Optimal Sensor Scheduling for Remote State Estimation Over Hidden Markovian Channels

This letter investigates the sensor scheduling problem in a multi-sensor, multi-channel remote state estimation system with time-varying channel states. Due to channel constraints, only a subset of sensors can transmit data to the remote state estimator at each time step. To prevent packet loss when transmitting when the channel state is busy, channel sensing is performed before transmission; however, sensing results are unreliable in practice. To address these challenges, we propose a channel state estimation algorithm using a Hidden Markov Model (HMM) to estimate the true channel state. We then formulate the sensor transmission scheduling problem as a Markov decision process (MDP) and prove the existence of a deterministic, stationary optimal policy. Additionally, we show that the optimal policy follows a monotone structure. Numerical examples are presented to illustrate the effectiveness of the proposed method.