Optimal sensor scheduling for two linear dynamical systems under limited resources in sensor networks

In this paper, we aim to design the optimal transmission scheme for two Gauss-Markov systems with finite resources. The setup that only two sensor nodes were scheduled, which monitor different linear dynamical systems, respectively. Two scenarios : the sensor has abundant calculation capability and the sensor has limited calculation capability are considered. For the second scenario, considering that the optimal schedule should collected a finite sequence of previous measurements. We are able to construct a quasi-optimal schedules. Due to bandwidth limitation and transmission power restriction, the sensors cannot communicate with the remote center and send the measurement data all the times. By exploiting the estimation error covariance at the remote estimation center to describe the quality of communication, the transmission schedule problem is formulated as an optimal problem. A necessary condition for the scheduling scheme of the sensors to be optimal is provided. Based on this necessary condition, we propose an explicit optimal periodic schedule, which is rigorously proved to have a minimal estimation error at the estimation center while satisfying the transmission power and channel bandwidth constraints. Simulation examples are given at last to verify the validity of the theoretical results.