  The problem of synthesizing an optimal sensor selection policy is pertinent
to a variety of engineering applications ranging from event detection to
autonomous navigation. We consider such a synthesis problem over an infinite
time horizon with a discounted cost criterion. We formulate this problem in
terms of a value iteration over the continuous space of covariance matrices. To
obtain a computationally tractable solution, we subsequently formulate an
approximate sensor selection problem, which is solvable through a point-based
value iteration over a finite "mesh" of covariance matrices with a user-defined
bounded trace. We provide theoretical guarantees bounding the suboptimality of
the sensor selection policies synthesized through this method and provide
numerical examples comparing them to known results.
