How can online schedules improve communication and estimation tradeoff?

We consider remote state estimation and investigate the tradeoff between the sensor-to-estimator communication rate and the remote estimation quality. It is well known that if the communication rate is one, e.g., the sensor communicates with the remote estimator at each time, then the remote estimation quality is the best. It degrades when the communication rate drops. We present one optimal offline schedule and two online schedules and show that the two online schedules provide better tradeoff between the communication rate and the estimation quality than the optimal offline schedule. Simulation examples demonstrate that significant communication savings can be achieved under the two online schedules which only introduce small increment of the estimation errors.