  Joint estimation and scheduling for sensor networks is considered in a system
formed by two sensors, a scheduler and a remote estimator. Each sensor observes
a Gaussian source, which may be correlated. The scheduler observes the output
of both sensors and chooses which of the two is revealed to the remote
estimator. The goal is to jointly design scheduling and estimation policies
that minimize a mean-squared estimation error criterion. The person-by-person
optimality of a policy pair called "max-scheduling/mean-estimation" is
established, where the measurement with the largest absolute value is revealed
to the estimator, which uses a corresponding conditional mean operator. This
result is obtained for independent sources, and in the case of correlated
sources and symmetric variances. We also consider the joint design of
scheduling and linear estimation policies for two correlated Gaussian sources
with an arbitrary correlation structure. In this case, the optimization problem
can be cast a difference-of-convex program, and locally optimal solutions can
be efficiently found using a simple numerical procedure.
