Relative pose estimation from bearing measurements of three unknown source points

This paper unveils a novel discovery that the full relative pose of a monocular camera moving in a three dimensional space can be estimated exploiting bearing measurements of only 3 unknown source points (together with velocity measurements) without any additional knowledge if the camera translational motion is sufficiently exciting. The epipolar constraint commonly used in Computer Vision algebraic algorithms for the determination of the so-called essential matrix (all of them require at least 5 source points) is here exploited in the design of the proposed Riccati observer for pose estimation. One remarkable feature of this work is the determination of an explicit persistence of excitation condition that guarantees uniform observability and, subsequently, (local) exponential stability of the proposed observer. Convincing simulation results are provided to support the proposed approach.