| Summary: | This paper studies the problem of localising a Global Positioning System (GPS)-denied Unmanned Aerial Vehicle (UAV) in two-dimensional space. Suppose there are two vehicles, one which is equipped with GPS and the other is GPS-denied (but has an inertial navigation system (INS) and so is able to determine its trajectory in a local coordinate frame, but not a global coordinate frame). The GPS-equipped vehicle broadcasts its global coordinates to the GPS-denied vehicle and the GPS-denied vehicle also obtains, in its local coordinate frame, a bearing measurement of the GPS-equipped UAV. The paper shows that with four or more such measurements and generic trajectories of the two UAVs, localisation in a global coordinate frame of the GPS-denied UAV is achievable. Certain nongeneric trajectories for which localisation is impossible are also identified. While in the first instance, the solution assumes zero noise in the measurements, the techniques are then extended to deal with the presence of measurement noise.
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