to be very flexible and could be easily adapted to include observations of non-conservative accelerations, such as (to be) provided by satellites like CHAMP, GRACE, and GOCE. A serious drawback of the method is its large sensitivity to satellite velocity errors. Existing orbit determination strategies need to be altered or augmented to include algorithms that focus on optimizing the accuracy of estimated velocities. 相似文献
13.
Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally
adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential
recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential.
The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus,
we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients,
in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly,
the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization
and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization
by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly,
the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level
of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the
fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state
Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process
converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive
to the synthesis of unobserved gravity gradients. 相似文献
14.
Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition 总被引：3，自引：0，他引：3
We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach
is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm
for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and
block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure.
Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the
algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation
of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime
results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming
satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month
of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations
and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion
strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development
stage, the LSQR method appears ready to deal with real-data applications. 相似文献
15.
Space-wise approach to satellite gravity field determination in the presence of coloured noise 总被引：2，自引：2，他引：2
For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed. 相似文献
16.
Johannes Bouman 《Journal of Geodesy》2012,86(4):287-304
The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection
of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations
have found application in satellite altimetry with the implicit assumption that the neglected terms—using remove-restore—are
sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are
made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives
in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives
on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements
on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity
gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected
terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted
for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small
when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical
approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it
appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the
vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term
is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite
altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case
the curvilinear term is needed, which is not readily available. 相似文献
17.
18.
Exploring the possibilities for star-tracker assisted calibration of the six individual GOCE accelerometers 总被引：1，自引：0，他引：1
P. N. A. M. Visser 《Journal of Geodesy》2008,82(10):591-600
A method has been developed and tested for estimating calibration parameters for the six accelerometers on board the Gravity
field and steady-state Ocean Circulation Explorer (GOCE) from star tracker observations. These six accelerometers are part
of the gradiometer, which is the prime instrument on board GOCE. It will be shown that by taking appropriate combinations
of observations collected by the accelerometers, by modeling acceleration terms caused by gravity gradients from an a priori
low-degree spherical harmonic expansion, and by modeling rotational acceleration terms derived from star-tracker observations,
scale factors of each of the accelerometers can be estimated for each axis. Simulated observations from a so-called end-to-end
simulator were used to test the method. This end-to-end simulator includes a detailed model of the GOCE satellite, its instruments
and instrument errors, and its environment. Results of the tests indicate that scale factors of all six accelerometers can
be determined with an accuracy of around 0.01 for all components on a daily basis. 相似文献
19.
The use of sampling-based Monte Carlo methods for the computation and propagation of large covariance matrices in geodetic applications is investigated. In particular, the so-called Gibbs sampler, and its use in deriving covariance matrices by Monte Carlo integration, and in linear and nonlinear error propagation studies, is discussed. Modifications of this technique are given which improve in efficiency in situations where estimated parameters are highly correlated and normal matrices appear as ill-conditioned. This is a situation frequently encountered in satellite gravity field modelling. A synthetic experiment, where covariance matrices for spherical harmonic coefficients are estimated and propagated to geoid height covariance matrices, is described. In this case, the generated samples correspond to random realizations of errors of a gravity field model.
AcknowledgementsThe authors are indebted to Pieter Visser and Pavel Ditmar for providing simulation output that was used in the GOCE error generation experiments. Furthermore, the NASA/NIMA/OSU team is acknowledged for providing public ftp access to the EGM96 error covariance matrix. The two anonymous reviewers are thanked for their valuable comments. 相似文献
20.
不同于当前广泛使用的空域法、时域法、直接解法,本文尝试采用Torus方法处理GOCE实测数据,利用71 d的GOCE卫星引力梯度数据反演了200阶次GOCE地球重力场模型,实现了对参考模型的精化。首先,采用Butterworth零相移滤波方法加移去—恢复技术,处理引力梯度观测值中的有色噪声,并利用泰勒级数展开和Kriging方法对GOCE卫星引力梯度数据进行归算和格网化,计算得到了名义轨道上格网点处的引力梯度数据。然后,利用2D-FFT技术和块对角最小二乘方法处理名义轨道上数据,获得了200阶次的GOCE地球重力场模型GOCE_Torus。利用中国和美国的GPS/水准数据进行外部检核结果说明,GOCE_Torus与ESA发布的同期模型的精度相当;GOCE_Torus模型与200阶次的EGM2008模型相比,在美国区域精度相当,但在中国区域精度提高了4.6 cm,这充分体现了GOCE卫星观测数据对地面重力稀疏区的贡献。Torus方法拥有快速高精度反演卫星重力场模型的优势,可以在重力梯度卫星的设计、误差分析及在轨快速评估等方面得到充分应用。 相似文献