【作者】 游为；

【导师】 范东明；

【作者基本信息】 西南交通大学 ， 大地测量学与测量工程， 2011， 博士

【摘要】 随着CHAMP(CHAllenging Minisatellite Payload、GRACE(Gravity Recovery And Climate Experiment)、GOCE(Gravity field and steady-state Ocean Circulation Explorer)等低轨重力卫星的相继发射,卫星重力研究已成为大地测量学中继全球定位系统(GPS, Global Positioning System)之后又一次具有革命性突破的研究。虽然利用GRACE卫星跟踪数据能反演出高精度高分辨率的地球重力场模型,但目前GRACE卫星星间观测值所蕴含的地球重力场信息并没有完全被挖掘出来,本文主要研究了利用GRACE卫星轨道及星间观测数据反演地球重力场模型的理论和方法,比较了现有的数值计算方法,提出了几种改进的反演方法。论文主要内容及创新点概述如下：1.分析了卫星重力测量的重要意义,概述了目前地球重力场的研究现状,研究了利用卫星重力数据解算地球重力场模型的3种方法：直接法、时域法及空域法。2.详细给出了基于IERS2003规范的惯性坐标系统与地固坐标系统的坐标转换公式,计算了GRACE卫星所受的各种摄动力模型,比较了数值积分的几种方法,研究了基于移动窗口的多项式内插法,提出了一种消去局部未知参数的QR分解法,给出了预条件共轭梯度法解算法方程的详细计算步骤,讨论了地球重力场模型内外符合精度评定的方法。3.详细研究了基于GRACE卫星数据解算地球重力场模型的Kaula线性摄动法、点加速度法、短弧长积分法、平均加速度法、能量守恒法及动力学积分法的计算原理,分析了各种方法的优缺点,给出了星间距离或距离变率的观测方程。采用1个月GRACE卫星模拟星间距离数据解算80阶次地球重力场模型,验证了动力学积分法的有效性和可靠性。4.给出了一种基于卫星轨道扰动的严密重力反演方法,基于移动窗口的多项式内插公式首次推导了该方法的严密数值计算公式。采用1个月的模拟数据计算100阶次地球重力场模型验证了该方法的有效性、可靠性及实用性。5.在短弧长积分法的基础上,对力模型梯度改正,给出了梯度改正短弧长积分法的计算原理,分析了力模型梯度改正对轨道位置改正的影响。采用1个月的模拟数据计算120阶次的地球重力场模型,分析验证了该方法的精度。6.在短弧长积分法原理的基础上,通过采用另外一种力模型梯度改正的思想,首次提出了改进短弧长积分法,导出了该方法的严密数值计算公式,并采用1个月模拟数据计算表明该方法优于短弧长积分法；采用改进短弧长积分法,基于GRACE Follow-on卫星模拟数据分析了重力场模型的解算精度；研究了改进短弧长积分法中移动窗口多项式次数的选择问题。7.研制了卫星重力反演的一套软件系统SWJTU-GRS.该软件可进行GRACE卫星模拟数据计算、观测数据预处理、各种方法的模拟及实测数据解算、各种模型的内外符合精度检核计算。讨论了改进短弧长积分法中轨道与星间观测值的权重及弧段长度的优化等关键问题。8.通过理论分析及GRACE卫星1个月(2008.1.1-2008.1.31)的实测数据计算比较了几种方法的精度。结果表明弧段长度选择为30min,当只采用轨道观测值时,改进短弧长积分法与短弧长积分法、动力学积分法、梯度改正短弧长积分法的精度相当；但当采用星间观测数据时,改进短弧长积分法优于其它三种方法。9.分别采用梯度改正短弧长积分法及改进短弧长积分法基于近200天(2008.1.1～2008.8.1)的GRACE卫星轨道及星间观测数据,反演了两组120阶次的地球重力场模型SWJTU2010S1及SWJTU2010S2,模型分辨率为167km(半波长)。两组模型所表示的大地水准面精度分别为±14.00cm和±11.63cm,总体精度优于EIGEN-GRACE02S、EIGEN-GRACE01S模型,但低于EIGEN-CGO1C模型。10.给出了GOCE卫星精密轨道数据预处理的方法,推导了消去2类局部参数的法方程建立方法。采用短弧长积分法基于GOCE卫星61天(2009.11.2～2010.1.2)的精密轨道数据反演了110阶次地球重力场模型,其在106阶次的大地水准面误差为±9.6cm,且带谐位系数精度偏低；通过GOCE与GRACE卫星轨道联合反演了110阶次地球重力场模型,其在106阶次的大地水准面误差为±6.9cm,明显改善了带谐位系数精度。更多还原

