Observability properties of relative position and heading estimation with bearing-only measurements

We consider the problem of relative position and heading estimation between two vehicles modeled as Dubins cars. We assume that one vehicle, say vehicle 2, is equipped with a monocular camera sensor to obtain bearing measurements of vehicle 1. We investigate global observability properties of this problem when the linear speeds and the angular velocities of both vehicles are constant. We establish observability conditions when the velocity information of vehicle 1 is communicated to vehicle 2. We also illustrate unobservable scenarios when both vehicles are cruising or orbiting. We further prove that the relative state is observable without communication between the vehicles, if vehicle 1 and 2 are orbiting and cruising, respectively. When both vehicles are orbiting, we develop conditions on the angular velocities of the vehicles to ensure observability.