An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra

Riccardi, Annalisa and Tardioli, Chiara and Vasile, Massimiliano; Turner, J. D. and Wawrzyniak, G. G. and Cerven, W. T. and Majji, M., eds. (2015) An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. In: Astrodynamics 2015. Advances in Astrnautical Sciences . American Astronautical Society, USA, pp. 707-722. ISBN 9780877036296

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Abstract

The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra. Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost.

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