This paper studies angle-based sensor network localization (ASNL) in a plane, which is to determine locations of all sensors in a sensor network, given locations of partial sensors (called anchors) and angle measurements obtained in the local coordinate frame of each sensor. Firstly it is shown that a framework with a non-degenerate bilateration ordering must be angle fixable, implying that it can be uniquely determined by angles between edges up to translations, rotations, reflections and uniform scaling. Then ASNL is proved to have a unique solution if and only if the grounded framework is angle fixable and anchors are not all collinear. Subsequently, ASNL is solved in centralized and distributed settings, respectively. The centralized ASNL is formulated as a rank-constrained semi-definite program (SDP) in either a noise-free or a noisy scenario, with a decomposition approach proposed to deal with large-scale ASNL. The distributed protocol for ASNL is designed based on inter-sensor communications. Graphical conditions for equivalence of the formulated rank-constrained SDP and a linear SDP, decomposition of the SDP, as well as the effectiveness of the distributed protocol, are proposed, respectively. Finally, simulation examples demonstrate our theoretical results.

翻译：本文研究飞机上基于角的传感器网络定位(ASNL),即确定传感器网络中所有传感器的位置、部分传感器(所谓锚)和每个传感器当地协调框中获取的角度测量的指定位置。首先,该文件表明,一个具有非离子双切定序的框架必须是可固定的角,这意味着它可以由向翻译、旋转、反射和统一缩放的边缘之间的角的独特确定。然后,ASNL被证明有一个独特的解决方案,条件是:有根框架是可角固定的,而锚不是全部合金。随后,ASNL分别在中央和分布的环境下解决。中央的ASNL是一个受级限制的半分解程序(SDP),在无噪音或杂音的情景中制定,建议采用分解法方法来处理大规模非分解法。ASNL的分布式协议是建立在传感器之间通信的基础上设计的。为已拟订的分级SDP和线性 SDP的等同的图形条件和线性 SDP的理论模型分别展示了SDP的模拟结果。