A Robust Unscented Transformation for Uncertain Moments
Statistics Theory
2019-02-26 v1 Optimization and Control
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1902.09293,
title = {A Robust Unscented Transformation for Uncertain Moments},
author = {Hugo T. M. Kussaba and João Y. Ishihara and Leonardo R. A. X. Menezes},
journal= {arXiv preprint arXiv:1902.09293},
year = {2019}
}
Comments
26 pages, 3 figures, accepted by Journal of the Franklin Institute