Analysis of the covariance structure of the GOCE space-wise solution with possible applications

The estimation of a global gravity model from a satellite mission like GOCE is a tough task from the numerical point of view and the computa-tion of the error covariance structure of the solution is even tougher. This is due to the sophisticated treatment of the data and the large number of unknowns (e.g., 40,000) simultaneously processed. However information on such a covariance matrix can be derived from the Monte Carlo method, basically propagating simulated input noise to derive the error vector of the spherical harmonic coefficients. The estimated covariance then is just the sample covariance of the output error. Since the number of samples can be much smaller than the number of unknowns, although the individual covariances are consistently estimated, the overall covariance structure cannot be caught by such a Monte Carlo estimate. This fact is studied with some detail for the Monte Carlo covariance matrix of the GOCE space-wise solution, in order to confirm in the positive sense the conjecture that the solution organized by orders has a prevailing block diagonal structure. Starting from this result, the problem of combining two sets of spherical harmonic coefficients is investigated. In particular this problem is studied in the framework of the space-wise approach that requires the combination between coefficients derived from a grid of potential and coefficients derived from a grid of second radial derivatives. Different combination strategies are considered, including one based on a Bayesian approach. All these strategies, however, lead to similar results in terms of accuracy of the final model