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We consider a general form of the sensor scheduling problem for stateestimation of linear dynamical systems, which involves selecting sensors thatminimize the trace of the Kalman filter error covariance (weighted by apositive semidefinite matrix) subject to polyhedral constraints on the selectedsensors. This general form captures several well-studied problems includingsensor placement, sensor scheduling with budget constraints, and LinearQuadratic Gaussian (LQG) control and sensing co-design. We present a mixedinteger optimization approach that is derived by exploiting the optimality ofthe Kalman filter. While existing work has focused on approximate methods tospecific problem variants, our work provides a unified approach to computingoptimal solutions to the general version of sensor scheduling. In simulation,we show this approach finds optimal solutions for systems with 30 to 50 statesin seconds.

A Unified Approach to Optimally Solving Sensor Scheduling and Sensor Selection Problems in Kalman Filtering