  Active state tracking is needed in object classification, target tracking,
medical diagnosis and estimation of sparse signals among other various
applications. Herein, active state tracking of a discrete-time, finite-state
Markov chain is considered. Noisy Gaussian observations are dynamically
collected by exerting appropriate control over their information content, while
incurring a related sensing cost. The objective is to devise sensing strategies
to optimize the trade-off between tracking performance and sensing cost. A
recently proposed Kalman-like estimator \cite{ZoisTSP14} is employed for state
tracking. The associated mean-squared error and a generic sensing cost metric
are then used in a partially observable Markov decision process formulation,
and the optimal sensing strategy is derived via a dynamic programming
recursion. The resulting recursion proves to be non-linear, challenging control
policy design. Properties of the related cost functions are derived and
sufficient conditions are provided regarding the structure of the optimal
control policy enabling characterization of when passive state tracking is
optimal. To overcome the associated computational burden of the optimal sensing
strategy, two lower complexity strategies are proposed, which exploit the
aforementioned properties. The performance of the proposed strategies is
illustrated in a wireless body sensing application, where cost savings as high
as $60\%$ are demonstrated for a $4\%$ detection error with respect to a static
equal allocation sensing strategy.
