Multi-sensor Power Allocation for Remote Estimation Over Semi-Markov Fading Channels

This paper investigates the multi-sensor power allocation (MSPA) problem for remote state estimation in cyber-physical systems (CPSs). Multiple sensors observe different linear time-invariant processes and send their estimates to the remote estimator over semi-Markov fading channels (SMFCs). The probability of successful data transmission depends on the SMFC state and the transmission power used by the sensor. We focus on how to allocate the power of sensors to trade off the remote estimation error and transmission cost. Firstly, in the framework of the Markov decision process (MDP), the double threshold structure of the optimal MSPA strategy with respect to the age-of-information (AoI) state and the SMFC state is derived, which significantly reduces the computational complexity. Secondly, the necessary and sufficient condition (NSC) of guaranteeing remote terminal stability is given from the probabilistic sense, which is related to system parameters, channel parameters and packet dropout rate. Finally, a simulation example is provided to verify theoretical results.