On the uniform observability of the relative pose estimation problem using bearing measurements and epipolar constraints

This paper proposes a comprehensive observability analysis of the relative pose estimation of a monocular camera (moving in three-dimensional space) from bearing measurements and epipolar constraints. It extends our previous work on observer design for the particular case of 3-source points with unknown 3D coordinates. The paper addresses the observability analysis of the more general case of n-source points (n ≥ 3) using persistence of excitation of the translational motion and bearing references (or equivalently, the position of the origin of the reference frame with respect to the source points). The key contribution of this work is to show that the persistence of excitation is not enough to guarantee uniform observability. In particular, we show that uniform observability also depends on bearing references and the number of observed source points.