This paper studies the status update performance in wireless sensor networks when status, describing the physical reality that is being sensed, is temporally and spatially correlated. The status is modeled as a time-varying Gauss-Markov Random Field (GMRF), whereby the estimation error of status update at the fusion center is analyzed. The transmission latency introduced by wireless networks is modeled as exponentially distributed random variables. We extend the existing queuing analysis results for Age of Information (AoI) with uncorrelated sources to GMRF in the considered scenario. Closed-form expressions of average remote estimation error are obtained for both one- and two-dimensional GMRFs assuming the exponential time-correlation function, both First-Come First-Served (FCFS) and Last-Come First-Served (LCFS) service disciplines, and a single wireless link. The analytical results are then extended to scenarios wherein multi-packet reception, i.e., multiple concurrent wireless links, is enabled; the difficulty of analyzing obsolete updates in this case is addressed leveraging a reasonable approximation validated by theoretical analysis in the regime where the number of sensors is far more than that of wireless links. Monte-Carlo simulation results are also presented which agree with our theoretical analysis. Based on the results, optimal time and spatial domain sampling rates (e.g., sensor density) can be obtained, providing helpful guidance to wireless sensor deployment.

中文翻译：

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具有时间和空间相关观察值的传感器状态更新的误差分析

本文研究了无线传感器网络中的状态更新性能，这些状态描述了被感知的物理现实在时间和空间上的相关性。将状态建模为时变的高斯-马尔可夫随机场（GMRF），从而分析融合中心状态更新的估计误差。无线网络引入的传输延迟被建模为指数分布的随机变量。在考虑的情况下，我们将不相关来源的现有信息年龄（AoI）排队分析结果扩展到GMRF。假定指数时间相关函数（先到先得（FCFS）和最后来先到（LCFS）服务学科），对于一维和二维GMRF，均获得一维和二维GMRF的平均远程估计误差的封闭式表达式。 ，和一条无线链接。然后将分析结果扩展到启用多数据包接收（即，多个并发无线链接）的场景；在这种情况下，分析过时的更新的难度得到了解决，这是通过一种合理的近似方法来解决的，该近似方法在传感器数量远远超过无线链路数量的情况下通过理论分析得到了验证。蒙特卡洛仿真结果也与我们的理论分析相吻合。根据结果​​，可以获得最佳的时间和空间域采样率（例如，传感器密度），为无线传感器的部署提供有用的指导。在这种情况下，分析过时的更新的难度得到了解决，这是通过一种合理的近似方法来解决的，该近似方法在传感器数量远远超过无线链路数量的情况下通过理论分析得到了验证。蒙特卡洛仿真结果也与我们的理论分析相吻合。根据结果​​，可以获得最佳的时间和空间域采样率（例如，传感器密度），为无线传感器的部署提供有用的指导。在这种情况下，分析过时的更新的难度得到了解决，这是通过一种合理的近似方法来解决的，该近似方法在传感器数量远远超过无线链路数量的情况下通过理论分析得到了验证。蒙特卡洛仿真结果也与我们的理论分析相吻合。根据结果​​，可以获得最佳的时间和空间域采样率（例如，传感器密度），为无线传感器的部署提供有用的指导。