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1.
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
2.
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
3.
Wenbin Shen Jin Li Jiancheng Li Zhengtao Wang Jinsheng Ning Dingbo Chao 《地球空间信息科学学报》2008,11(4):273-278
Given the second radial derivative Vrr（P） ｜δs of the Earth＇s gravitational potential V（P） on the surface δS corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVrr（P）^＊ and a fictitious second radial gradient field V：（P） in the domain outside an inner sphere Ki can be determined, which coincides with the real field V（P） in the domain outside the Earth. Vrr^＊（P）could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrV（P）^＊ could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain. In another aspect, the fictitious field V^＊（P） defined in the domain outside the inner sphere, which coincides with the real field V（P） in the domain outside the Earth, could be also expressed as a spherical harmonic expansion series. Then, the harmonic coefficients contained in the series expressing V^＊（P） can be determined, and consequently the real field V（P） is recovered. Preliminary simulation calculations show that the second radial gradient field Vrr（P） could be recovered based only on the second radial derivative V（P）｜δs given on the satellite boundary. Concerning the final recovery of the potential field V（P） based only on the boundary value Vrr （P）｜δs, the simulation tests are still in process. 相似文献
4.
M. Kern T. Preimesberger M. Allesch R. Pail J. Bouman R. Koop 《Journal of Geodesy》2005,78(9):509-519
The satellite missions CHAMP, GRACE, and GOCE mark the beginning of a new era in gravity field determination and modeling. They provide unique models of the global stationary gravity field and its variation in time. Due to inevitable measurement errors, sophisticated pre-processing steps have to be applied before further use of the satellite measurements. In the framework of the GOCE mission, this includes outlier detection, absolute calibration and validation of the SGG (satellite gravity gradiometry) measurements, and removal of temporal effects. In general, outliers are defined as observations that appear to be inconsistent with the remainder of the data set. One goal is to evaluate the effect of additive, innovative and bulk outliers on the estimates of the spherical harmonic coefficients. It can be shown that even a small number of undetected outliers (<0.2 of all data points) can have an adverse effect on the coefficient estimates. Consequently, concepts for the identification and removal of outliers have to be developed. Novel outlier detection algorithms are derived and statistical methods are presented that may be used for this purpose. The methods aim at high outlier identification rates as well as small failure rates. A combined algorithm, based on wavelets and a statistical method, shows best performance with an identification rate of about 99%. To further reduce the influence of undetected outliers, an outlier detection algorithm is implemented inside the gravity field solver (the Quick-Look Gravity Field Analysis tool was used). This results in spherical harmonic coefficient estimates that are of similar quality to those obtained without outliers in the input data. 相似文献
5.
R. Pail 《Journal of Geodesy》2005,79(4-5):231-241
In the recent design of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, the gravity gradients are defined in the gradiometer reference frame (GRF), which deviates from the actual flight direction (local orbit reference frame, LORF) by up to 3–4°. The main objective of this paper is to investigate the effect of uncertainties in the knowledge of the gradiometer orientation due to attitude reconstitution errors on the gravity field solution. In the framework of several numerical simulations, which are based on a realistic mission configuration, different scenarios are investigated, to provide the accuracy requirements of the orientation information. It turns out that orientation errors have to be seriously considered, because they may represent a significant error component of the gravity field solution. While in a realistic mission scenario (colored gradiometer noise) the gravity field solutions are quite insensitive to small orientation biases, random noise applied to the attitude information can have a considerable impact on the accuracy of the resolved gravity field models. 相似文献
6.
根据重力梯度观测各分量的方差及协方差信息,提出了利用GOCE梯度数据计算径向重力梯度的优化方法。首先给出了径向重力梯度的计算方法,并深入分析了误差传播规律,通过建立相应的条件极值问题,给出了计算径向重力梯度最优组合因子的方法;通过模拟数据验证了本文所提出的优化因子的优越性。实际数据计算表明:相对于传统方法,采用优化组合因子可使反演所得引力位模型的累积大地水准面精度在250阶时提高约2 cm。由于径向重力梯度不仅可以用于地球引力场模型的求解,也可直接应用于地球物理问题的讨论,因此本文所提出的优化方法也可对部分地球动力学问题的讨论提供方便。 相似文献
7.
One of the aims of the Earth Explorer Gravity Field and Steady-State Ocean Circulation (GOCE) mission is to provide global
and regional models of the Earth's gravity field and of the geoid with high spatial resolution and accuracy. Using the GOCE
error model, simulation studies were performed in order to estimate the accuracy of datum transfer in different areas of the
Earth. The results showed that with the GOCE error model, the standard deviation of the height anomaly differences is about
one order of magnitude better than the corresponding value with the EGM96 error model. As an example, the accuracy of the
vertical datum transfer from the tide gauge of Amsterdam to New York was estimated equal to 57 cm when the EGM96 error model
was used, while in the case of GOCE error model this accuracy was increased to 6 cm. The geoid undulation difference between
the two places is about 76.5 m. Scaling the GOCE errors to the local gravity variance, the estimated accuracy varied between
3 and 7 cm, depending on the scaling model.
Received: 1 March 2000 / Accepted: 21 February 2001 相似文献
8.
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9.
徐新强 《大地测量与地球动力学》2015,35(5):853-856
针对EGM08重力场模型构建过程中存在的不足,提出用GOCE重力场模型替换EGM08模型的中低频部分,用剩余地形模型RTM拓展EGM08模型的甚高频信号。模拟分析表明,GOCE模型能大幅提高高程异常计算的精度,而RTM对高程异常的贡献也不可忽视。实测GPS/水准数据表明,GOCE模型对高程异常的贡献达到43%,而RTM也贡献了1cm的精度。 相似文献
10.
利用GOCE模拟观测反演重力场的Torus法 总被引：1，自引：1，他引：0
在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61dGOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022mm和0.099mm。在沿轨卫星引力梯度模拟数据中加入5mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58cm和1.45cm,累积误差最大值分别为6.37cm和5.55cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。 相似文献