The freshness of sensor data is critical for all types of cyber-physical systems. An established measure for quantifying data freshness is the Age-of-Information (AoI), which has been the subject of extensive research. Recently, there has been increased interest in multi-sensor systems: redundant sensors producing samples of the same physical process, sensors such as cameras producing overlapping views, or distributed sensors producing correlated samples. When the information from a particular sensor is outdated, fresh samples from other correlated sensors can be helpful. To quantify the utility of distant but correlated samples, we put forth a two-dimensional (2D) model of AoI that takes into account the sensor distance in an age-equivalent representation. Since we define 2D-AoI as equivalent to AoI, it can be readily linked to existing AoI research, especially on parallel systems. We consider physical phenomena modeled as spatio-temporal processes and derive the 2D-AoI for different Gaussian correlation kernels. For a basic exponential product kernel, we find that spatial distance causes an additive offset of the AoI, while for other kernels the effects of spatial distance are more complex and vary with time. Using our methodology, we evaluate the 2D-AoI of different spatial topologies and sensor densities.

翻译：传感器数据的新鲜度对所有类型的网络物理系统都至关重要。衡量数据新鲜度的一个既定指标是信息年龄（AoI），该指标已得到广泛研究。近年来，人们对多传感器系统的兴趣日益增长：例如冗余传感器对同一物理过程进行采样、相机等传感器产生重叠视场，或分布式传感器产生相关样本。当特定传感器的信息过时，来自其他相关传感器的新鲜样本可能具有参考价值。为量化距离较远但相关样本的效用，我们提出了一种二维（2D）AoI模型，该模型在年龄等效表示中考虑了传感器距离。由于我们将2D-AoI定义为与AoI等效，因此可将其与现有AoI研究（尤其是并行系统研究）直接关联。我们将物理现象建模为时空过程，并推导出不同高斯相关核下的2D-AoI。对于基本的指数乘积核，我们发现空间距离会导致AoI产生加性偏移；而对于其他核函数，空间距离的影响更为复杂且随时间变化。基于该方法论，我们评估了不同空间拓扑和传感器密度下的2D-AoI。