State estimation in energy harvesting systems

We consider a discrete time scalar Kalman filtering problem over an erasure channel with an energy harvesting transmitter both with and without side information about the erasure state of the channel available at the transmitter. The cost of transmitting an observation is one unit of energy and the transmitter controls its energy expenditure by leveraging the available energy storage and side information. In this setting, the observations are intermittently available at the receiver and this intermittency is controlled by the transmitter. We study the threshold for the growth rate of the dynamics that guarantees the boundedness of the asymptotic expected state estimation error covariance under different system settings.