  Motivated by the Internet-of-things and sensor networks for cyberphysical
systems, the problem of dynamic sensor activation for the centralized tracking
of an i.i.d. time-varying process is examined. The tradeoff is between energy
efficiency, which decreases with the number of active sensors, and fidelity,
which increases with the number of active sensors. The problem of minimizing
the time-averaged mean-squared error over infinite horizon is examined under
the constraint of the mean number of active sensors. The proposed methods
artfully combine Gibbs sampling and stochastic approximation for learning, in
order to create a high performance, energy efficient tracking mechanisms with
active sensor selection. Centralized tracking of i.i.d. process with known
distribution as well as an unknown parametric distribution are considered. For
an i.i.d. process with known distribution, convergence to the global optimal
solution with high probability is proved. The main challenge of the i.i.d. case
is that the process has a distribution parameterized by a known or unknown
parameter which must be learned; one key theoretical result proves that the
proposed algorithm for tracking an i.i.d. process with unknown parametric
distribution converges to local optima. Numerical results show the efficacy of
the proposed algorithms and also suggest that global optimality is in fact
achieved in some cases.
