  This paper introduces a novel method for the automatic detection and handling
of nonlinearities in a generic transformation. A nonlinearity index that
exploits second order Taylor expansions and polynomial bounding techniques is
first introduced to rigorously estimate the Jacobian variation of a nonlinear
transformation. This index is then embedded into a low-order automatic domain
splitting algorithm that accurately describes the mapping of an initial
uncertainty set through a generic nonlinear transformation by splitting the
domain whenever some imposed linearity constraints are non met. The algorithm
is illustrated in the critical case of orbital uncertainty propagation, and it
is coupled with a tailored merging algorithm that limits the growth of the
domains in time by recombining them when nonlinearities decrease. The low-order
automatic domain splitting algorithm is then combined with Gaussian mixtures
models to accurately describe the propagation of a probability density
function. A detailed analysis of the proposed method is presented, and the
impact of the different available degrees of freedom on the accuracy and
performance of the method is studied.
