基于角度测量的平面点嵌入的可实现性
Realizability of Planar Point Embeddings from Angle Measurements
摘要：
节点定位问题是机器人学和传感器网络中的一个重要而深入的研究课题。本文研究了内角定位理论。我们专注于具有挑战性的情况下，没有锚的位置是已知的。受欧氏距离矩阵的启发，我们研究了内角集对应于可实现点集的情况。特别是，我们发现线性和非线性的约束，可证明是必要的，我们猜想也足以表征可实现的角度集。我们证实了这一点，在广泛的数值模拟，我们说明了使用这些约束去噪的角度测量以及重建一个有效的点集。
英文摘要：
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case where no anchor locations are known. Inspired by Euclidean distance matrices, we investigate when a set of inner angles corresponds to a realizable point set. In particular, we find linear and non-linear constraints that are provably necessary, and we conjecture also sufficient for characterizing realizable angle sets. We confirm this in extensive numerical simulations, and we illustrate the use of these constraints for denoising angle measurements along with the reconstruction of a valid point set.
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