【作者】 钟波；

【导师】 宁津生； 罗志才；

【作者基本信息】 武汉大学 ， 大地测量学与测量工程， 2010， 博士

【摘要】 地球重力场研究历来是大地测量学领域的核心任务之一。随着卫星重力测量技术的突破性进展,以及和空间技术、卫星精密定轨技术发展的交叉并进,使得我们以前所未有的精度与分辨率确定地球重力场的精细结构成为可能。卫星跟踪卫星(SST)和卫星重力梯度测量(SGG)被国际上公认为当今获取全球高精度高分辨率地球重力场及其时变信息的最有效技术手段。以CHAMP、GRACE为代表的SST技术使地球重力场模型在中长波部分的精度提高了1～2个量级,而以更高精度(100km分辨率、1cm大地水准面)为目标的GOCE卫星也于2009年3月17日成功发射,它结合了SST-hl和SGG两种技术模式,有望使地球重力场的研究取得更大突破。随着GOCE卫星的成功发射,围绕GOCE数据处理和应用研究将成为今后几年地学研究的热点问题之一。与此同时,国际三大卫星重力计划(CHAMP、GRACE和GOCE)的相继成功实施对我国大地测量学及相关领域的研究既存在机遇又不乏挑战,加紧开展卫星重力测量技术的研究,建设我国自主的重力卫星系统已是发展所需,因此,当前对卫星重力测量数据处理理论与方法的研究更具有现实意义。在此背景下,本文研究基于GOCE卫星重力测量技术确定地球重力场的理论和方法,研制GOCE卫星重力测量数据处理软件包与仿真模拟平台,不仅为GOCE实测数据处理和相关应用研究奠定基础,同时也为发展我国自主的重力卫星系统积累经验。本文的主要研究工作及贡献如下：1.在详细论述GOCE卫星重力测量系统的基础上,重点对GOCE观测数据及其噪声进行了模拟研究,包括卫星轨道数据、重力梯度数据和重力梯度测量有色噪声等数据。基于仿真实验,估计和分析了潮汐摄动对GOCE卫星运动和重力梯度测量的影响,结果表明：各项潮汐摄动对SST-hl测量影响较大(最大量级均大于1.0×109m/s2),而对SGG测量影响相对较小(影响量级均小于GOCE重力梯度仪的测量精度3mE)。2.深入研究了基于高低卫-卫跟踪技术确定地球重力场的加速度法原理和实用解算模型,在分析卫星加速度误差的有色噪声特性基础上,提出采用去相关滤波抑制卫星加速度的高频误差,并构造了基于三点差分的白化滤波器和ARMA模型的白化滤波器。采用不同噪声背景的GOCE卫星模拟轨道数据进行解算,结果表明去相关滤波法解算的重力场模型精度均要比传统等权方法解算的模型精度高。同时,基于加速度法模拟分析了GOCE轨道误差、加速度计误差和观测粗差对恢复重力场的影响,并对加速度法和能量法恢复重力场的性能进行了比较,得出了有益结论。3.详细推导了基于卫星瞬时加速度或均值加速度同时求解加速度计校准参数和重力场位系数的平差模型,并提出了一整套利用加速度法恢复地球重力场的数据处理方案及流程。采用46天的CHAMP数据恢复了60阶次的重力场模型WHUCHAMP-ACC60KP和WHUCHAMP-ACC60KA,结果表明两个模型的精度相当,并且优于EIGEN-1S模型,与EIGEN-2模型精度接近,验证了方法的可行性与实用性。另外,基于加速度法提出利用抗差估计控制粗差或异常值对重力场解算结果的影响,并以98天的CHAMP数据为例,采用IGG3等价权迭代解算了70阶次的重力场模型WHUCHAMP-ACC70K,其精度优于EIGEN-1S和EIGEN-2模型,验证了抗差估计的有效性。4.深入研究了GOCE重力场严密求解的空域最小二乘法原理和实用解算模型,分析结果表明GOCE卫星位置误差对重力梯度测量的影响远小于梯度仪测量误差,因此可将卫星轨道作为已知进行直接求解。模拟研究了GOCE重力场解算中病态法方程的Tikhonov正则化方法,结果表明FOT和Kaula正则矩阵的实际处理效果差别较小,两者均能达到稳定求解的目的。实现了GOCE重力梯度观测值有色噪声的ARMA时域滤波方法,数值模拟结果表明该滤波方法实用有效。5.提出了基于球谐分析方法确定GOCE卫星重力场模型的数据处理方案,给出了球谐分析方法恢复GOCE重力场所涉及的数据归算、格网化和极空白(PG)等关键问题的解决途径,实现了GOCE沿轨重力梯度测量有色噪声的Wiener滤波预处理方法,并通过数值模拟对其有效性进行了验证,为空域法解算GOCE重力场模型中有色噪声的滤波预处理提供了有效工具。6.基于时域最小二乘误差分析方法,设计了卫星重力梯度测量系统关键技术指标仿真分析的计算方案和流程,并分析了轨道高度、倾角、采样间隔、时间跨度、重力梯度测量精度与测量带宽等指标参数、以及不同梯度分量组合与重力场恢复精度的响应关系,研究结果可为重力梯度卫星关键技术指标的设计与论证提供参考。对GOCE预期恢复重力场的性能进行了模拟,采用6个月、1s采样的SGG (Vxx,Vyy,Vzz,Vxz)数据恢复大地水准面和重力异常累积到200阶的误差分别为21.57cm和0.412mGal,而SGG和SST(5s采样的扰动位)联合解对应大地水准面和重力异常的累积误差分别为1.31cm和0.239mGal,这表明必须将SGG和SST联合求解才能达到GOCE的预期目标。7.推导了SST和SGG两类数据的最小二乘联合平差模型,给出了观测值最优权确定的方差分量估计(VCE)和参数协方差方法(PCA)。基于加速度法和空域最小二乘法,采用30天、5s采样的GOCE模拟轨道和SGG (Vxx,Vyy,Vzz)数据联合求解了200阶次的重力场模型,结果表明：SST和SGG等权求解并不能得到最优结果,并且VCE和PCA方法得到的加权因子与理论最优值存在一定的偏差,但VCE优于PCA方法；在纬度±83°范围内,SGG (Vxx,Vyy,Vzz)与SST最优联合解算模型的大地水准面和重力异常精度分别为3.81cm和1.056mGal,它比仅采用Vzz分量与SST最优联合求解模型的大地水准面和重力异常精度分别提高了1.0cm和0.280mGal。8.深入研究了卫星重力边值问题的随机边值解法,推导出球近似下以GOCE卫星轨道面扰动位T和径向重力梯度Trr为边界条件的超定边值问题随机边值解。同时,以地面重力异常△g为约束边界条件,导出了以卫星轨道面和地面边界条件组成的二界面超定边值问题的随机边值解。采用模拟的GOCE轨道面扰动位T(SST)、径向重力梯度Trr (SGG)和地面重力异常(△g)数据进行联合求解,结果表明：联合解算模型是介于各单类数据解算模型之间的最优解,并且SST+SGG解算模型的中低阶精度相比SGG解算模型有明显提高,而SST+SGG+Δg解算模型的中高阶精度相比SST+SGG解算模型也有明显改善。9.研究了最小二乘谱组合的基本原理,推导了多种类型观测数据联合处理的谱权及其谱组合的一般公式。基于球谐分析方法推导出GOCE轨道面扰动位T和径向重力梯度Trr谱组合所对应谱权的具体形式,并在该条件下证明了谱组合方法与卫星重力边值问题随机边值解法的等价性。此外,采用30天、5s采样的GOCE模拟轨道和重力梯度数据(对角线3分量),分别由加速度法和空域最小二乘法独立解算的位系数谱组合求解了200阶次的重力场模型,结果表明：在纬度±83°范围的大地水准面和重力异常精度分别为3.84cm和1.058mGal,该精度与联合平差解算模型的精度相当。更多还原

【Abstract】 etermination of the earth’s gravity field is always one of the main tasks of geodesy. The breakthrough of the satellite gravimetry technique as well as spatial technique and satellite positioning technique makes it possible to determine the fine structure of the earth’s gravity field with unprecedented precision and resolution. The Satellite-to-Satellite Tracking (SST) and Satellite Gravity Gradiometry (SGG) are regarded as the most effective techniques for the determination of the earth’s gravity field and its temporal variation. The SST technique represented mainly by CHAMP and GRACE satellite gravity missions has improved the accuracy of