This paper proposes a nonlinear estimator for the position of a quadrotor in waypoint navigation using squared range measurements perturbed by white noise. The convergence of the state estimate is studied along with an investigation of the stationary distribution of the estimation error. The stationary distribution is proved to converge to a zero-mean Gaussian with adjustable variance. Moreover, the proposed method is applied to pipeline inspection carried out by an autonomous quadrotor Uninhabited Air Vehicle (UAV). The simulation results demonstrate a stable estimation error that consistently converged to a neighborhood of zero and the quadrotor maintained its flight path directly above the pipeline geometry. The proposed nonlinear estimator is compared favorably with other methods in the literature in terms of convergence time and error (accuracy).

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.