  This paper proposes a robust version of the unscented transform (UT) for
one-dimensional random variables. It is assumed that the moments are not
exactly known, but are known to lie in intervals. In this scenario, the moment
matching equations are reformulated as a system of polynomial equations and
inequalities, and it is proposed to use the Chebychev center of the solution
set as a robust UT. This method yields a parametrized polynomial optimization
problem, which in spite of being NP-Hard, can be relaxed by some algorithms
that are proposed in this paper.
