Joint estimation and scheduling for sensor networks is considered in a system formed by two sensors, a scheduler, and a remote estimator. Each sensor observes distinct Gaussian random variables, which may be correlated. This system can be analyzed as a team decision problem with two agents: the scheduler and the remote estimator. The scheduler observes the output of both sensors and chooses which of the two is revealed to the remote estimator. The goal is to jointly design scheduling and estimation policies that minimize a mean-squared estimation error criterion. The person-by-person optimality of a policy pair called “max-scheduling/mean-estimation” is established, where the measurement with the largest absolute value is revealed to the estimator, which uses a corresponding conditional mean operator. This result is obtained for independent Gaussian random variables, and correlated Gaussian random variables with symmetric variances. Finally, the joint design of scheduling and linear estimation policies for any two Gaussian random variables with an arbitrary correlation structure is considered. In this case, the optimization problem is recast as a difference-of-convex program, and locally optimal solutions can be found using a simple numerical procedure.

中文翻译：

---

观测驱动的两个高斯随机变量的远程估计调度

在由两个传感器，一个调度程序和一个远程估计器组成的系统中考虑了传感器网络的联合估计和调度。每个传感器观察不同的高斯随机变量，这些变量可能是相关的。该系统可以作为具有两个代理的团队决策问题进行分析：调度程序和远程估计器。调度程序观察两个传感器的输出，并选择将两个传感器中的哪个显示给远程估计器。目标是共同设计最小化均方估计误差准则的调度和估计策略。建立称为“最大调度/均值估计”的策略对的逐人最佳性，其中将最大绝对值的度量显示给估计器，该估计器使用相应的条件均值算子。对于独立的高斯随机变量以及具有对称方差的相关高斯随机变量，可以获得此结果。最后，考虑了具有任意相关结构的任意两个高斯随机变量的调度和线性估计策略的联合设计。在这种情况下，将优化问题重铸为凸差程序，并且可以使用简单的数值程序找到局部最优解。