Position estimation from direction or range measurements

This paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, also when the measured velocity is biased by an unknown constant vector or when direction measurements are corrupted by an unknown constant bias. With respect to prior contributions on these subjects they provide a coherent generalization of existing solutions with the preoccupation of pointing out general and explicit persistent excitation (p.e.) conditions whose satisfaction ensures uniform exponential stability of the observers.