B6


Advances in uncertainty propagation using Curvilinear coordinates

Javier Hernando-AyusoiThe University of Tokyoj, Claudio BombardelliiTechnical University of Madridj


An orbit is determined from a set of observations which must be input into an estimator or filter, yielding not only a nominal orbit but also an uncertainty region where the real orbit could lay on. The uncertainty region is actually centered at the nominal orbit, and the small deviations between the nominal orbit and the real orbit can be studied using the relative motion between them. While the nominal orbit propagation has been extensively studied, more advances techniques are needed to better characterize the evolution of the uncertainty probability distribution function. Linearization methods are able to propagate this uncertainty region as a first approximation, and additionally Gaussian distribution remain Gaussian when used, which makes them good candidates. A novel method based on the linearization around an analytical solution of the relative motion expressed in Curvilinear coordinates is presented. The main advantages of this method are: a) the nominal orbit is propagated at low computational cost   th high accuracy; b) the new method can be seen as a more accurate version of the Clohessy-Wiltshire equations; c) when applied to an uncertainty cloud, the Curvilinear-coordinates-based method can retain better the uncertainty probability distribution when compared to techniques based on Cartesian coordinates. The method is finally applied to study potential collisions between a derelict object and an active satellite in GEO.