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给出四类可用于重力场解算的正则化矩阵(零次、一次、二次和Kaula),以及用于确定正则化参数的L曲线法和GCV方法的数学模型。基于SA方法,利用模拟数据分析讨论了零次、一次以及Kaula正则化矩阵应用于GOCE全球重力场模型确定的有效性,并由Kaula正则化矩阵分析L曲线法和GCV方法确定正则化参数的可行性。数值结果表明三类正则化矩阵获得的最优解(以大地水准面MSE最小为准则确定)的精度水平相近,关键在于相应正则化参数的确定,数值结果同时说明了GCV方法和L曲线法可用于确定正则化参数,且前者较后者具有更好的稳定性。 更多还原

【Abstract】 The Tikhonov regularization is widely applied in the geodesy,the principle of which is discussed in this paper,including the mathematical models of four types of regularization matrices(zero-order,first-order,second-order and Kaula)and the regularization parameter selection methods:L-curve and GCV.The validation of zero-order,first-order and Kaula regularization matrices applied in the gravity field determination with GOCE simulated data is analyzed based on the SA method.And the applicability o... 更多还原