  The paper addresses the problem of minimizing the impact of non-linearities
when dealing with uncertainty propagation in the perturbed two-body problem.
The recently introduced generalized equinoctial orbital element set (GEqOE) is
employed as a means to reduce non-linear effects stemming from J$_2$ and higher
order gravity field harmonics. The uncertainty propagation performance of the
proposed set of elements in different Earth orbit scenarios, including
low-thrust orbit raising, is evaluated using a Cram\'er-von Mises test on the
Mahalanobis distance of the uncertainty distribution. A considerable
improvement compared to all sets of elements proposed so far is obtained.
