The higher order unscented filter

This article proposes a technique for the selection of the σ-set for a probability distribution approximation filter, i.e., the unscented filter. The σ-set is selected so as to capture the higher order input statistics. The Taylor series expansion is used to illustrate that the 3^rd order and higher statistics of the nonlinear transformation can be reproduced while the unscented filter captures the statistics up to the 3^rd order only. Two benchmark problems are used to corroborate the proposed solution.