Recent advances in sensing technology have enabled sensor nodes to measure interior angles with respect to their neighboring nodes. However, it is unknown which combination of angle measurements is necessary to make a sensor network localizable, and it is also unidentified if there is a distributed localization algorithm whose required communication only consists of the sensor nodes’ measured angles and estimated positions. Motivated by these two challenging problems, this paper develops triangular angle rigidity for those networks consisting of a set of nodes and triangular angle constraints in 2D. First, we transfer the geometric constraint of each triangle into an angle-induced linear constraint. Based on the linear constraint, we show that different from angle rigidity, triangular angle rigidity implies global triangular angle rigidity. More importantly, inspired by Laman’s theorem, we propose a topological, necessary and sufficient condition to check generic triangular angle rigidity. Based on the results on triangular angle rigidity, both algebraic and topological localizability conditions are developed, which are necessary and sufficient when the number of anchor nodes in the network is two. Both continuous and discrete localization algorithms are proposed, in which only measured angles and estimated positions are communicated among the sensor nodes. Finally, a simulation example with 32 sensor nodes is used to validate the effectiveness of the proposed approaches.

传感技术的最新进展使传感器节点能够测量相对于其相邻节点的内角。然而，尚不清楚哪种角度测量组合对于使传感器网络可定位是必要的，并且是否存在所需的通信仅由传感器节点的测量角度和估计位置组成的分布式定位算法也是未知的。受这两个具有挑战性的问题的启发，本文为由一组节点和二维三角角约束组成的网络开发了三角角刚性。首先，我们转移几何约束将每个三角形转化为角度诱导的线性约束。基于线性约束，我们表明与角刚度不同，三角角刚度意味着全局三角角刚度。更重要的是，受拉曼定理的启发，我们提出了一个拓扑的、必要的和充分的条件来检查泛三角角刚度。基于三角角刚度的结果，建立了代数和拓扑局部化条件，当网络中的锚节点数量为两个时，这些条件是必要和充分的。提出了连续和离散定位算法，其中只有测量的角度和估计的位置在传感器节点之间进行通信。最后，使用具有 32 个传感器节点的仿真示例来验证所提出方法的有效性。