测绘学报

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Tikhonov正则化方法在GOCE重力场求解中的模拟研究

徐新禹1,李建成2,王正涛3,邹贤才3   

  1. 1. 武汉大学
    2. 武汉大学 测绘学院
    3. 武汉大学测绘学院
  • 收稿日期:2009-11-02 修回日期:2010-03-15 出版日期:2010-10-25 发布日期:2010-10-25
  • 通讯作者: 徐新禹

The Simulation Research on the Tikhonov Regularization Applied in Gravity Field Determination of GOCE Satellite Mission

  • Received:2009-11-02 Revised:2010-03-15 Online:2010-10-25 Published:2010-10-25

摘要: 本文在阐述Tikhonov正则化方法基本原理的基础上,给出了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正则化矩阵分析了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。

Abstract: GOCE satellite has been launched in 17 March 2009, the main objective of which is to provide a global gravity field model up to the degree and order 200. At the same time, the accuracies of the geoid and the gravity anomaly are 1-2 cm and 1 mGal respectively. Because of the distribution of observation data (Polar Gap) and the downward continuation problem, to the determination of the high-degree gravity field model using GOCE data is usually an ill-posed problem, which can be dealt with by regularization techniques. The Tikhonov regularization is widely applied in the geodesy, the principle of which is discussed in this paper, also 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 also the applicability of L-curve and GCV is discussed using the simulated data. The results show that the accuracies of the optimized solutions (selected by minimizing geoid MSE) with the three types of regularization matrices are at the same level. The key point is the selection of the corresponding regularization parameter. The results also show that GCV and L-curve can be applied in the regularization parameter estimation, and the former method is more stable than the latter one.