This paper studies semantics-aware remote estimation of Markov sources. We leverage two complementary information attributes: the urgency of lasting impact, which quantifies the significance of consecutive estimation error at the transmitter, and the age of information (AoI), which captures the predictability of outdated information at the receiver. The objective is to minimize the long-run average lasting impact subject to a transmission frequency constraint. The problem is formulated as a constrained Markov decision process (CMDP) with potentially unbounded costs. We show the existence of an optimal simple mixture policy, which randomizes between two neighboring switching policies at a common regeneration state. A closed-form expression for the optimal mixture coefficient is derived. Each switching policy triggers transmission only when the error holding time exceeds a threshold that depends on both the instantaneous estimation error and the AoI. We further derive sufficient conditions under which the thresholds are independent of the instantaneous error and the AoI. Finally, we propose a structure-aware algorithm, Insec-SPI, that computes the optimal policy with reduced computation overhead. Numerical results demonstrate that incorporating both the age and semantics of information significantly improves estimation performance compared to using either attribute alone.

翻译：本文研究了马尔科夫源的语义感知远程估计问题。我们利用两种互补的信息属性：持续性冲击的紧迫性（该属性量化了发射端连续估计误差的重要性）以及信息年龄（AoI，该属性捕捉了接收端过时信息的可预测性）。目标是在满足传输频率约束的条件下，最小化长期平均持续性冲击。该问题被建模为具有潜在无界成本的受约束马尔科夫决策过程（CMDP）。我们证明了存在最优的简单混合策略，该策略在公共再生状态下对两种相邻切换策略进行随机化，并推导出最优混合系数的闭式表达式。每种切换策略仅在误差保持时间超过依赖于瞬时估计误差与AoI的阈值时触发传输。我们进一步推导了阈值独立于瞬时误差和AoI的充分条件。最后，提出了一种结构感知算法Insec-SPI，该算法能以较低的计算开销计算最优策略。数值结果表明，与单独使用任一属性相比，同时结合信息年龄与语义能显著提升估计性能。