  This paper reports the design of a high-accuracy spatial location estimation
method using ultrasound waves by exploiting the fixed geometry of the
transmitters. Assuming an isosceles triangle antenna configuration, where three
antennas are placed as the vertices of an isosceles triangle, the spatial
location problem can be formulated as a non-convex optimization problem whose
interior is shown to admit a Riemannian manifold structure. Our investigation
of the geometry of the newly introduced manifold (i.e., the manifold of all
isosceles triangles in R3) enables the design of highly efficient optimization
algorithms. Simulations are presented to compare the performance of the
proposed approach with 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 less
computation time compared to popular generic non-convex approaches.