the earth’s gravity field model by 1-2 order of magnitude in the part of long and mid wavelength. Aiming at an accuracy of lcm for the geoid at 100km resolution, the GOCE mission which combined SST-hl and SGG techniques was launched on 17 March 2009. This will bring greater breakthroughs for the investigation of the earth’s gravity field.ith the successful launch of GOCE satellite, studies on data processing and applications of GOCE mission will become a hot issue in geosciences for the next several years. At the same time, the successful implementation of three international satellite gravity missions (CHAMP, GRACE and GOCE) takes opportunity as well as challenge for our study of geodesy and related fields. Speeding up the research in satellite gravimetry technique, and constructing our own autonomous gravity satellite system has become an inevitable trend. Therefore, researches on the theory and methodology of satellite gravimetry data processing have more realistic significance at present. Under the background of the scientific research, the theory and methods for the determination of the earth’s gravity field based on GOCE satellite gravimetry technique are studied in this dissertation. And the corresponding GOCE data processing software package and analog simulation platform with autonomous copyright are developed. The ultimate purpose is not only to establish the foundation of the GOCE practical data processing and related application research, but also to accumulate experiences for the development of our country’s gravity satellite system in the future. The main work and contributions in this dissertation are as following:fter the GOCE mission is comprehensively introduced, emphasis is focused on simulation study of LGOCE satellite gravimetry data, including satellite orbit data, gravity gradiometry data, gradiometer colored noise series, and so on. The effects of tidal perturbations on the motion of GOCE satellite and its performance of gradiometer measurement are estimated based on the simulation experiments. The results show that the tidal perturbations have greater effects on the observation of SST-hl, the maximum magnitude of each perturbation is larger than 1.0×10-9m/s2, whereas the tidal effects on the observation of SGG are relatively small, the magnitude of each perturbation is much less than GOCE gradiometer measurement accuracy of 3mE.he principle and practical numerical model of the acceleration approach for determining the earth’s gravity field based on satellite orbit data are deeply studied. Because the noise in the orbit-derived satellite acceleration data is colored, whitening filters based on decorrelation technique are proposed to suppress the noise. Two whitening filters are constructed based on 3-points differential scheme and on ARMA model, respectively. As a test, simulated GOCE orbit data with different type of noises are used to recover the gravity field model. The results demonstrate that the gravity field models recovered from the decorrelation filtering methods have higher accuracy than those from equal weight method. Meanwhile, the effects of GOCE orbit error, accelerometer error and gross error on gravity field recovery are emulationally analyzed based on acceleration approach, and the performance of gravity field recovery using acceleration approach is also compared with energy balance approach, and then some useful conclusions are drawn.he adjustment models for simultaneously solving the calibration parameters of accelerometer and the potential coefficients based on point-wise accelerations or average accelerations are derived in detail, then a set of complete data processing scheme and process for recovering the earth’s gravity field