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研究利用卫星重力梯度径向分量确定地球引力场位系数的最小二乘配置(LSC)调和分析方法。首先论述最小二乘配置法的原理,推导扰动引力梯度观测量与球谐系数之间的协方差和自协方差矩阵。在扰动引力梯度观测数据为等经差规则网格数据的情况下,引力位与扰动引力梯度之间的协方差矩阵具有分块Toeplitz循环阵的结构,有效地利用FFT变换技术将其降阶。研究利用截断奇异值分解法(TSVD)减弱协方差阵的病态性。最后得到引力梯度径向分量的最小二乘配置调和分析的完整计算公式。模拟试算结果表明,基于TSVD的最小二乘配置调和分析方法,能够以较高的精度还原全球重力场,验证本文算法的有效性和实用性。 更多还原

【Abstract】 The least-squares collocation harmonic analysis method,which is used to determine the earth geopotential coefficients from the radial satellite gravity gradient,is deeply studied.The principle of the least-squares collocation is firstly dissertated,and the covariance and self-covariance matrix between the disturbing gravity gradients and spherical harmonics are derived.When the disturbing gravity gradients are in the regularized equi-longitude grid,the covariance matrix between geopotential and ... 更多还原