  We consider the classical sensor scheduling problem for linear systems where
only one sensor is activated at each time. We show that the sensor scheduling
problem has a close relation to the sensor design problem and the solution of a
sensor schedule problem can be extracted from an equivalent sensor design
problem. We propose a convex relaxation to the sensor design problem and a
reference covariance trajectory is obtained from solving the relaxed sensor
design problem. Afterwards, a covariance tracking algorithm is designed to
obtain an approximate solution to the sensor scheduling problem using the
reference covariance trajectory obtained from the sensor design problem. While
the sensor scheduling problem is NP-hard, the proposed framework circumvents
this computational complexity by decomposing this problem into a convex sensor
design problem and a covariance tracking problem. We provide theoretical
justification and a sub-optimality bound for the proposed method using dynamic
programming. The proposed method is validated over several experiments
portraying the efficacy of the framework.
