  In this paper, a new parametrization of the relative motion between two
satellites orbiting a central body is presented. The parametrization is based
on the nodal elements: a set of angles describing the orbit geometry with
respect to the relative line of nodes. These are combined with classical
orbital elements to yield a nonsingular relative motion description. The exact
nonlinear, perturbed dynamic model resulting from the new parametrization is
established. The proposed parameter set captures the fundamental Keplerian
invariants, while retaining a simple relationship with local orbital
coordinates. An angles-only relative navigation filter and a collision
avoidance scheme are devised by exploiting these features. The navigation
solution is validated on a case study of an asteroid flyby mission. It is shown
that a collision can be detected early on in the estimation process, which
allows one to issue a timely evasive maneuver.
