  Joint optimization of scheduling and estimation policies is considered for a
system with two sensors and two non-collocated estimators. Each sensor produces
an independent and identically distributed sequence of random variables, and
each estimator forms estimates of the corresponding sequence with respect to
the mean-squared error sense. The data generated by the sensors is transmitted
to the corresponding estimators, over a bandwidth-constrained wireless network
that can support a single packet per time slot. The access to the limited
communication resources is determined by a scheduler who decides which sensor
measurement to transmit based on both observations. The scheduler has an
energy-harvesting battery of limited capacity, which couples the
decision-making problem in time. Despite the overall lack of convexity of the
team decision problem, it is shown that this system admits globally optimal
scheduling and estimation strategies under the assumption that the
distributions of the random variables at the sensors are symmetric and
unimodal. Additionally, the optimal scheduling policy has a structure
characterized by a threshold function that depends on the time index and energy
level. A recursive algorithm for threshold computation is provided.
