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1.
地球重力场和海洋环流探测（gravity field and steady-state ocean circulation explorer,GOCE）卫星重力梯度数据有色噪声和低频系统误差的滤波处理是反演高精度地球重力场的一个关键问题。针对GOCE卫星重力梯度数据的滤波处理,基于移动平均（moving average,MA）方法和CPR(circle per revolution)经验参数方法设计了两类低频系统误差滤波器,并分别将这两类滤波器与基于自回归移动平均（auto-regressive and moving average,ARMA）模型设计的有色噪声滤波器组合起来形成级联滤波器。为了分析滤波器处理的实际效果,基于空域最小二乘法采用70 d的GOCE观测数据,并联合重力恢复与气候实验（gravity recovery and climate experiment,GRACE）数据分别反演了224阶次的重力场模型GOGR-MA(MA+ARMA级联滤波)和GOGR-CPR(CPR+ARMA级联滤波)。将反演模型与采用同期数据求解的第一代GOCE系列模型及GOCE和GRACE联合模... 相似文献
2.
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
3.
The GOCE satellite observes gravity gradients with unprecedented accuracy and resolution. The GOCE observations are reliable within a well-defined measurement bandwidth. In this study, different finite and infinite impulse response filters have been designed to obtain the demanded pass. Exhaustive time and frequency domain investigations prove that the proposed infinite impulse response filter can be a real competitor of the existing solution of the filtering problem. 相似文献
4.
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
5.
Alternative method for angular rate determination within the GOCE gradiometer processing 总被引：2，自引：1，他引：1
The most crucial part of the GOCE gradiometer processing is, besides the internal calibration of the gradiometer, the determination
of the satellite’s inertial angular rate. This paper describes a new method for the angular rate determination. It is based
on the stochastic properties of the GOCE star sensors and the gradiometer. The attitude information of both instrument types
is combined at the level of angular rates. The combination is done in the spectral domain by Wiener filtering, and thus using
an optimal relative weighting of the star sensor and gradiometer attitude information. Since the complete processing chain
from raw measurements to gravity field solutions is performed, the results are not only analyzed at the level of gravity gradients,
but also of gravity field solutions. Compared to the nominal method, already the resulting gravity gradients show a significantly
improved performance for the frequencies (mainly) below the gradiometer measurement bandwidth. This can be verified by analysis
of the gravity gradient trace. The improvement is propagated to the level of gravity field models, where a better accuracy
can be observed for selected groups of coefficients at characteristic bands at orders k × 16, with integer k, up to high harmonic degrees. 相似文献
6.
Christian Siemes 《Journal of Geodesy》2018,92(1):33-45
The GOCE gravity gradiometer measured highly accurate gravity gradients along the orbit during GOCE’s mission lifetime from March 17, 2009, to November 11, 2013. These measurements contain unique information on the gravity field at a spatial resolution of 80 km half wavelength, which is not provided to the same accuracy level by any other satellite mission now and in the foreseeable future. Unfortunately, the gravity gradient in cross-track direction is heavily perturbed in the regions around the geomagnetic poles. We show in this paper that the perturbing effect can be modeled accurately as a quadratic function of the non-gravitational acceleration of the satellite in cross-track direction. Most importantly, we can remove the perturbation from the cross-track gravity gradient to a great extent, which significantly improves the accuracy of the latter and offers opportunities for better scientific exploitation of the GOCE gravity gradient data set. 相似文献
7.
Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets 总被引：1，自引：0，他引：1
Jakob Flury 《Journal of Geodesy》2006,79(10-11):624-640
The GRACE (gravity recovery and climate experiment) and GOCE (gravity field and steady-state ocean circulation explorer) dedicated gravity satellite missions are expected to deliver the long-wavelength scales of the Earth’s gravity field with extreme precision. For many applications in Earth sciences, future research activities will have to focus on a similar precision on shorter scales not recovered by satellite missions. Here, we investigate the signal power of gravity anomalies at such short scales. We derive an average degree variance and power spectral density model for topography-reduced gravity anomalies (residual terrain model anomalies and de-trended refined Bouguer anomalies), which is valid for wavelengths between 0.7 and 100 km. The model is based on the analysis of gravity anomalies from 13 test regions in various geographical areas and geophysical settings, using various power spectrum computation approaches. The power of the derived average topography-reduced model is considerably lower than the Tscherning–Rapp free air anomaly model. The signal power of the individual test regions deviates from the obtained average model by less than a factor of 4 in terms of square-root power spectral amplitudes. Despite the topographic reduction, the highest signal power is found in mountainous areas and the lowest signal power in flat terrain. For the derived average power spectral model, a validation procedure is developed based on least-squares prediction tests. The validation shows that the model leads to a good prediction quality and realistic error measures. Therefore, for least-squares prediction, the model could replace the use of autocovariance functions derived from local or regional data. 相似文献
8.
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
9.
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
10.
11.
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
12.
Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface
from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy.
However, this implies combination of data with fundamentally different characteristics and different spatial resolutions.
Spectral consistency would imply the removal of the short-scale features of the altimetric sea surface height by filtering,
to provide altimetric data consistent with the resolution of the geoid field. The goal must be to lose as little as possible
from the high precision of the altimetric signal. Using a one-dimensional example we show how the spectrum is changing when
a function defined only on a limited domain (ocean in the real case) is extended or not as to cover the complete domain (the
whole sphere in the real case). The results depend on the spectral characteristics of the altimetric signal and of the applied
filter. Referring to the periodicity condition, as it is requested in the case of Fourier analysis, the action of the two
classical filters (Ideal Low Pass and Gauss filter) and of two alternative procedures (wavelets and Slepian) is studied. 相似文献
13.
卫星重力径向梯度数据的最小二乘配置调和分析 总被引：3，自引：2，他引：1
本文深入研究了利用卫星重力梯度径向分量确定地球引力场位系数的最小二乘配置(LSC)调和分析方法。首先论述了最小二乘配置法的原理,推导了扰动引力梯度观测量与球谐系数之间的协方差和自协方差矩阵,在扰动引力梯度观测数据为等经差规则网格数据的情况下,引力位与扰动引力梯度之间的协方差矩阵具有分块Toeplitz循环阵的结构,有效的利用FFT变换技术将其降阶;研究利用截断奇异值分解法（TSVD）解决协方差阵的病态性问题;最后得到了引力梯度径向分量的最小二乘配置调和分析的完整计算公式。模拟试算结果表明,基于TSVD的最小二乘配置调和分析方法,能够以较高的精度还原全球重力场,验证了本文算法的有效性和实用性。 相似文献
14.
利用最小二乘直接法反演卫星重力场模型的MPI并行算法 总被引：2，自引：0，他引：2
针对海量卫星重力数据反演高阶次地球重力场模型的密集型计算任务与高内存耗用问题,基于MPI实现了最小二乘直接法恢复高阶次位系数的并行算法。引入并行读写、分块存储与分块计算等方式完成了设计矩阵的构建、法方程的形成与求解等密集型计算任务的并行算法,数值计算结果表明三者的并行相对效率峰值可分别达到95%、68%、63%。利用GOCE轨道跟踪和径向扰动重力梯度数据(共518 400个历元)分别反演了120、240阶次地球重力场模型,计算时间仅为40 min、7 h,内存耗用峰值仅为290 MB、1.57 GB;采用与GOCE同等噪声水平的观测数据恢复的重力场模型精度与GOCE已发布模型的解算精度相一致,联合GRACE和GOCE的解算模型能够实现二者独立信息的频谱互补,表明本文方法可高效稳定地恢复高阶次地球重力场模型。 相似文献
15.
16.
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
17.
