Construction of nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors

Abstract

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.

Keywords

• nonsingular
• gravity field model
• satellite gravity gradient
• variance
• covariance