Optimal Sensor and Relay Nodes Power Scheduling for Remote State Estimation with Energy Constraint

We study the sensor and relay nodes' power scheduling problem for the remote state estimation in a Wireless Sensor Network (WSN) with relay nodes over a finite period of time given limited communication energy. We also explain why the optimal infinite time and energy case does not exist. Previous work applied a predefined threshold for the error covariance gap of two contiguous nodes in the WSN to adjust the trade-off between energy consumption and estimation accuracy. However, instead of adjusting the trade-off, we employ an algorithm to find the optimal sensor and relay nodes' scheduling strategy that achieves the smallest estimation error within the given energy limit under our model assumptions. Our core idea is to unify the sensor-to-relay-node way of error covariance update with the relay-node-to-relay-node way by converting the former way of the update into the latter, which enables us to compare the average error covariances of different scheduling sequences with analytical methods and thus finding the strategy with the minimal estimation error. Examples are utilized to demonstrate the feasibility of converting. Meanwhile, we prove the optimality of our scheduling algorithm. Finally, we use MATLAB to run our algorithm and compute the average estimation error covariance of the optimal strategy. By comparing the average error covariance of our strategy with other strategies, we find that the performance of our strategy is better than the others in the simulation.