Nonlinear Observer for Quadrotor Waypoint Navigation Using Only Range Measurements

This paper proposes a novel nonlinear estimator for the position of a quadrotor in waypoint navigation using range measurements. It is assumed that the flying vehicle follows a straight line at a constant altitude between two waypoints. The positions of the waypoints are known and the measurements are assumed to be the squared distance to the point source located at the departure waypoint. The measurement is corrupted by additive noise. Under these conditions it is shown that the dynamics of the estimation error are described by a nonlinear Verhulst logistc equation. This observation unveils a link between navigation of a vehicle using range measurements and population dynamics, which to the best of the authors' knowledge is new. The stability of the error dynamics and the stationary distribution of the error are investigated for both constant and ramp velocity inputs. The performance of the proposed estimator is evaluated and compared with a Kalman filter for an augmented system. A numerical example illustrates the proposed method.