  The unscented transform uses a weighted set of samples called sigma points to
propagate the means and covariances of nonlinear transformations of random
variables. However, unscented transforms developed using either the Gaussian
assumption or a minimum set of sigma points typically fall short when the
random variable is not Gaussian distributed and the nonlinearities are
substantial. In this paper, we develop the generalized unscented transform
(GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal
components of the skewness and kurtosis tensors of most probability
distributions. Constraints can be analytically enforced on the sigma points
while guaranteeing at least second-order accuracy. The GenUT uses the same
number of sigma points as the original unscented transform while also being
applicable to non-Gaussian distributions, including the assimilation of
observations in the modeling of infectious diseases such as coronavirus
(SARS-CoV-2) causing COVID-19.
