This work considers the sensor scheduling for multiple dynamic processes. We consider n linear dynamic processes. The state of each process is measured by a sensor, which transmits its local state estimate over one wireless channel to a remote estimator with certain communication costs. At each time step, only a portion of the sensors are allowed to transmit data to the remote estimator and the packet might be lost due to unreliability of the wireless channels. Our goal is to find a scheduling policy which coordinates the sensors in a centralized manner to minimize the total expected estimation error of the remote estimator and the communication costs. We formulate the problem as a Markov decision process. We develop an algorithm to check whether there exists a deterministic stationary optimal policy. We show the optimality of monotone policies, which saves the computational effort of finding an optimal policy and facilitates practical implementation. Nevertheless, obtaining an exact optimal policy still suffers from curse of dimensionality when the number of processes is large. We further provide an index-based heuristic to avoid brute force computation. We derive analytic expressions of the indices and show that this heuristic is asymptotically optimal. Numerical examples are presented to illustrate the theoretical results.Index Terms-Kalman filtering; Sensor scheduling; lossy network; monotone policy; Markov decision process; index policy
I. INTRODUCTIONThe development of device, sensing and communication technologies enables wide range of applications of wireless sensor networks. After the pioneering work on event-based sensor data scheduling proposed in [1], a variety of studies has been done to balance the estimation performance and the communication overhead in [2]- [4].A large number of works on sensor scheduling focused on remote estimation of a linear time-invariant (LTI) dynamic process. There are also some other works addressing static processes and nonlinear models. However, the static models [5], [6] are special cases of LTI systems and nonlinear models either involve approximation of a linear system [7], [8] or the solution method requires numerically solving a partially observable Markov decision process, which is computationally inefficient [9]-[11]. A few works [12], [13] considered control