Observer design for position and velocity bias estimation from a single direction output

This paper addresses the problem of estimating the position of an object moving in ℝn from direction and velocity measurements. After addressing observability issues associated with this problem, a nonlinear observer is designed so as to encompass the case where the measured velocity is corrupted by a constant bias. Global exponential convergence of the estimation error is proved under a condition of persistent excitation upon the direction measurements. Simulation results illustrate the performance of the observer.