Single range navigation in the presence of constant unknown drifts

This paper addresses the problem of navigation/source localization by mobile agents based on the range to a single source. The agent is allowed to have a constant unknown drift relative to an inertial reference frame, which is common, for example, in ocean robotic vehicles in the presence of sea currents, and the source may also have a constant unknown velocity relative to the inertial frame. The contribution of the paper is twofold: i) necessary and sufficient conditions on the observability of the system are derived that are useful for the motion planning and control of the agent; ii) a linear model is developed that mimics the exact dynamics of the nonlinear range-based system, and a Kalman filter is synthesized to estimate the position of the source, as well as the difference between the agent and the source drift velocities. Simulation results that illustrate the performance of the proposed solution in the presence of realistic measurement noise are presented and discussed.