On sensor scheduling of linear dynamical systems with error bounds

Consider a set of sensors estimating the state of a process in which only one of these sensors can operate at each time-step due to constraints on the overall system. The problem addressed here is to choose which sensor should operate at each time-step to minimize a function of the error covariance of the state estimation at each time-step. Previously, the authors developed tractable algorithms to solve for the optimal and suboptimal sensor schedule. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. As the tuning parameter is increased the complexity of the problem significantly decreases but the overall affect on the quality of the solution has not been completely characterized as of yet. This work concentrates on developing an upper bound on the distance from the optimal solution through two different approaches. The first approach exploits the peak estimation error, and the second method decomposes the covariance into two factors to linearly propagate the effects of perturbations. Numerical simulations are also performed to demonstrate the performance of the suboptimal algorithm for various tuning parameters.