Efficient sampling and remote estimation is critical for a plethora of wireless-empowered applications in the Internet of Things and cyber-physical systems. Motivated by such applications, this work proposes decentralized policies for the real-time monitoring and estimation of autoregressive processes over random access channels. Two classes of policies are investigated: (i) oblivious schemes in which sampling and transmission policies are independent of the processes that are monitored, and (ii) non-oblivious schemes in which transmitters causally observe their corresponding processes for decision making. In the class of oblivious policies, we show that minimizing the expected time-average estimation error is equivalent to minimizing the expected age of information. Consequently, we prove lower and upper bounds on the minimum achievable estimation error in this class. Next, we consider non-oblivious policies and design a threshold policy, called error-based thinning, in which each source node becomes active if its instantaneous error has crossed a fixed threshold (which we optimize). Active nodes then transmit stochastically following a slotted ALOHA policy. A closed-form, approximately optimal, solution is found for the threshold as well as the resulting estimation error. It is shown that non-oblivious policies offer a multiplicative gain close to $3$ compared to oblivious policies. Moreover, it is shown that oblivious policies that use the age of information for decision making improve the state-of-the-art at least by the multiplicative factor $2$. The performance of all discussed policies is compared using simulations. Numerical comparison shows that the performance of the proposed decentralized policy is very close to that of centralized greedy scheduling.

中文翻译：

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分散随机接入信道中的远程估计

有效的采样和远程估计对于物联网和网络物理系统中的大量无线应用至关重要。受此类应用程序的启发，这项工作提出了分散的策略，用于实时监控和估计随机访问信道上的自回归过程。研究了两类策略：(i) 不经意的方案，其中采样和传输策略独立于被监控的过程，以及 (ii) 不经意的方案，其中发射机因果地观察其相应的决策过程。在不经意的策略类中，我们表明最小化预期时间平均估计误差等效于最小化信息的预期年龄。最后，我们证明了此类中可实现的最小估计误差的下限和上限。接下来，我们考虑非遗忘策略并设计一个阈值策略，称为基于错误的细化，其中如果每个源节点的瞬时错误超过固定阈值（我们对其进行优化），则它变得活跃。然后，活动节点按照时隙 ALOHA 策略随机传输。为阈值以及由此产生的估计误差找到了一个封闭形式的近似最优解。结果表明，与遗忘政策相比，非遗忘政策提供了接近 3 美元的倍增收益。此外，结果表明，使用信息时代进行决策的不经意的政策至少提高了最新技术的乘法因子 $2$。使用模拟比较所有讨论的策略的性能。