GOCE+EGM08+RTM组合模型计算高程异常

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。     

基于非全张量卫星重力梯度数据的张量不变量法

在非全张量卫星重力梯度观测数据的处理过程中,由于卫星姿态角误差、梯度观测数据误差和非全张量观测等原因,重力梯度值从卫星重力梯度仪系转换到地固系后,精度损失严重.本文研究了张量不变量法以解决上述问题.首先在重力梯度张量不变量线性化的基础上,建立了基于卫星轨道面的不变量观测模型,完整地推导了两类重力梯度张量不变量的球近似和顾及地球扁率影响的球面边值问题的求解公式.针对GOCE卫星任务非全张量观测数据类型,分析了张量不变量的计算误差;结果表明,重力梯度观测误差在不变量的计算中并没有被放大.最后运用广义轮胎调和分析方法进行了模拟试验,数值试验证明,在卫星姿态误差较大时,处理张量不变量比处理张量分量更具优势,并且张量不变量法能有效地解决非全张量观测的问题.     

基于时空域混合法利用Kaula正则化精确和快速解算GOCE地球重力场

为了研究卫星重力梯度技术对中高频地球重力场反演精度的影响,本文基于时空域混合法,利用Kaula正则化反演了250阶GOCE地球重力场.模拟结果表明:第一,时空域混合法是精确和快速求解高阶地球重力场的有效方法;第二,Kaula正则化是降低正规阵病态性的重要方法;第三,基于改进的预处理共轭梯度迭代法可快速求解大型线性方程组...     

联合GOCE轨道和梯度数据反演地球重力场模型

基于Fortran语言编写了一套恢复重力场模型的软件系统实现GOCE卫星。基于傅里叶展开式设计了一种重力梯度的滤波方法。分别对GOCE PKI轨道数据和引力梯度数据进行了反演计算,恢复了几个重力场模型。结果显示,GOCE轨道的反演能力约在120阶次以内;两极空白对梯度数据反演计算的影响大于轨道数据。联合2009-11-02一2010-O1-10共70 d的GOCE轨道数据和重力梯度数据恢复了一个200阶次的地球重力场模SWJTU2013GO,通过内外符合精度评定,判定了该模型的整体精度略低于ICGEM公布的同类型模型GO_CONS_GCF_2_TIM_R3.     

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.     

Calibrating the GOCE accelerations with star sensor data and a global gravity field model

A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated on a weekly basis with accuracies better than 2 × 10⁻³ for the ultrasensitive and 10⁻² for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with accuracies in general better than 10⁻³.     

利用卫星重力梯度恢复局部地球重力场的研究进展

简述了SGG数据恢复局部重力场的理论本质以及卫星重力梯度边值问题;详细介绍了当前国内外利用SGG进行局部重力场求解的研究进展,并将已有的求解方法总结归纳为三类：模型法、计算法和组合法,同时对各种方法的概念和研究现状作了详细介绍;最后总结了SGG数据求解局部重力场的发展前景和思考建议。     

缔合Legendre函数二阶导数的快速稳定递推算法

根据初等代数的基本原理,推导了一种缔合Legendre函数二阶导数的快速稳定递推算法。数值测试结果表明,在阶次高达3 600时,该方法与其他几种现有方法的计算精度相当,但计算效率比其他方法提高了一倍以上,并且该方法没有奇异性,适用于快速精确地计算任意纬度的缔合Legendre函数二阶导数值     

GOCE Quick-Look Gravity Solution: Application of the Semianalytic Approach in the Case of Data Gaps and Non-Repeat Orbits

The satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), the first Core Mission of the Earth Explorer Programme funded by ESA (European Space Agency), is dedicated to the precise modelling of the Earth's gravity field, with its launch planned for 2006. The mathematical models for parameterizing the Earth's gravity field are based on a series expansion into spherical harmonics, yielding a huge number of unknown coefficients. Their computation leads to the solution of very large normal equation systems. An efficient way to handle these equation systems is the so-called semianalytic or lumped coefficients approach, which theoretically requires an uninterrupted, continuous time series of observations, recorded along an exact circular repeat orbit. In this paper the consequences of violating these conditions are analyzed. The effects of an interrupted observation stream onto the estimated spherical harmonic coefficients are demonstrated, and an iterative strategy, which reduces the negative influence depending on the characteristics of the data gaps, is proposed. Additionally, the impact of an imperfectly closing orbit (non-repeat orbit) on the gravity field model is analyzed, and a strategy to minimize the corresponding errors is presented. The applicability of the semianalytic approach also to a joint inversion of satellite-to-satellite tracking data in high-low mode (hl-SST) and satellite gravity gradiometry (SGG) observations is demonstrated, where the analysis of the former component is based on the energy conservation law. Several realistic case studies prove that the semianalytic approach is a feasible tool to generate quick-look gravity solutions, i.e. fast coefficient estimates using only partial data sets. This quick-look analysis shall be able to detect potential distortions of statistical significance (e.g. systematic errors) in the input data, and to give a fast feedback to the GOCE mission control.     

融合GOCE和GRACE卫星数据的无约束重力场模型Tongji-GOGR2019S

本文在法方程层面融合GOCE卫星的V_xx、V_yy、V_zz和V_xz重力梯度分量观测数据和GRACE卫星观测数据,采用直接法解算了220阶次的重力场模型Tongji-GOGR2019S.首先利用ⅡR带通滤波器在5~41 mHz的重力梯度带宽范围内对约24个月的GOCE重力梯度观测方程进行无相移滤波处理,并组成解算220阶次重力场模型的法方程,各梯度分量根据相对于参考模型统计精度进行定权;然后与13.5 a GRACE数据建立的180阶次Tongji-Grace02s重力场模型的法方程进行叠加,解算了220阶次的无约束纯卫星重力场模型Tongji-GOGR2019S.利用EIGEN-6C4重力场模型、GNSS/水准数据、DTU15重力异常数据以及欧洲区域似大地水准面模型EGG2015等数据对Tongji-GOGR2019S模型精度进行全面的检核评定,结果表明：引入GOCE卫星梯度数据后,高于72阶的位系数精度优于Tongji-Grace02s模型,Tongji-GOGR2019S模型的整体精度接近同阶次的DIR-R6等GOCE卫星第6代模型.