引用本文: 苏勇, 范东明, 谷延超. 利用能量守恒法和GOCE卫星轨道数据反演地球重力场模型[J]. 武汉大学学报 ( 信息科学版), 2014, 39(9): 1043-1046.
SU Yong, FAN Dongming, GU Yanchao. Gravity Field Modeling Using Energy ConservationApproach and GOCE Orbits[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1043-1046.
 Citation: SU Yong, FAN Dongming, GU Yanchao. Gravity Field Modeling Using Energy ConservationApproach and GOCE Orbits[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1043-1046.

## Gravity Field Modeling Using Energy ConservationApproach and GOCE Orbits

• 摘要: 目的 利用傅立叶级数拟合GOCE卫星的耗散能,解决了基于能量守恒法恢复GOCE重力场模型时耗散能的计算问题。采用Helmert-Wolf参数估计法统一求解位系数、能量常数和耗散能的傅立叶级数拟合参数,并采用消局部参数的最小二乘法求解位系数。该方法不需要任何初始值或参考模型,不需要采用差分方法处理能量常数,也不需要进行迭代计算。利用GOCE卫星2009-11-01～2010-02-12共103d的精密轨道数据反演了三组100阶次的重力场模型GOCE-ECP01S、GOCE-ECP02S和GOCE-ECP03S,并与EIGEN-5C、EIGEN-CHAMP05S和GOCO03S模型进行比较。结果表明,采用一阶傅立叶级数拟合GOCE卫星的耗散能效果最好,反演的GOCE-ECP01S模型精度最高,整体精度优于EIGEN-CHAMP05S,但较GOCO03S模型的精度偏低;在100阶次的大地水准面误差为±3.2cm,但由于极空白的影响,恢复模型的带谐项位系数精度偏低。

Abstract: Objective The dissipative energy of the GOCE satellite is fitted by a Fourier series,this method cansolve the calculation problem for dissipative energy when the GOCE gravity field model is recoveredbased on an energy conservation approach.The Helmert-Wolf parameter estimation method is adoptedto provide an integer estimate for potential coefficients,the energy constant and Fourier series fittingparameters of dissipative energy.The potential coefficients are solved by elimination for the regionalparameter by least squares.Three gravity field models,up to the degree and order 100,namedGOCE-ECP01S,GOCE-ECP02Sand GOCE-ECP03S,are recovered based on the GOCE orbits for103-days from 2009-11-01to 2010-02-12.Finally,the models are compared with the existing EIGEN-6C,ITG-CHAMP05Sand GOCO03Smodels.The results show that the GOCE-ECP01Smodel is themost accurate when GOCE satellite dissipative energy is fitted by an one order Fourier series which ishigher than the ITG-CHAMP05Smodel,but lower than the model GOCO03S.The geoid error in theGOCE-ECP01Smodel is±3.2cm for the degree and order 100,but the precision of zonal coefficientsis low due to the polar gap.

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