Single range aided navigation and source localization: Observability and filter design

This paper addresses the problems of navigation and source localization by mobile agents based on the range to a single source, in addition to relative velocity readings. The contribution of the paper is two-fold: (i) necessary and sufficient conditions on the observability of the nonlinear system are derived, which are useful for trajectory planning and motion control of the agent; and (ii) a nonlinear system, which given the input and output of the system is regarded as linear time-varying, is proposed and a Kalman filter is applied to successfully estimate the system state. Simulation results are presented in the presence of realistic measurement noise that illustrate the performance achieved with the proposed solution.