Riccati observers for position and velocity bias estimation from direction measurements

This paper addresses the problem of estimating the position of a body moving in n (≥ 2)-dimensional Euclidean space using body velocity measurements and the measurements of direction(s) between the body and one (or several) source point(s) whose location(s) is (are) known. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, even when the measured body velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to previous contributions on the subject the proposed framework encompasses the static case, when the body is motionless and at least two source points are needed to recover its position, and the non-static case, when body motion and a single source are sufficient. Simple and explicit observability conditions under which uniform exponential stability is achieved are also worked out for each case. Simulation results illustrate the performance of the proposed observers.