Recent advances on hardware accelerators and edge computing are enabling substantial processing to be performed at each node (e.g., robots, sensors) of a networked system. Local processing typically enables data compression and may help mitigate measurement noise, but it is still usually slower compared to a central computer (i.e., it entails a larger computational delay). Moreover, while nodes can process the data in parallel, the computation at the central computer is sequential in nature. On the other hand, if a node decides to send raw data to a central computer for processing, it incurs a communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of local preprocessing in order to maximize the network performance. Here we consider the case where the network is in charge of estimating the state of a dynamical system and provide three key contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks, in the presence of communication and computation delays. Second, we develop analytical results for the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system. In particular, we show how to compute the optimal amount of local preprocessing to minimize the estimation error and prove that sending raw data is in general suboptimal in the presence of communication delays. Third, we consider the realistic case of a heterogeneous network that monitors a discrete-time multi-variate linear system and provide practical algorithms (i) to decide on a suitable preprocessing at each node, and (ii) to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial: the more may not be the merrier. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.

中文翻译：

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处理网络实时估计中的计算-通信权衡和传感器选择

硬件加速器和边缘计算的最新进展使得能够在网络系统的每个节点（例如机器人、传感器）上执行大量处理。本地处理通常支持数据压缩并可能有助于减轻测量噪声，但与中央计算机相比，它通常仍然较慢（即，它需要更大的计算延迟）。此外，虽然节点可以并行处理数据，但中央计算机的计算本质上是顺序的。另一方面，如果节点决定将原始数据发送到中央计算机进行处理，则会导致通信延迟。这导致了基本的通信-计算权衡，其中每个节点必须决定本地预处理的最佳数量，以最大限度地提高网络性能。在这里，我们考虑网络负责估计动态系统状态并提供三个关键贡献的情况。首先，在存在通信和计算延迟的情况下，我们为处理网络中的最佳实时估计提供了严格的问题公式。其次，我们针对监控连续时间标量线性系统的同构网络（其中所有传感器具有相同的计算）的情况开发分析结果。特别是，我们展示了如何计算本地预处理的最佳数量以最小化估计误差，并证明在存在通信延迟的情况下发送原始数据通常是次优的。第三，我们考虑监控离散时间多元线性系统的异构网络的现实情况，并提供实用算法（i）决定每个节点的合适预处理，以及（ii）当计算约束产生时选择传感器子集使用所有传感器都不理想。数值模拟表明，选择传感器至关重要：越多未必越好。此外，我们表明，如果节点应用我们算法建议的预处理策略，它们可以在很大程度上提高网络估计性能。