Wiener filters and collocation in satellite gradiometry

Abstract

Many years ago the problem was addressed in satellite geodesy whether the collocation scheme based on covariances estimated on the rotation group, under the hypothesis of stochastic invariance of the underlying random field, could be directly applied to the time-wise data analysis, which should be typically based on a prior hypothesis of time stationarity.

The answer was indeed in the negative, for the very simple reason that couples of points separated by constant time differences do not have equal spherical distances, not even in the case of a perfectly circular motion, due to earth rotation.

Nevertheless a direct computation based on simple examples shows that the variations of such distances are at most of a few percent up to half a cycle and that the covariances based on spherical models do agree quite well with those computed along the orbit if the estimation time is long enough, e.g. 1 month.

This has been verified in particular for functionals of the anomalous potential that are of direct interest for a gradiometric mission like GOCE; for instance this is true for T itself, for T _r and T _rr .