We investigate remote estimation over a packet drop channel with state and with feedback. We consider a system with two agents---one power controller/transmitter and one estimator.
The channel is modeled as a packet drop channel, where the
state of the channel evolves as a Markov chain and the packet drop probability depends on the input power of the channel. The channel state is observed by the receiver and fed back to the power controller/transmitter with one unit delay. In
addition, the power controller gets ACK/NACK feedback for
successful/unsuccessful transmission. We consider two models for the source---finite state Markov chains and first-order autoregressive processes. For the first model, using ideas from team theory we establish the structure of optimal power control and estimation strategies and
identify a dynamic program to determine optimal strategies with that
structure. For the second model, we assume that the noise
process has unimodal and symmetric distribution. Using ideas from majorization
theory, we show that the optimal transmission strategy has a threshold
structure and the optimal estimation strategy is Kalman-filter like.