The Conjugate Unscented Transform — An approach to evaluate multi-dimensional expectation integrals

This paper presents an extension to the unscented transformation to evaluate expectation integrals in general N-dimensional space by satisfying higher order moment equations. New sets of sigma points are defined to satisfy moment equations up to eighth order. The proposed methodology can be used as an efficient alternative to Gaussian quadrature rule with significantly reduced number of function evaluations but without any loss in accuracy. Numerical simulation results illustrates the effectiveness of the proposed methodology in computing high dimension expectation integrals with significantly reduced number of function evaluations.