In this study, we consider the point coverage problem and aim to locate heterogeneous sensor networks under target uncertainty. Target location uncertainty phenomenon is commonly seen in some fields such as military and security, where only probabilistic information regarding target location is usually available via intelligence, historical data, and expert opinions. In these circumstances, possible scenarios are usually generated and several courses of action are developed to address these scenarios. Taking into account this real-life phenomenon as well as the realistic constraints associated with it, we firstly develop an integer nonlinear program for locating a heterogeneous sensor network with hub-spoke topology for a given target scenario. In this topology, wireless sensors constitute the lower level network, while the hubs constitute the upper level by collecting data from the sensors and fusioning the transmitted detection data. Secondly, we propose a linear approximation for the nonlinear model which provides computational efficiency for solving large size problem instances. Then, utilizing the p-robustness concept, we develop a robust counterpart of the deterministic formulation which accounts for multiple scenarios simultaneously and generates a compromise solution that ensures a predefined threshold for regret percentages of individual scenarios. For the first time in the point coverage literature, we define the heterogeneous sensor network location problem within target location uncertainty concept and propose an efficient robust optimization approach for solving it. Finally, we present an illustrative case study to show the applicability of the proposed robust solution approach.

在这项研究中，我们考虑了点覆盖问题，旨在在目标不确定性下定位异构传感器网络。目标位置不确定现象在军事和安全等领域很常见，这些领域通常只能通过情报、历史数据和专家意见获得有关目标位置的概率信息。在这些情况下，通常会产生可能的情景，并制定若干行动方案来应对这些情景。考虑到这种现实生活中的现象以及与之相关的现实约束，我们首先开发了一个整数非线性程序，用于为给定的目标场景定位具有轮辐拓扑的异构传感器网络。在这种拓扑结构中，无线传感器构成了下层网络，而集线器通过从传感器收集数据并融合传输的检测数据构成上层。其次，我们提出了非线性模型的线性近似，它为解决大型问题实例提供了计算效率。然后，利用p -鲁棒性概念，我们开发了确定性公式的稳健对应物，它同时考虑了多个场景，并生成了一个折衷解决方案，确保为单个场景的遗憾百分比设置一个预定义的阈值。在点覆盖文献中，我们第一次在目标位置不确定性概念中定义了异构传感器网络定位问题，并提出了一种有效的鲁棒优化方法来解决它。最后，我们提出了一个说明性案例研究，以展示所提出的稳健解决方案方法的适用性。