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 $R^n$ 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.