Optimal Scheduling of Multiple Sensors Over Lossy and Bandwidth Limited Channels

This article 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 that 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 the 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.