Optimal Sensor Scheduling and Remote Estimation over an Additive Noise Channel
It extends known sensor scheduling results to noisy channels, providing optimal solutions for a constrained class of distributions.
The paper addresses sensor scheduling and remote estimation with additive channel noise, deriving optimal policies that minimize the expected sum of communication and estimation costs for specific distributions.
We consider a sensor scheduling and remote estimation problem with one sensor and one estimator. At each time step, the sensor makes an observation on the state of a source, and then decides whether to transmit its observation to the estimator or not. The sensor is charged a cost for each transmission. The remote estimator generates a real-time estimate on the state of the source based on the messages received from the sensor. The estimator is charged for estimation error. As compared with previous works from the literature, we further assume that there is an additive communication channel noise. As a consequence, the sensor needs to encode the message before transmitting it to the estimator. For some specific distributions of the underlying random variables, we obtain the optimal solution to the problem of minimizing the expected value of the sum of communication cost and estimation cost over the time horizon.