Finite-time Online Sensor Power Scheduling for Remote State Estimation with Communication Energy Constraint

We build an online algorithm for a WSN (Wire-less Sensor Network) with a feedback loop to reduce the estimation error over a finite time horizon under a limited energy budget. Our algorithm decides to send a high or low power signal at the current time step, and due to the energy limit, the sensor can only send a limited number of high power signals. The high power signal guarantees a successful transmission and the low power signal arrives at the estimator with a certain packet drop rate. When there is no feedback, the previous study has shown the optimal scheduling should be as close to a uniform distribution as possible. However, with the feedback information, the sensor knows whether the low power signal has arrived successfully at the remote estimator. The successfully arrived low power signals can thus be regarded as high power signals, so we can improve the state estimation accuracy of the optimal offline sensor scheduling by these bonus high power signals. Therefore our algorithm re-schedules the sensor scheduling strategy at every time step. According to the feedback information our algorithm chooses to send a high or low power signal and this choice makes full use of the feedback information and reduces the expected error covariance over the remaining time horizon. Finally, the Matlab simulation shows that our algorithm improves the performance of the estimation.