Revisiting Estimation Quality: Significance-Aware Age of Consecutive Error

We study the semantics-aware remote state estimation of a Markov chain with prioritized states. The aim is to exploit the significance of information through the history of system realizations to determine the optimal timing of transmission, thereby reducing the amount of uninformative data transmitted in the network. To this end, we introduce the significanceaware Age of Consecutive Error (AoCE) that captures three semantic attributes: the significance of estimation error, the cost of consecutive error (or lasting impact, for short), and the urgency of lasting impact. We identify the optimal transmission problem as a countably infinite state Markov decision process (MDP) with unbounded costs. We give sufficient conditions under which an optimal policy exists to have bounded average costs. We show that the optimal policy exhibits a switching structure and, under certain conditions, degenerates into a simple threshold policy. A structured policy iteration (SPI) algorithm is proposed to compute an asymptotically optimal policy with reduced computation overhead. An important takeaway is that the more semantic attributes we utilize, the fewer transmissions are needed.