Sensor scheduling with limited communication energy and bandwidth

In this paper, we consider the problem of sensor scheduling with limited resources. Two sensors are used to measure the state of a discrete-time linear process. We assume that each sensor has a maximum duty cycle and at most one sensor can communicate with a remote estimator at each time step due to the limited communication bandwidth. When a sensor is scheduled to send data, it sends the most recent D measurement data to the estimator. Upon receiving the measurement data from the sensors, the estimator computes the optimal estimate of the state of the process. We first present a necessary condition for a sensor scheduling scheme to be optimal. Based on this necessary condition, we construct an optimal scheduling scheme that minimizes the estimation error at the estimator and at the same time satisfies the energy and communication bandwidth constraints. We also provide a sufficient condition on the minimum D such that an optimal scheduling scheme can be constructed. Examples are provided throughout the paper to demonstrate the results developed.