Importance-aware Sampling of a Two-State Markov Source for Real-time Tracking

This work considers the problem of real-time remote tracking and reconstruction of a two-state Markov process for actuation. The transmitter sends samples from an observed information source to a remote monitor over an unreliable wireless channel. We propose a state-aware randomized stationary sampling and transmission policy, which considers the importance of different states and their impact on the communication objective. We then analyze the performance of the proposed policy and compare it with existing goal-oriented joint sampling and transmission policies using relevant metrics. Specifically, we assess the real-time reconstruction error, the cost of actuation error, and the consecutive error metrics. Furthermore, a constrained optimization problem is formulated and solved so as to minimize the average cost of actuation error by determining optimal sampling probabilities. Our results show that the optimal state-aware randomized stationary policy outperforms other policies in scenarios with constrained sampling for fast-evolving sources. In addition, when the source changes slowly, although the semantics-aware policy tends to be more effective, the optimal state-aware randomized stationary policy excels under certain conditions.