GOCE gravity gradient predictions by Taylor-Karman structured covariance tensor

The modern space missions, e.g. ERS, SPOT, and the FORMOSAT etc., have offered a number of data and images for Earth's resource exploration and environment monitoring. Recently, the Gravity-field and steady-state Ocean Circulation Explorer (GOCE) satellite mission provides highly precise gradiometric measurement data for recovery of Earth's gravity field from space. When using the gravity gradients (the second derivatives of the gravitational potential) for prediction and filtering by stochastic processes like the Kolmogorov-Wiener or Gauss-Markov method, we have to first give the fourth-order variance-covariance/correlation matrices of the gravity gradient signals. For the consistency, this paper aims at the development of the fourth-order variance-covariance matrices by the famous Taylor-Kármán structured tensor. The variance-covariance Tensors developed here can be as prior information for fitting the discrete data from observations. Numeric examples illustrate the adaptation of our variance-covariance matrices.