We consider semantics-aware remote estimation of a discrete-state Markov source with both normal (low-priority) and alarm (high-priority) states. Erroneously announcing a normal state at the destination when the source is actually in an alarm state (i.e., missed alarm) incurs a significantly higher cost than falsely announcing an alarm state when the source is in a normal state (i.e., false alarm). Moreover, consecutive estimation errors may cause significant lasting impacts, such as maintenance costs and misoperations. Motivated by this, we introduce two new metrics, the Age of Missed Alarm (AoMA) and the Age of False Alarm (AoFA), to capture the lasting impacts incurred by different estimation errors. Notably, these two age processes evolve interdependently and distinguish between different error types. Our goal is to design a transmission policy that achieves an optimized trade-off between lasting impact and communication cost. The problem is formulated as a countably infinite-state Markov decision process (MDP) with an unbounded cost function. We show the existence of a simple switching policy with distinct thresholds for each age process and derive closed-form expressions for its performance. For symmetric and non-prioritized sources, we show that the optimal policy reduces to a threshold policy with identical thresholds. For numerical tractability, we propose a finite-state approximate MDP and prove that it converges exponentially fast to the original MDP in the truncation size. Finally, we develop an efficient search algorithm to compute the optimal switching policy and validate our theoretical findings with numerical results.

翻译：我们研究具有正常（低优先级）和告警（高优先级）状态的离散状态马尔可夫源的语义感知远程估计问题。当信源实际处于告警状态时，若在目的地错误宣告正常状态（即漏警），其产生的代价远高于信源处于正常状态时错误宣告告警状态（即误警）。此外，连续的估计误差可能导致显著的持续影响，例如维护成本和误操作。受此启发，我们引入两个新指标——漏警时效（AoMA）和误警时效（AoFA），以刻画不同估计误差引发的持续影响。值得注意的是，这两个时效过程相互关联且能区分不同的错误类型。我们的目标是设计一种传输策略，在持续影响与通信成本之间实现优化权衡。该问题被建模为具有无界代价函数的可数无限状态马尔可夫决策过程（MDP）。我们证明存在一种对每个时效过程设置不同阈值的简单切换策略，并推导了其性能的闭式表达式。对于对称且无优先级的信源，我们证明最优策略可简化为具有相同阈值的阈值策略。为提升数值计算的可行性，我们提出一种有限状态近似MDP，并证明其在截断规模上以指数速度收敛于原始MDP。最后，我们开发了一种高效搜索算法来计算最优切换策略，并通过数值结果验证了理论结论。