In this paper, we consider a status update system, where an access point collects measurements from multiple sensors that monitor a common physical process, fuses them, and transmits the aggregated sample to the destination over an erasure channel. Under a typical information fusion scheme, the distortion of the fused sample is inversely proportional to the number of measurements received. Our goal is to minimize the long-term average age while satisfying the average energy and general age-based distortion requirements. Specifically, we focus on the setting in which the distortion requirement is stricter when the age of the update is older. We show that the optimal policy is a mixture of two stationary, deterministic, threshold-based policies, each of which is optimal for a parameterized problem that aims to minimize the weighted sum of the age and energy under the distortion constraint. We then derive analytically the associated optimal average age-cost function and characterize its performance in the large threshold regime, the results of which shed critical insights on the tradeoff among age, energy, and the distortion of the samples. We have also developed a closed-form solution for the special case when the distortion requirement is independent of the age, arguably the most important setting for practical applications.

翻译：本文研究了一个状态更新系统，其中接入点从监测同一物理过程的多个传感器收集测量数据，融合这些数据，并通过擦除信道将聚合样本传输至目的地。在典型信息融合方案下，融合样本的失真度与接收到的测量数量成反比。我们的目标是在满足平均能量和基于年龄的通用失真要求的同时，最小化长期平均年龄。具体而言，我们关注当更新年龄增大时失真要求更加严格的情形。研究表明，最优策略是两种平稳、确定性、基于门限的策略的混合，每种策略分别针对一个参数化问题最优，该问题旨在失真约束下最小化年龄与能量的加权和。随后，我们解析推导了相关的最优平均年龄-成本函数，并刻画了其在大门限状态下的性能，所得结果揭示了年龄、能量与样本失真度之间的关键权衡。针对失真要求与年龄无关这一实际应用中最重要的特例，我们还提出了封闭形式的解。