An error model for the GOCE space-wise solution by Monte Carlo method

The aim of the data analysis of the GOCE satellite mission is to estimate spherical harmonic coefficients of the gravitational potential and the corresponding error covariance matrix. However this error estimation is generally very complicated and computationally demanding because of the large number of observations. In particular, this is true for the space-wise approach, which is a collocation solution implemented by several steps. Up to now the error covariance matrix for this approach has been computed under simplifying hypotheses. In order to get a more realistic assessment of the true estimation error a Monte Carlo method can be applied. This requires the generation of several stochastic simulations and the computation of the corresponding solutions. This procedure is made numerically feasible by storing and not recomputing every time the operators that form the space-wise approach. Tests on realistic scenarios are performed and positive results are achieved.