Goal-oriented Real-time Tracking in a Status Update System Under Imperfect Feedback

We consider a status update system consisting of a finite-state Markov source, an energy-harvesting-enabled transmitter, and a sink. The forward and feedback channels between the transmitter and the sink are error-prone. We study the problem of minimizing the time average of a distortion function subject to an energy limitation constraint. Due to the error-prone feedback channel, the transmitter has only partial knowledge about the estimate of the source state at the sink. Therefore, we model the problem as a partially observable Markov decision process (POMDP), which is then cast as a belief-MDP problem. By truncating the belief-state space, we formulate a finite-state belief-MDP problem, which is then solved using the relative value iteration algorithm (RVIA). Simulation results show the effectiveness of the proposed policy compared to a baseline policy.