Unique Localization Solutions via Anchor Positions

In this paper, the authors present a novel approach for localizing networks based on angle-displacement invariance. The proposed method leverages the known anchor positions and one type of local relative measurements to determine the network position. The key idea is to formulate the localization problem as finding the best estimate of the network position that preserves the angles and displacements of the anchor nodes.
To achieve this, the authors first define an angle-displacement rigidity matrix, which represents the relationship between the angles and displacements of adjacent nodes in the network. They then introduce a localization cost function that minimizes the difference between the estimated network position and the known anchor positions, while ensuring that the angles and displacements of the anchor nodes are preserved.
The authors demonstrate the effectiveness of their approach through numerical experiments on several benchmark networks. The results show that their method outperforms existing localization techniques in terms of accuracy and computational efficiency.
In simple terms, the authors propose a localization method for networks by treating them as rigid bodies that can be moved around while preserving their angles and displacements. By formulating the problem as finding the best estimate of the network position that satisfies these constraints, they are able to develop an efficient and accurate approach for determining the position of a network.
The key insight behind this method is that networks can be thought of as having a "skeleton" or "frame" that remains fixed while the rest of the network moves around it. By leveraging this invariance, the authors are able to reduce the localization problem to a simpler optimization problem that can be solved efficiently.
Overall, this paper presents a significant advance in the field of network localization by introducing a novel and effective approach based on angle-displacement invariance. The proposed method has important implications for applications such as robotics, computer vision, and IoT, where accurate localization is crucial for task performance and network operation.