  This paper designs a high accuracy spatial location estimation method using
ultrasound waves by exploiting the fixed geometry of the transmitters. Assuming
an equilateral triangle antenna configuration, where three antennas are placed
as the vertices of an equilateral triangle, the spatial location problem can be
formulated as a non-convex optimization problem whose interior is shown to
admit a Riemannian manifold structure. The investigation of the geometry of the
newly introduced manifold, i.e. the manifold of all equilateral triangles in
R^3, allows the design of highly efficient optimization algorithms. Simulation
results are presented to compare the performance of the proposed approach
against popular methods from the literature. The results suggest that the
proposed Riemannian-based methods outperform the state-of-the-art methods.
Furthermore, the proposed Riemannian methods require much smaller computation
time as compared with popular generic non-convex approaches.
