Conjugate Unscented Transformation: Applications to Estimation and Control

This paper presents a computationally efficient approach to evaluate multidimensional expectation integrals. Specifically, certain nonproduct cubature points are constructed that exploit the symmetric structure of the Gaussian and uniform density functions. The proposed cubature points can be used as an efficient alternative to the Gauss–Hermite (GH) and Gauss–Legendre quadrature rules, but with significantly fewer number of points while maintaining the same order of accuracy when integrating polynomial functions in a multidimensional space. The advantage of the newly developed points is made evident through few benchmark problems in uncertainty propagation, nonlinear filtering, and control applications.