Energy integral method for gravity field determination from satellite orbit coordinates

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.     

基于GNSS水准和重力场误差特性的大地水准面精度评估方法

缺乏有效的大地水准面成果精度评估方法,是高程基准现代化及其成果应用面临的关键问题。本文基于GNSS水准高程异常与重力场频域误差特性,研究GNSS水准与重力地面高程异常融合的技术要求,进而提出一种大地水准面成果的误差表达与精度评估方法。经示例测试分析,得出主要结论如下:①实用地面高程异常(即融合后的似大地水准面)精度,应采用随距离非线性变化的高程异常差误差曲线表达;②似大地水准面的精度评估,推荐采用两项误差指标和两条误差曲线共4个要素完整表达,即重力地面高程异常差误差、实用地面高程异常内部误差、实用地面高程异常差误差曲线与GNSS水准高程异常差误差曲线;③当两个GNSS水准点间距离接近或小于所有GNSS水准点平均间距时,GNSS水准高程异常对实用地面高程异常的贡献起主要作用;④较大空间尺度的实用地面高程异常精度主要依靠重力地面高程异常控制。     

GRACE时变重力场的滤波理论及质量变化分析

正由于GRACE(gravity recovery and climate experiment)时变重力场模型直接解算质量变化时存在较大的误差,需要对其进行相应的滤波处理,提高质量变化的反演精度。本文总结了GRACE监测全球与区域质量变化的研究进展,分析了最新时变重力场模型的精度及其滤波方法;提出了基于重力位系数协方差阵的时变重力场滤波方法;分析了南极冰盖的质量变化、亚马孙流域陆地水质量和海平面变化。本文的研究成果及创新点主要包括以下几个方面:     

基于时间序列分解的GPS卫星钟差预报

根据二次多项武和灰色模型在卫星钟差预报中的特点,本文提出以ARMA(Autoregressive Moving Aver-age)模型分别进行改进;对IGS(International GPS Service for Geodynamic)提供的精密钟差进行时间序列分解,根据预报时间的长短,趋势项分别采用二次多项式和灰...     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

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.     

多源卫星重力场模型精度与频谱分析

针对新一代卫星重力探测技术对地球重力场的频谱贡献问题,该文提出了一种基于GPS/水准数据获取多源卫星重力场模型频谱变化特征的方法。采用GPS/水准外符合检验,有效分析评估了多源卫星重力场模型在中国东、西部地区的精度水平。研究结果表明,以CHAMP、GRACE和GOCE卫星为代表的高-低卫星跟踪卫星、低-低卫星跟踪卫星和卫星重力梯度技术,对地球重力场的频谱贡献分别集中在600km以上的长波和中长波、300km以上的中波、200~350km之间的中短波部分。     

Regularization of gravity field estimation from satellite gravity gradients

 The performance of the L-curve criterion and of the generalized cross-validation (GCV) method for the Tikhonov regularization of the ill-conditioned normal equations associated with the determination of the gravity field from satellite gravity gradiometry is investigated. Special attention is devoted to the computation of the corner point of the L-curve, to the numerically efficient computation of the trace term in the GCV target function, and to the choice of the norm of the residuals, which is important for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) in the presence of colored observation noise. The trace term in the GCV target function is estimated using an unbiased minimum-variance stochastic estimator. The performance analysis is based on a simulation of gravity gradients along a 60-day repeat circular orbit and a gravity field recovery complete up to degree and order 300. Randomized GCV yields the optimal regularization parameter in all the simulations if the colored noise is properly taken into account. Moreover, it seems to be quite robust against the choice of the norm of the residuals. It performs much better than the L-curve criterion, which always yields over-smooth solutions. The numerical costs for randomized GCV are limited provided that a reasonable first guess of the regularization parameter can be found. Received: 17 May 2001 / Accepted: 17 January 2002     

一种北斗卫星钟差短期预报组合方法

针对北斗卫星钟差预报研究较少的情况,基于灰色模型与BP神经网络模型,构建一种全新的组合预测模型. 该组合钟差预测模型通过最优权方法有效结合两种单一模型的优点,实现北斗钟差的短期预报. 最后,以北斗三种型号卫星所携带的原子钟数据为例,计算出每种单一模型的权重,通过构建最优权预报模型实现了钟差的短期预报,预报结果优于两种单一模型,证明了该组合预报模型在钟差短期预测方面有效性与适用性.      

基于最优权组合方法的北斗卫星钟差预报

基于北斗卫星全球服务开通运行,北斗精密定位与导航中钟差预报至关重要。本文深入研究灰色模型与神经网络模型钟差预报之后,通过最优权组合方法将二者有效的结合,最优权组合模型融合二者预报模型的优点,实现北斗钟差精准预报。最后,以北斗钟差数据为例,通过北斗三种卫星携带的原子钟,建立最优权组合钟差预报模型,确定组合模型中单模型的权重值,最终预测钟差结果验证了该组合模型预报精度高于单模型,该组合模型对北斗钟差预报具有适用性与有效性。     

Space-wise approach to satellite gravity field determination in the presence of coloured noise

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.     

