Optimal online transmission schedule for remote state estimation over a hidden Markovian channel

This paper investigates the optimal transmission scheduling problem in remote state estimation systems over an unreliable wireless channel where the channel state evolves as a Markov chain. However, due to inaccurate observations of the channel state, the wireless channel is modeled as a hidden Markov chain. We propose a prediction algorithm based on the Viterbi algorithm to estimate the channel state. To save the wireless sensor's energy, we consider scheduling the transmission of sensor transmissions while balancing between estimation performance and sensor energy expenditure. By jointly considering performance and energy, we formulate the scheduling problem as a Markov decision process. We prove the existence of the optimal transmission policy and derive a threshold structure of the optimal strategy. Finally, the performance of the proposed method is evaluated through simulations.