An Almost Global Estimator on SO(3) with Measurement on S²

This paper presents an almost globally convergent state estimator for the orientation of a rotating rigid body. The estimator requires knowledge of the angular velocity of the body at each time instant and the measurement consists of a single unit vector on the body, which we take without loss of generality to be the first column of the rotation matrix. The stability proof involves a relatively simple Lyapunov and invariance-like analysis. A mild non-degeneracy constraint on the control input guarantees the fulfillment of the invariance criterion. We apply the result to needle-tip orientation estimation for tip-steerable needles.