  Motivated by the Internet-of-things and sensor networks for cyberphysical
systems, the problem of dynamic sensor activation for the tracking of a
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 three key ingredients: Gibbs sampling, stochastic approximation for
learning, and modifications to consensus algorithms to create a high
performance, energy efficient tracking mechanisms with active sensor selection.
The following progression of scenarios are considered: centralized tracking of
an i.i.d. process; distributed tracking of an i.i.d. process and finally
distributed tracking of a Markov chain. The 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. The key theoretical results prove that the
proposed algorithms converge to local optima for the two i.i.d process cases;
numerical results suggest that global optimality is in fact achieved. The
proposed distributed tracking algorithm for a Markov chain, based on
Kalman-consensus filtering and stochastic approximation, is seen to offer an
error performance comparable to that of a competetive centralized Kalman
filter.
