英汉双语版论文摘要-14研综英2班-地图制图.docx

Computation of three stochastic modifications of Stokessformula for regional geoid determinationArtu EllmannDepartment of Infrastructure, Royal Institute of Technology, SE-100 44 Stockholm, SwedenReceived 14 May 2004; received in revised form 9 December 2004; accepted 5 January 2005AbstractIn the regional geoid studies, the modified Stokes formula is often used nowadays. This method combines local terrestrial data with an appropriate global geopotential model in a truncated form of Stokes integral. This paper is devoted to three stochastic least-squares (LS) modifications, which were originally proposed by Sjoberg(Least squares modification of Stokes and Vening-Meinesz formulas by accounting for errors of truncation, potential coefficients and gravity data. Report No. 27, Department of Geodesy, University of Uppsala, 16pp.) in 1984 (with later developments). The main principles of the LS modifications and some spectral models of the gravity field characteristics are reviewed. Certain difficulties may be encountered when computing the modification parameters from a system of linear equations. In particular, the design matrices of the unbiased and optimum LS modifications suffer from numerical ill-conditioning. Two mathematical regularization strategies are selected in order to find a practical solution for the sought modification parameters. Typical numerical outcome of the regularization and the applicability of the obtained LS parameters are discussed. The present contribution tackles the LS modification-related problems in the context of a specially designedMatlab software package. The core quantities of the stochastic LS modifications can be computed by this software, which is made available on the Computers & Geosciences server.Keywords: Gravimetric geoid; Least-squares parameter estimation; Singular value decomposition; Regularization; Geodesy翻译Computation of three stochastic modifications of Stokes formula for regional geoid determination斯托克斯的三个随机修改计算区域大地水准面精化公式Artu Ellmann埃尔曼Abstract:摘要：In the regional geoid studies, the modified Stokes formula is often used nowadays. 在区域大地水准面的研究方面，现在经常使用修改后的斯托克斯公式。 This method combines local terrestrial data with an appropriate global geopotential model in a truncated form of Stokess integral.这种方法结合了本地地面数据和一个适当的全球重力势模型截断的斯托克斯形式的积分。This paper is devoted to three stochastic least-squares (LS) modifications, which were originally proposed by Sjoberg (Least squares modification of Stokes and VeningVening-Meinesz formulas by accounting for errors of truncation, potential coefficients and gravity data. Report No. 27, Department of Geodesy, University of Uppsala, 16pp.) in 1984 (with later developments). The main principles of the LS modifications and some spectral models of the gravity field characteristics are reviewed.本文致力于三个随机最小二乘(LS)修改，这是最初提出的舍贝里(最小二乘法修正的斯托克斯会计错误和Vening-Meinesz公式的截断,潜力系数和重力数据。报告编号27日，大地测量，乌普萨拉大学16页) 1984年(与后来的发展)。LS的主要原则的修改，一些光谱模型的重力场特征进行了综述。Certain difficulties may be encountered when computing the modification parameters from a system of linear equations.计算从线性方程系统的修正参数时，可能会遇到一些困难。In particular, the design matrices of the unbiased and optimum LS modifications suffer from numerical ill-conditioning.特别是，无偏的设计矩阵和最优LS修改数值病态。 Two mathematical regularization strategies are selected in order to find a practical solution for the sought modification parameters.为了寻求修改找到一个实用的解决方案，两个数学正则化策略的选择。Typical numerical outcome of the regularization and the applicability of the obtained LS parameters are discussed.正规化和所获得的LS参数的适用性的典型数值结果进行了讨论。The present contribution tackles the LS modification-related problems in the context of a specially designed Matlab software package. The core quantities of the stochastic LS modifi