  This paper presents a novel design methodology for optimal transmission
policies at a smart sensor to remotely estimate the state of a stable linear
stochastic dynamical system. The sensor makes measurements of the process and
forms estimates of the state using a local Kalman filter. The sensor transmits
quantized information over a packet dropping link to the remote receiver. The
receiver sends packet receipt acknowledgments back to the sensor via an
erroneous feedback communication channel which is itself packet dropping. The
key novelty of this formulation is that the smart sensor decides, at each
discrete time instant, whether to transmit a quantized version of either its
local state estimate or its local innovation. The objective is to design
optimal transmission policies in order to minimize a long term average cost
function as a convex combination of the receiver's expected estimation error
covariance and the energy needed to transmit the packets. The optimal
transmission policy is obtained by the use of dynamic programming techniques.
Using the concept of submodularity, the optimality of a threshold policy in the
case of scalar systems with perfect packet receipt acknowledgments is proved.
Suboptimal solutions and their structural results are also discussed. Numerical
results are presented illustrating the performance of the optimal and
suboptimal transmission policies.
