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 $\mathbb {R}^3$ ) 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.

中文翻译：

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使用超声波进行高精度空间位置估计的流形优化

本文报告了通过利用发射机的固定几何形状使用超声波的高精度空间位置估计方法的设计。假设等腰三角形天线配置，其中三个天线放置为等腰三角形的顶点，空间位置问题可以表述为非凸优化问题，其内部显示允许黎曼流形结构。我们对新引入的流形（即所有等腰三角形的流形）的几何形状的研究$\mathbb {R}^3$ ) 可以设计高效的优化算法。提供了模拟以将所提出的方法的性能与文献中的流行方法进行比较。结果表明，所提出的基于黎曼的方法优于最先进的方法。此外，与流行的通用非凸方法相比，所提出的黎曼方法需要更少的计算时间。