using acceleration approach is presented. Two earth’s gravity field models up to degree and order 60 named WHUCHAMP-ACC60KP and WHUCHAMP-ACC60KA are respectively recovered by acceleration approach from 46 days of CHAMP kinematic orbits and accelerometer data. The results show that the above two models have the same accuracy, which is near to the accuracy of EIGEN-2, and better than EIGEN-1S. In addition, robust estimation is employed to suppress the influence of outliers remained in the preprocessed data, for gravity field recovery using acceleration approach. And a gravity field model up to degree and order 70 named WHUCHAMP-ACC70K is achieved by robust reweighting method based on IGG3 equivalent weight from 98 days of CHAMP data. The results show that WHUCHAMP-ACC70K has a higher accuracy than EIGEN-1S and EIGEN-2, which validate the effectiveness of robust estimation method.he principle and practical numerical model of the space-wise least-squares method for rigorously determining GOCE gravity field model are deeply studied. Analysis results show that the effect of GOCE orbit error on SGG is much less than the gradiometer measurement error, so the satellite orbit can be regard as known for GOCE gravity field recovery from gravity gradiomtery data. Two regularization algorithms, including FOT and Kaula, used in the GOCE gravity field determination are discussed. Numerical simulation shows that the two regularization methods can stabilize the solution and the difference of their treatment effects is very small. The ARMA recursive filtering method used to deal with GOCE gravity gradiometry colored noises is realized, and simulation results verify that this filtering method is practicability and effectiveness.ata processing scheme and process for the GOCE gravity field recovery based on spherical harmonic analysis approach are presented. The key problems such as data reduction, griding and polar gaps involved in spherical harmonic analysis approach are discussed and their solutions are also given. The wiener orbit filter (WOF) is designed and realized for preprocessing of the GOCE gravity gradiometry colored noises, and its effectiveness is verified by the numerical simulation results. It also provides an effective tool to preprocess of colored noises data for GOCE gravity field determination based on other space-wise methods, such as least-squares collocation method.ased on the principle of time-wise least square errors analysis, the calculation scheme and process for analog simulation analysis of the key technical indexes of SGG system are designed. Then the influences of various factors on the gravity field recovery from SGG data are analyzed. These influence factors include orbit height, orbital inclination, sampling interval, time span, gradiometer accuracy, measurement band-width, and combination of different gradient components. The simulation results can be as a reference for design and demonstration of the key technical indexes of SGG system. By simulation, the expected accuracy of GOCE mission is estimated. Using 6 months of SGG (Vxx,Vyy,Vzz,Vxz) data with 1 s sampling interval, the cumulative geoid height errors and cumulative gravity anomaly errors of the estimated gravity field model up to degree and order 200 are 21.57 cm and 0.412 mGal, respectively. When SGG and SST (with 5s sampling interval of disturbing potential) data are combined to estimate the gravity field, the corresponding cumulative errors are decreasing to 1.31 cm and 0.239 mGal, respectively. It proves that in order to achieve the aim of GOCE mission, SGG and SST data must be combined together for the gravity field recovery.he combined adjustment model for processing of SST and SGG data is