Online Optimal Transmission Scheduling of an Energy Harvesting Sensor for Remote State Estimation

We investigate an online optimal sensor transmission scheduling problem for remote state estimation. We consider the energy harvesting sensor, which can absorb external energy and use the energy to transmit the local state estimates to the remote estimator over an unreliable wireless channel. Furthermore, we consider that the sensor has two different transmission energy levels, where different energy levels correspond to different data reception ratios. Considering the trade-off between estimation performance and energy consumption, we hope to design an optimal transmission policy that minimizes the convex combination of the estimation error covariance and the energy for data transmission. We formulate the optimization problem as a Markov decision process, which can be solved by dynamic programming. Then, we introduce the concept of submodularity to prove that there is an optimal threshold policy on the error covariance, given sensor battery and collected energy. Eventually, simulations are given to illustrate the aforementioned results.