【Abstract】 With the launching of Low Earth Orbit (LEO) gravity satellites such as CHAllenging Minisatellite Payload (CHAMP)、Gravity Recovery And Climate Experiment (GRACE)、 Gravity field and steady-state Ocean Circulation Explorer (GOCE), satellite gravity observation has become another revolutionary breakthrough in Geodesy following the Global Positioning System (GPS). The Earth’s gravitational field with high precision and resolution can be recovered by GRACE satellite data. However, the gravity information contained in the GRACE range and range-rate observations has not still been fully utilized up to now. This project mainly studies the theory and methodology to recover the Earth’s gravitational field using GRACE satellite observations. The existing numerical methods are compared, and several improved methods are proposed. The main contents and innovation of the thesis are summarized as follows:1. The significance of satellite gravity observations is analyzed and the latest research progress of Earth’s gravitational field has been reviewed. Three approaches to determine the Earth’s gravitational field with satellite gravity data, i.e., direct approach, time-wise approach and space-wise approach, have been studied.2. The coordinate transform formulae between the quasi-inertial coordinate system and the Earth fixed coordinate system have been specified in detail following IERS conventions2003. A variety of force models of GRACE satellites have been calculated. Several numerical integration methods have been analyzed. The interpolation method of shifted polynomial has been studied. The method of QR decomposition to eliminate the local unknown parameters has been introduced. The detailed calculation steps of the preconditioned conjugate gradient algorithm to resolve the normal equations have been presented. The accuracy assessment methods of the Earth’s gravitational field model have been described.3. Six methods (Kaula linear perturbation approach, point acceleration approach, short-arc integral approach, average acceleration approach, energy conservation approach and traditional dynamical integral approach) have been studied. The advantages and disadvantages of each approach have been analyzed. The observation equations of satellite range and range-rate have been presented. I has used one month simulated GRACE satellite data to recover the Earth’s gravitational field up to degree and order80to verify the validity and reliability of the traditional dynamical integral approach.4. A method based on strict satellite’s orbital perturbation theory has been introduced. The strict numerical calculation formulae of the approach have been derived based on the interpolation formulae of shifted polynomial. One month simulated satellite data have been used to recover the Earth’s gravitational field with degree and order100, which verifies the validity and reliability of the approach.5. A short-arc integral approach with gradient correction has been presented. The impact of gradient correction of force models on satellite orbit has been analyzed. One month simulated data have been used to recover the Earth’s gravitational field with degree and order120, which validates the precision of the approach.6. An improved short-arc integral approach has been first proposed based on another gradient correction. The mathematical formulae of the approach have been closely derived. The results of one month simulated data show that the improved approach is better than the short-arc integral approach. One month of simulated GRACE Follow-on satellite data have been used to analyze the precision of the resolved Earth’s gravitational field model with the improved approach. The degree choice about the interpolation formulae of shifted polynomial has also been analyzed.7. A set of satellite gravity recovery software SWJTU-GRS has been developed. The software can be used to simulate GRACE satellite observations, prepocess GRACE satellite data, recover the Earth’s gravitational field with various approaches, calculate and check the internal and external precision of the gravitational field model. The optimal arc and the weight between orbit and satellite-to-satellite observations in the improved short-arc integral approach have been analyzed.8. Four approaches have been compared through both theoretical analysis and the numerical calculation of one month of GRACE satellite data between2008.1.1-2008.1.31. The results show that the four approaches have almost the same accuracy when using only orbital observations. However, the improved short-arc integral approach is better than the short-arc integral approach, traditional dynamical integral approach and the gradient corrected short-arc integral approach when using satellite range observations.9. The gradient corrected short-arc integral approach and improved short-arc integral approach have been used respectively to derive two Earth’s gravitational field models SWJTU2010S1and SWJTU2010S2up to degree and order120based on nearly200days of GRACE satellite orbits, ranges and range-rates from2008.1.1to2008.8.1. The resolution of the two models is167km (half wavelength) and the overall geoid accuracies are14.00cm and11.63cm, respectively. The overall accuracy of the two models is better than the model EIGEN-GRACE02S, EIGEN-GRACE0lS but less than the model EIGEN-CG01C.10. The preprocessing approach of GOCE precise orbits has been presented. The approach to establish normal equations has been derived to eliminate two classes of local parameters. I has used the short-arc integral approach to recover an Earth’s gravitational field with degree and order110based on GOCE orbits of61days from2009.11.2to2010.1.2. The geoid height error of the model at degree106is±9.6cm and the model has low precision in zonal spherical harmonic coefficients. Another Earth’s gravitational field model with degree and order110has been derived by combined satellite orbits of GOCE and GRACE. The geoid height error of the model at degree106is±6.9cm and the accuracy of zonal spherical harmonic coefficients has been significantly improved.更多还原