In this article, we establish a comprehensive theoretical framework for remote estimation in a networked system composed of a source that is observed by a sensor, a remote monitor that needs to estimate the state of the source in real time, and a communication channel that connects the source to the monitor. The source is a partially observable dynamical process, and the communication channel is a packet-erasure channel with feedback. We consider a novel communication model that captures implicit information. Our main objective is to identify the optimal strategies and the fundamental performance limits of the underlying system in the sense of a causal tradeoff between the packet rate and the mean square error when both forward and backward channels are unreliable. We characterise an optimal coding policy profile consisting of a scheduling policy for an encoder and an estimation policy for a decoder, collocated with the source and the monitor, respectively. We derive the recursive equations that must be solved online by the encoder and the decoder. In addition, we prove that the value function, originally defined over an expanding information set, admits a lower-dimensional representation depending only on two variables. We discuss the structural properties of the optimal policies, and analyse the computational complexity of an algorithm proposed for their computation. We then examine a range of special cases derived from our main theoretical results. We complement the theoretical results with a numerical analysis, and compare the performance of different remote estimation tasks in various operating regimes.

翻译：本文针对由观测源的传感器、需实时估计源状态的远程监视器以及连接源与监视器的通信信道所构成的网络化系统，建立了一个完整的远程估计理论框架。源是一个部分可观测的动态过程，通信信道为带反馈的包擦除信道。我们提出了一种能够捕获隐式信息的新型通信模型。主要研究目标是在前向与反向信道均不可靠的情况下，从数据包速率与均方误差之间的因果权衡角度，确定该系统的最优策略与基本性能极限。我们刻画了一个由编码器调度策略（与源共置）和解码器估计策略（与监视器共置）构成的最优编码策略组合。推导了编码器与解码器必须在线求解的递归方程。此外，我们证明了最初定义在扩展信息集上的值函数，可简化为仅依赖于两个变量的低维表示。讨论了最优策略的结构特性，并分析了所提出计算算法的复杂度。随后基于主要理论结果推导了一系列特殊情形。通过数值分析对理论结果进行补充，比较了不同运行机制下各类远程估计任务的性能表现。