Discrete search-based determination of a local orbital frame in unknown environments

A local orbital frame is an important and often applied coordinate frame in attitude and orbit control. Usually, a navigation filter estimates the position and velocity vector, which are used to build up this reference frame. It is beneficial for many space applications, such as communication or Earth observation missions, or for conducting orbit control maneuvers to change the orbit plane. Furthermore, satellite formation flying can require an orbital frame to describe relative motion. This work investigates the feasibility of determining the local-vertical local horizontal (LVLH) frame without full knowledge of the orbit. This scenario often applies to non-characterized small bodies like asteroids or comets. A discrete search method is used to determine the complete LVLH frame in real-time, assuming that one axis, a line-of-sight vector to the body's center of mass, is known. By minimizing an objective function, the remaining axes can be determined. The estimated parameters are the inclination and the right ascension of the ascending node of the osculating orbit plane. This study investigates the feasibility of this concept and then applies it to perturbed orbits and sensor noise. The proposed method demonstrates that a discrete search can determine the LVLH frame. The approach can be seen as a step toward increasing the autonomy of a spacecraft near small bodies with unknown environments.