GOCE: dealing with large attitude variations in the conceptual structure of the space-wise approach

The space-wise approach to the analysis of GOCE data utilizes a grid of convenient “geographic” second order derivatives on a boundary sphere at satellite altitude. These derivatives are to be predicted from actually observed data, which include second derivatives along instrumental axes by a suitable time dependent rotation; in fact the instrumental and geographic frames are not perfectly aligned (e.g. the z-axis is not radial). The prediction can be performed by collocation by exploiting the full covariance (and cross-covariance) of the second derivatives tensors in two arbitrarily rotated frames. This solution is being implemented by the University of Copenhagen and it has to work only with local data for the well known limitation in the numerical handling of collocation formulas. Since the “radial” component Trr is the most informative one, we are particularly interested in the effect of the misalignment on the prediction of Trr. In this respect Tzz is the most important contributor because the z-axis is very close to the radial axis. In the paper we present a study on the possibility of performing this prediction by applying a Wiener filter along the orbit, exploiting the full spatial covariance structure of T, as it has been recently studied by the Politecnico di Milano, in a simpler context. This is done by applying the observational equation of Trr as expressed in terms of Tzz and then iterating on the complicated, but small, part of the relevant operator. With the noise behaviour as designed till the end of 2003, the method proves to be convergent. With the latest noise parameters, due to the dismission of the micro-propulsion system, it is not anymore; fortunately an extended treatment of GOCE data, to be presented in another paper in this volume [5], can overcome this drawback.