Noisy localization on the sphere: A preliminary study

The problem of sensor network localization or target localization based on distance measurements has been well studied. In previous work, the problem is considered in the plane or in 3-dimensional space. This work deals with the problem of great distance localization on the surface of the earth when the planar assumption becomes invalid, but there remain the constraint that the points lie in a 2-dimensional manifold. The challenge lies with finding an appropriate technique to cope with noisy measurements when the conventional formulation for a planar model cannot be used. To this end, we adopt a tool recently applied to the planar model, the Cayley-Menger matrix. Simulation results show that the proposed method is effective and robust to noise. Open questions are also identified.