Monitoring GOCE gradiometer calibration parameters using accelerometer and star sensor data: methodology and first results 总被引：3，自引：1，他引：2
Christian Siemes Roger Haagmans Michael Kern Gernot Plank Rune Floberghagen 《Journal of Geodesy》2012,86(8):629-645
The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite, launched on 17 March 2009, is designed to measure the Earth’s mean gravity field with unprecedented accuracy at spatial resolutions down to 100?km. The accurate calibration of the gravity gradiometer on-board GOCE is of utmost importance for achieving the mission goals. ESA’s baseline method for the calibration uses star sensor and accelerometer data of a dedicated calibration procedure, which is executed every 2?months. In this paper, we describe a method for monitoring the evolution of calibration parameter during that time. The method works with star sensor and accelerometer data and does not require gravity field models, which distinguishes it from other existing methods. We present time series of calibration parameters estimated from GOCE data from 1 November 2009 to 17 May 2010. The time series confirm drifts in the calibration parameters that are present in the results of other methods, including ESA’s baseline method. Although these drifts are very small, they degrade the gravity gradients, leading to the conclusion that the calibration parameters of the ESA’s baseline method need to be linearly interpolated. Further, we find a correction of ?36 × 10?6 for one calibration parameter (in-line differential scale factor of the cross-track gradiometer arm), which improves the gravity gradient performance. The results are validated by investigating the trace of the calibrated gravity gradients and comparing calibrated gravity gradients with reference gradients computed along the GOCE orbit using the ITG-Grace-2010s gravity field model. 相似文献
18.
GOCE gravitational gradients along the orbit 总被引：6，自引：3，他引：3
Johannes Bouman Sophie Fiorot Martin Fuchs Thomas Gruber Ernst Schrama Christian Tscherning Martin Veicherts Pieter Visser 《Journal of Geodesy》2011,85(11):791-805
GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is,
the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational
field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving
the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational
gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational
gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V
XX
, V
YY
, V
ZZ
and V
XZ
are much more accurate than V
XY
and V
YZ
, and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured
GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed.
We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared
their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity
field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is
below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V
XX
and V
YY
is approximately at the level of the requirement on the gravitational gradient trace, whereas the V
ZZ
error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated
GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived
from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially
in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients
is good and that with this type of data valuable new gravity field information is obtained. 相似文献
19.
GOCE卫星引力梯度仪的精确校准是反演高精度重力场的前提之一,本文利用GOCE卫星L1b数据中的引力梯度仪及恒星敏感器数据实现了卫星引力梯度的内部校准。以最小二乘联合多个恒星敏感器观测数据确定内部校准使用的角速度,有效避免了单个恒星敏感器低精度角速度分量对坐标转换过程的影响。考虑到恒星敏感器坐标系与梯度仪坐标系间旋转矩阵随时间的变化,本文在ESA官方内部校准方法的基础上,提出了顾及旋转矩阵校准参数的内部校准模型,并利用2009年11月的GOCE实测数据验证了该方法的效果。结果表明,该旋转矩阵校准参数数值约100″,且在该月存在3″~30″的漂移;与GOCE官方内部校准方法对比,从卫星引力梯度精度结果来看,在低于0.005 Hz频段内,同时解算旋转矩阵的校准参数与梯度仪内3个加速度计对的校准参数的内部校准模型优于仅考虑加速度计对校准参数的模型;除此之外,本文讨论了以该模型为基础的GOCE梯度仪数据校准的可能方法,为GOCE及后续重力卫星的数据处理工作提供参考。 相似文献
20.
重力梯度仪校准参数的确定是GOCE重力梯度观测数据处理的关键环节。本文对GOCE卫星重力梯度观测值中的时变信号与粗差进行了分析,利用高精度全球重力场模型,确定了GOCE重力梯度观测值各分量的尺度因子与偏差,并对校准结果进行了精度评定。结果表明,在测量带宽内,海潮对重力梯度观测值影响在mE量级,与重力梯度仪的精度水平相当,陆地水等非潮汐重力场时变信号略小于海潮,量级约为10~(-4)E;各分量重力梯度观测值的粗差比例均大于0.2%;除EGM96模型外的其他模型对GOCE重力梯度仪进行校准后,Vxx、Vyy、Vzz、Vyz分量上尺度因子的稳定性均在10~(-4)量级,Vxz分量能达到10~(-5)量级,Vxy分量为10~(-2)量级,这与梯度观测值各分量的精度水平一致。 相似文献