  We consider a general form of the sensor scheduling problem for state
estimation of linear dynamical systems, which involves selecting sensors that
minimize the trace of the Kalman filter error covariance (weighted by a
positive semidefinite matrix) subject to polyhedral constraints on the selected
sensors. This general form captures several well-studied problems including
sensor placement, sensor scheduling with budget constraints, and Linear
Quadratic Gaussian (LQG) control and sensing co-design. We present a mixed
integer optimization approach that is derived by exploiting the optimality of
the Kalman filter. While existing work has focused on approximate methods to
specific problem variants, our work provides a unified approach to computing
optimal solutions to the general version of sensor scheduling. In simulation,
we show this approach finds optimal solutions for systems with 30 to 50 states
in seconds.
