Uncertainty treatment in the GOCE re-entry

This paper presents the work to characterize and propagate the uncertainties on the atmospheric re-entry time of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite done with the framework of an ESA ITT project. Non-intrusive techniques based on Chebyshev polynomial approximation, and the Adaptive High Dimensional Model Representation multi-surrogate adaptive sampling have been used to perform uncertainty propagation and multivariate sensitivity analyses when both 3 and 6 degrees-of-freedom models where considered, considering uncertain-ties on initial conditions, and atmospheric and shape parameters. Two different uncertainty quantification/characterization approaches have been also proposed during the project. The same interpolation techniques used for non-expensive non-intrusive methods for uncertainty propagation, allowed the development of two methods based on direct optimization approaches, the Boundary Set Approach and the Inverse Uncertainty Quantification. Moreover, an innovative approach to treat the empirical accelerations has been proposed, based on polynomial expansions in the state variables. The method has been tested and further developed to consider uncertainties in the initial conditions, leading to a statistical characterization of the coefficients and representation of the possible trajectories. Finally, the investigation on the use of meta-modeling techniques to directly map a range of initial conditions and model uncertainties, as well as characteristics of the considered object, into the parameters of the skew-normal distribution that usually characterizes the re-entry time windows, bringing to a very fast characterization of the output PDF not requiring any further propagation at all, is also briefly described.