A dynamic estimator on SE(3) using range-only measurements

This paper addresses the problem of estimating the attitude and position of a rigid body when the available measurements consist only of the relative distances between a set of body fixed beacons and a set of Earth fixed landmarks. The proposed solution is given in terms of a dynamical system evolving on the Special Euclidean group SE(3), the trajectories of which are shown to locally converge to the actual attitude and position of the rigid body. Local asymptotic stability of the dynamical system is proven by using a suitable Lyapunov function, under the assumption that there is a set of noncoplanar landmarks and beacons. Simulation results are shown to illustrate the behaviour of the proposed estimator.