UAV circumnavigation of an unknown target without location information using noisy range-based measurements

This paper proposes a control algorithm for a UAV to circumnavigate an unknown target at a fixed radius when the location information of the UAV is unavailable. By assuming that the UAV has a constant velocity, the control algorithm makes adjustments to the heading angle of the UAV based on range and range rate measurements from the target, which may be corrupted by additive measurement noise. The control algorithm has the added benefit of being globally smooth and bounded. Exploiting the relationship between range rate and bearing angle, we transform the system dynamics from Cartesian coordinate in terms of location and heading to polar coordinate in terms of range and bearing angle. We then formulate the addition of measurement errors as a stochastic differential equation. A recurrence result is established showing that the UAV will reach a neighborhood of the desired orbit in finite time. Some statistical measures of performance are obtained to support the technical analysis.