Entropy-Driven Sampling for Remote Estimation in Internet of Things Systems

Remote state estimation plays a critical role in internet of things (IoT) systems, where distributed sensors report dynamic processes to remote estimators for control and monitoring. Traditional freshness metrics, such as age of information (AoI), do not necessarily capture the information value degradation caused by random transmission latency and content dynamics. In this paper, we evaluate the value of information through the lens of Shannon entropy by adopting theuncertainty of information(UoI), which quantifies the receiver’s uncertainty in estimating the source state caused by stale information delivery. We study a remote estimation system where a binary Markov source is sampled and transmitted over a randomly delayed channel with a long-term sampling frequency constraint. This problem is formulated as a constrained partially observable semi-Markov decision process (C-POSMDP), solved through Dinkelbach’s transformation and Lagrangian relaxation combined with the relative value iteration (RVI) algorithm. To mitigate the complexity of RVI, we further develop a low-complexity index-based policy by approximating the Bellman equation under relatively high delay. Numerical results show that both proposed policies outperform zero-wait, uniform, and AoI-optimal baselines, with the sub-optimal policy achieving near-optimal performance in relatively high delay regimes.