The Conjugate Unscented Transform - A Method to Evaluate Multidimensional Expectation Integrals
MetadataShow full item record
This thesis presents an extension to the unscented transformation to evaluate expectation integrals in general N -dimensional space by satisfying higher order moment constraint equations. New sets of sigma points are defined to satisfy moment equations up to order 8. The proposed methodology can be used as an efficient alternative to Gaussian quadrature rule with significantly reduced number of function evaluations while maintaining accuracy. The cubature rules documented in this thesis is compared to the Gauss Hermite product rule and other computational algorithms with illustrative examples. In the realm of nonlinear filtering, the new set of sigma points have the potential to provide a significant advantage in terms of accuracy and reduced computational complexity, thus providing a promising application in on-line non-linear filtering. Numerical simulations of a typical Air traffic problem are illustrated that show the effectiveness of the proposed methodology in better computing high dimension expectation integrals thus better estimates in the filtering process. Keywords: Gaussian Quadratures,Sparse Grid Quadratures, Minimal Cubature Rules, Unscented Transform, State Estimation, Unscented Kalman Filter.