Single beacon navigation: Observability analysis and filter design

This paper addresses the problem of navigation of autonomous vehicles based on the range to a single beacon. The vehicle is equipped with a standard Inertial Measurement Unit (IMU) and range measurements to a single source are available as an aiding observation, in addition to angular velocity readings. The contribution of the paper is twofold: i) necessary and sufficient conditions on the observability of the system are derived that can be used for the motion planning and control of the vehicle; ii) a linear model is developed that mimics the exact dynamics of the nonlinear range-based system, and a Kalman filter is applied to estimate the relative position of the source, as well as the linear velocity of the vehicle and the acceleration of gravity, all expressed in body-fixed coordinates. Simulation results are presented in the presence of realistic measurement noise that illustrate the performance achieved with the proposed solution.