Stochastically convergent localization of objects by mobile sensors and actively controllable relative sensor-object

The problem of object (network) localization using a mobile sensor is examined in this paper. Specifically, we consider a set of stationary objects located in the plane and a single mobile nonholonomic sensor tasked at estimating their relative position from range and bearing measurements. We derive a coordinate transform and a relative sensor-object motion model that leads to a novel problem formulation where the measurements are linear in the object positions. We then apply an extended Kalman filter-like algorithm to the estimation problem. Using stochastic calculus we provide an analysis of the convergence properties of the filter. We then illustrate that it is possible to steer the mobile sensor to achieve a relative sensor-object pose using a continuous control law. This last fact is significant since we circumvent Brockett's theorem and control the relative sensor-source pose using a simple controller.