Noisy localisation on the sphere

Localisation is a vital problem in a multitude of research fields, such as navigation, tracking, sensor networks and so on. In previous work, the problem is considered in the plane or in three-dimensional space. This work deals with the problem of distance-based localisation on the surface of the earth when the points lie in a two-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. We also quantify the effect of a planar approximation.