On the use of positive polynomials for the estimation of upper and lower expectations in orbital dynamics

Vasile, Massimiliano and Tardioli, Chiara; Vasile, Massimiliano and Minisci, Edmondo and Summerer, Leopold and McGinty, Peter, eds. (2018) On the use of positive polynomials for the estimation of upper and lower expectations in orbital dynamics. In: Stardust Final Conference. Astrophysics and Space Science Proceedings . Springer, NLD, pp. 99-107. ISBN 9783319699561 (https://doi.org/10.1007/978-3-319-69956-1_6)

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Abstract

The paper presents the use of positive polynomials, in particular Bernstein polynomials, to represent families of probability distributions in orbital dynamics. The uncertainty in model parameters and initial conditions is modeled with p-boxes to account for imprecision and lack of knowledge. The resulting uncertainty in the quantity of interest is estimated by representing the upper and lower expectations with positive polynomials with interval coefficients. The impact probability of an asteroid subject to a partially known Yarkovsky effect is used as an illustrative example.

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