Locations of mobile agents are often requisite information for wireless applications such as sensor networks and Internet of Things (IoT). As the network size increases, verifying the localizability of all nodes in a network quickly becomes intractable. In this article, we turn to analyzing the unbounded localizability of infinite stochastic networks under sequential localization methods. Specifically, we prove the existence of the phase transition on the probability of localizing an unbounded subnetwork from a bounded initial anchor set in Poisson point process networks. The phase transition occurs when the node intensity of the network reaches a critical intensity, which is determined by the adopted sequential localization method. Furthermore, we develop a simulation method to obtain tight upper and lower bounds of the critical intensity for two-dimensional (2-D) networks with high confidence, and provide the numerical bounds under several typical sequential localization methods. We also show by simulation that the percentage of localizable nodes increases rapidly near the critical intensity, which provides guidelines for network design and deployment.

中文翻译：

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无界连续定位的临界强度

移动代理的位置通常是无线应用（如传感器网络和物联网 (IoT)）的必要信息。随着网络规模的增加，验证网络中所有节点的可定位性很快变得棘手。在本文中，我们转而分析在顺序定位方法下无限随机网络的无界定位性。具体来说，我们证明了从泊松点过程网络中的有界初始锚集定位无界子网的概率存在相变。当网络的节点强度达到临界强度时发生相变，这是由所采用的顺序定位方法确定的。此外，我们开发了一种模拟方法，以高置信度获得二维 (2-D) 网络临界强度的严格上限和下限，并提供几种典型顺序定位方法下的数值界限。我们还通过模拟表明，可定位节点的百分比在临界强度附近迅速增加，这为网络设计和部署提供了指导。