测绘学报

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卫星重力梯度数据确定地球重力场的Slepian局部谱分析方法

朱广彬1,李建成2,文汉江3,常晓涛1,王正涛4,邹贤才5   

  1. 1. 国家测绘局卫星测绘应用中心
    2. 武汉大学 测绘学院
    3. 中国测绘科学研究院
    4. 武汉大学
    5. 武汉大学测绘学院
  • 收稿日期:2011-01-13 修回日期:2011-05-31 出版日期:2012-02-25 发布日期:2012-02-25
  • 通讯作者: 朱广彬

Slepian Localized Spectral Analysis of the Determination of the Earth’s Gravity Field Using Satellite Gravity Gradiometry Data

  • Received:2011-01-13 Revised:2011-05-31 Online:2012-02-25 Published:2012-02-25

摘要: 卫星大地测量中的极空白问题导致了在地球重力位模型的解算中,低次球谐系数的估计精度较低。在引入Slepian局部谱分析方法的基础上,详细分析了Slepian函数的数学特性,采用Grünbaum算子提高了Slepian方法求解的稳定性和效率。在此基础上,推导了卫星重力梯度数据确定地球重力场的Slepian方法表达式。通过仿真分析,就Slepian方法在卫星重力梯度数据确定地球重力位模型中的应用和前景进行了分析和讨论。研究表明,Slepian函数在整个球面和球带上具有双正交性,其频谱能量分布特征与卫星轨道的测量特点具有很好的一致性。Slepian频域内的地球重力场求解精度较之球谐域内的结果要高,但其对大地水准面空间分布的恢复精度贡献不明显。

Abstract: The polar gaps in satellite geodesy lead to poor estimability of low order spherical harmonic coefficients of the Earth’s gravity field model. The Slepian localized spectral analysis method is introduced in this paper and its mathematical characteristics are analyzed. Grünbaum operator is introduced into the solution process in order to improve the computational efficiency and stability. Then, the practical formulas of Slepian method for recovering the gravity field with satellite gravity gradiometry data are educed and numerical analysis are done. The results indicate that, Slepian function is orthogonal in both the sphere and the belt, and its spectral energy distribution characteristic is in accord with the orbit characteristic. Also, the accuracy of Slepian method in Slepian domain is better than that of Legendre solution in spherical harmonic domain. However, the contribution of Slepian method to the improvement of geoid is limited.