derived, and two approaches for the determination of optimal weight are also investigated, including variance component estimate (VCE) and parametric covariance approach (PCA). On the basis of acceleration approach and space-wise least-squares method, the combined gravity field model up to degree and order 200 is recovered from 30 days of simulated GOCE orbits and SGG (Vxx,Vyy,Vzz) data with 5s sampling interval. The results show that the combined solution from combining SST and SGG data with equal weight is not optimal, and VCE method is better than PCA method for determining the optimal weight. However, the optimal weight determinated by VCE method also has some deviations from the theoretically optimal value that derived from the criterion of minimum RMS geoid error. For the SST and SGG optimal combined model, its accuracy of geoid heights and gravity anomalies between±83°latitude areas are 3.81cm and 1.056mGal respectively. Comparing to the combined solution solved from SST and component Vzz only, the accuracy of SST and SGG combined solution are improved about 1.0cm in geoid heights and 0.280mGal in gravity anomalies, respectively.atellite gravimetry boundary value problem solved from random boundary value conditions is investigated in detail. The solution of overdetermined random boundary value problem is derived, with spherical approximation boundary conditions of disturbing potential T and the radial gradient component Trr from the GOCE orbital plane. Furthermore, the solution of two boundaries (satellite orbital plane and earth’s surface) overdetermined boundary value problem is also given, with terrestrial gravity anomaliesΔg as a constrained boundary condition. As a test, simulated disturbing potential T (SST) and radial gradient component Trr(SGG) on the GOCE orbital plane, and terrestrial gravity anomalies (Δg) data are combined to recover the gravity field model. The results show that the combined models are the optimal solution than those solved from only one type of observations. The combined solution from SST+SGG observations has an obvious improvement in the part of mid and low degrees, comparing with the solution from SGG observations only. And the accuracy of combined model from SST+SGG+Δg observations is better than the combined model from SST+SGG observations, especially in the part of high and mid degrees.he principle of least-squares spectral combination is studied, and then the general formulae of spectral weight and spectral combination for combining different type of observations are derived. On the basis of spherical harmonic analysis, the concrete forms of spectral weights corresponding to the disturbing potential T and radial gradient component Trr from the GOCE orbital plane are derived in detail. And the spectral combination formulae for processing of disturbing potential T and gradient component Trr are also given. We find that the solution of spectral combination is equivalent to the solution of satellite gravimetry boundary value problem, and their formulae have the same form and effectiveness. Furthermore, a spectral combination gravity field model up to degree and order 200 is constructed based on the principle of potential coefficients combination, using 30 days of simulated GOCE orbits and SGG (Vxx,Vyy,Vzz) data with 5s sampling interval. The above spectral combination model is combined from SST and SGG model, the SST model is solved by acceleration approach, and the SGG model is recovered from space-wise least-squares method. The results show that the accuracy of geoid heights and gravity anomalies between±83°latitude areas are 3.84cm and 1.058mGal respectively, which are similar to the accuracy of combined adjustment solution.更多还原