GOCE卫星重力梯度观测值的时变重力场变化改正及影响分析

GOCE卫星重力梯度观测值为高阶静态重力场反演提供了重要的数据支撑,但其在使用前需考虑扣除时变重力场变化的影响.本文研究了GOCE卫星重力梯度观测值的时变重力场变化改正方法,更新了ESA标准和背景模型,以更好地扣除时变重力场变化的影响,自主实现了由GOCE卫星Level1b重力梯度数据直接进行重力场反演.本文通过3种时...     

GOCE实测数据反演高阶重力场模型的Torus方法

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。     

新一代重力卫星简化动力学精密定轨实验分析

针对重力卫星轨道低,大气阻力和太阳光压等较为复杂难以模型化的问题,该文基于简化动力学方法,采用GRACE-FO星载GPS双频观测数据,结合CODE提供的精密星历与钟差产品对GRACE-FO卫星进行精密定轨实验与分析.通过与美国喷气动力实验室(JPL)官方提供的事后精密轨道对比、K波段测距系统(KBR)进行星间测距数据检...     

基于GM(1,1)灰色模型卫星钟差短期预报的精度分析

为了提高GPS快速单点定位的精度,必须及时获得高精度的精密星历。基于卫星钟差变化的灰色特性,建立GPS卫星钟差GM(1,1)灰色模型,对卫星钟差进行短期预报。计算结果表明,灰色模型GM(1,1)用于卫星钟差短期预报,只需要使用少数几个历元的已知卫星钟差进行建模,不仅减少建模数据量,提高建模速度,而且预报精度较高,可以满足GPS快速单点定位的实际需要;并对卫星搭载的原子钟精度进行分析,得出基于灰色模型GM(1,1)分析的Rb钟的精度和稳定性要优于Cs钟。     

Gravity field determination from satellite gradiometry

An orbiting gradiometer measures simultaneously several gravity quantities, ideally all six second-order derivatives of the gravitational potential. These contain information on the orbit, on the structure of the gravity field, and on the attitude of the space-craft. Due to the availability of several components simultaneously it is possible to separate orbit determination from attitude or gravity field recovery. This facilitates the analysis of the gradiometer measurements and allows the use of the principles of fast spherical harmonic analysis. The separation of gravity field recovery and orbit determination is tested numerically with a simplified gravity field (with a purely zonal spherical harmonic expansion) up to degree 300. For both the potential coefficients and for the orbit an almost exact recovery is attained after two iteration steps.     

A preliminary error analysis of the gravity field recovery from a lunar Satellite-to-Satellite mission

Summary A low cost lunar Satellite-to-Satellite radio tracking mission in a low-low configuration could considerably improve the existing knowledge about the lunar gravity field. The impact of various mission parameters that may contribute to the recovery of the gravity field, such as satellite altitude, satellite separation, mission duration, measurement precision and sampling interval were quantified using the Jekeli-Rapp algorithm. Preliminary results indicate that the gravity field resolution up to harmonic degree 40 to 80 is feasible depending on various mission configurations. Radio tracking data from a six-month mission with a precision of 1 mm s^–1 every 10 s and 300 km satellite separation at 150 km altitude will permit the determination of 5^o×5^o mean gravity anomalies with an error of approximately 15 mgals. Consideration of other unaccounted error sources of instrumental, operational as well as environmental nature may lower this resolution.     

卫星重力梯度数据重力异常的精度分析

针对GOCE卫星确定的地球重力场模型精度的不确定性,对比分析GOCE位模型与多个不同重力场模型确定的重力异常,并将其分别与船测重力数据、南极航空重力数据、北极重力数据以及美国和中国台湾地面重力数据比较研究。结果表明:GOCE位模型的内符合精度最高,与地面重力观测数据符合最优;与船测以及航空重力测量符合相对较差、精度较低。研究表明,在一定精度前提下,GOCE卫星确定的重力数据可用于无人区,从而提高重力观测数据的覆盖率。     

A geopotential error analysis for a non planar satellite to satellite tracking mission

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. Compared against a coplanar mission an improvement is predicted in errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme is developed to model the range rate residuals. It is flexible enough to model the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. This scheme should allow the possibility of larger planar separations than previously since no small angle approximation is made. The effects of such an orientation on gravity field recovery can therefore be analysed by means of an extensive error analysis. The results of this analysis indicate that a significant improvement in the errors of the near sectorial coefficients are obtained when the satellite's orbital planes are separated. Received: 9 April 1996; Accepted: 26 September 1996     

利用卫星重力数据计算地幔对流应力场

针对我国东南边缘及其邻近区域地幔对流应力场分布形态与地表构造活动特征的相关性问题,提出利用Runcorn模型及高阶卫星重力球谐系数计算欧亚板块与菲律宾板块复合接触带及其邻近区域的地幔对流应力场。结果显示,地幔对流应力矢量特征与地震应力场分布具有较好的一致性。在两大板块的接触部位均出现了显著的应力增强与汇聚趋势,同时在琉球海沟的弧后扩张带上出现的较强的地幔对流应力发散带。而在各板块相对稳定的内部区域存在微弱的地幔发散流。通过计算和分析得出,该区域下地壳小尺度的地幔对流可能是控制这一区域型构造过程的重要因素之一。