Modern IoT and sensor networks generate vast amounts of data, posing significant challenges for storage, transmission, and real-time processing. Traditional approaches, such as compressive sensing and machine learning-based compression, often suffer from computational inefficiencies and irreversible data loss. This paper introduces Information Density as a quantitative metric to support sensor deployment and enable AI-driven virtual sensing. We propose a framework that leverages spatial, temporal and inter-modal correlations among sensor signals to perform sensing tasks even in the absence of physical sensors. Two complementary measures: (i) Phase in Eigen Space and (ii) Mutual Information, are developed to quantify and assess information density, enabling the selection of optimal sensor configurations across both intra-modality and cross-modality scenarios. Validated using real-world data from Madrid's smart city infrastructure, this framework demonstrates the feasibility of replacing physical sensors with virtual ones under bounded error conditions (e.g., achieving $<3.21\%$ mean error with a single sensor). The results highlight the potential for scalable and energy-efficient sensing systems in smart environments.

翻译：现代物联网与传感器网络生成海量数据，对存储、传输和实时处理构成了重大挑战。传统方法（如压缩感知和基于机器学习的压缩）常面临计算效率低下和不可逆数据丢失等问题。本文引入信息密度作为支持传感器部署和实现人工智能驱动虚拟传感的定量度量指标。我们提出一个框架，利用传感器信号间的空间、时间及跨模态关联，在缺少物理传感器的情况下完成感知任务。研究开发了两种互补度量方法：（i）特征空间相位和（ii）互信息，用于量化与评估信息密度，从而在模态内和跨模态场景中优化传感器配置方案。基于马德里智慧城市基础设施的真实数据进行验证，该框架证明了在有限误差条件下（例如，使用单个传感器实现低于3.21%的平均误差）用虚拟传感器替代物理传感器的可行性。研究结果凸显了在智能环境中构建可扩展高能效感知系统的潜力。