Journal of Grodesy and Geodynamics (大地测量与地球动力学) 2013/4:4 PP.1-8
When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem.In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first-and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors.
 Lu Zhonglian. Theory and method of the Earth's gravity field. Beijing: PLA Publishing House, 1996.(in Chinese)
 Zhang Chuanding. Satellite gravimetry: foundation, modeling methods, and data processing algorithms. Zhengzhou: Information Engineering University, 2000. (in Chinese)
 Li Yingchun. Theories and method of the recovery of the Earth's gravity field using satellite gravity gradients. Zhengzhou: Information Engineering University, 2004. (in Chinese)
 Wu Xing. Research of methods of spherical harmonic analysis of the Earth's gravity field. Zhengzhou: Information Engineering University, 2009. (in Chinese)
 Luo Zhicai. Theories and method of the determination of the Earth's gravity field using satellite gravity gradients. Wuhan: Wuhan Technical University of Surveying and Mapping, 1996. (in Chinese)
 Xu Xinyu. Study of determining the Earth's gravity field from satellite gravity gradient and satellite~to~satellite tracking data. Wuhan: Wuhan University, 2008. (in Chinese)
 Zhong Bo. Study on the determination of the Earth's gravity field from satellite gravimetry mission GOCE. Wuhan: Wuhan University, 2010.(in Chinese)
 Liu Xiaogang. Theory and methods of the Earth's gravity field model recovery from GOCE data. Zhengzhou: Information Engineering University, 2011. (in Chinese)
 Wan Xiaoyun. Gravity field recovery using GOCE gradients data and its application. Beijing: The University of Chinese Academy of Sciences, 2013. (in Chinese)
 Hotine M and Morrison F. First integrals of the equations of satellite motion. Journal of Geodesy, 1969, 43(1): 41-45.
 Ilk K H. Ein Beitrag zur Dynamik ausgedehnter K,rper~Gravitationswechselwirkung. Deutsche Geod,tische Kommission, Reihe C, Heft Nr.288, Muchen, 1983.
 Balmino G, Barriot J and Valès N. Non~singular formulation of the gravity vector and gravity gradient tensor in spherical Harmonic. Manuscript Geodaetica, 1990, 15(1): 11-16.
 Bettadpur S V. Hotine's Geopotential Formulation: revisited. Bulletin Géodésique, 1995, 69: 135-142.
 Petrovskaya M S and Vershkov A N. Non~singular expressions for the gravity gradients in the local north~oriented and orbital reference frames. Journal of Geodesy, 2006, 80: 117-127.
 Petrovskaya M S and Vershkov A N. Local orbital derivatives of the Earth potential expressed in terms of the satellite cartesian coordinates and velocity. Artificial Satellites, 2007, 42(1):17-39.
 Casotto S and Fantino E. Evaluation of methods for spherical harmonic synthesis of the gravitational potential and its gradients. Adv Space Res., 2007, 40(1): 69-75.
 Eshagh M. Non~singular expressions for the vector and the gradient tensor of gravitation in a geocentric spherical frame. Computers & Geosciences, 2008, 34(12): 1762-1768.
 Eshagh M and Sj,berg L E. Topographic and atmospheric effects on GOCE gradiometric data in a local north~oriented frame: a case study in Fennoscandia and Iran. Studia Geophysica et Geodaetica, 2009, 53(1):61-80.
 Fantino E and Casotto S. Methods of harmonic synthesis for global geopotential models and their first, second and third order gradients. Journal of Geodesy, 2009, 83(7): 595-619.
 Yu Jinhai and Wan Xiaoyun. Non~singular formulae for computing derivatives of legendre functions. Journal of Geomatics Science and Technology, 2010, 27(1):1-3. (in Chinese)
 Liu Xiaogang, Wu Xiaoping, Zhao Dongming and Wu Xing. Non -singular expression of the disturbing gravity gradients. Geodaetica et Cartographica Sinica, 2010, 39(5): 450-457. (in Chinese)
 Wan Xiaoyun. New derivation of nonsingular expression for gravitational gradients calculation. Geomatics and Information Science of Wuhan University, 2011, 36(12): 1486-1489. (in Chinese)
 Liu Xiaogang, Wu Juan and Ji Jianfeng. Construction of non-singular computational model of trajectory disturbing gravity. Progress in Geophysics, 2013, 28(2): 579-584. (in Chinese)