标题： 哪个传感器进行观测？ 带有模型预测控制的联合马尔可夫信源的及时跟踪 显示英文标题

标题： Which Sensor to Observe? Timely Tracking of a Joint Markov Source with Model Predictive Control

摘要： 在本文中，我们研究了使用多个传感器对离散时间联合马尔可夫过程进行远程估计的问题。 每个传感器观察联合马尔可夫过程的不同组成部分，在每个时间槽中，监控器通过向其中一个传感器发送拉取请求来获得部分状态值。 监控器通过使用获得的部分状态观测值（这些观测值具有不同的新鲜度级别）选择传感器序列，以最小化错误信息的平均年龄（MAoII）。 例如，监控器可能希望通过在不同时间槽中从两个传感器获取观测值来跟踪一个物体的位置，这两个传感器分别观测物体的$x$和$y$坐标。 然后，监控器需要根据历史记录决定在下一个时间槽中观察哪个坐标。 除了马尔可夫过程状态的部分可观测性之外，每个传感器和监控器之间还有一个具有固定一跳延迟的删除信道。 首先，我们通过使用所有拉取请求和观测的历史记录，得到一个充分统计量，即\emph{信念}，它表示错误信息年龄（AoII）和观测过程当前状态的联合分布。 然后，我们将问题建模为一个连续状态空间的马尔可夫决策问题（MDP），即信念MDP。 为了解决这个问题，我们提出了两种模型预测控制（MPC）方法，即无终端成本的MPC（MPC-WTC）和强化学习MPC（RL-MPC），它们在实现上具有不同的优势。 显示英文摘要

摘要： In this paper, we investigate the problem of remote estimation of a discrete-time joint Markov process using multiple sensors. Each sensor observes a different component of the joint Markov process, and in each time slot, the monitor obtains a partial state value by sending a pull request to one of the sensors. The monitor chooses the sequence of sensors to observe with the goal of minimizing the mean of age of incorrect information (MAoII) by using the partial state observations obtained, which have different freshness levels. For instance, a monitor may be interested in tracking the location of an object by obtaining observations from two sensors, which observe the $x$ and $y$ coordinates of the object separately, in different time slots. The monitor, then, needs to decide which coordinate to observe in the next time slot given the history. In addition to this partial observability of the state of Markov process, there is an erasure channel with a fixed one-slot delay between each sensor and the monitor. First, we obtain a sufficient statistic, namely the \emph{belief}, representing the joint distribution of the age of incorrect information (AoII) and the current state of the observed process by using the history of all pull requests and observations. Then, we formulate the problem with a continuous state-space Markov decision problem (MDP), namely belief MDP. To solve the problem, we propose two model predictive control (MPC) methods, namely MPC without terminal costs (MPC-WTC) and reinforcement learning MPC (RL-MPC), that have different advantages in implementation.