On efficient sensor scheduling for linear dynamical systems

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 weighted function of the error covariance of the state estimation at each time-step. This work investigates the development of tractable algorithms to solve for the optimal and suboptimal sensor schedule. First, a condition on the non-optimality of an initialization of the schedule is presented. Second, using this condition, both an optimal and a suboptimal algorithm are devised to prune the search tree of all possible sensor schedules. This pruning enables the solution of larger systems and longer time horizons than with enumeration alone. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. Third, a hierarchical algorithm is formulated to decrease the computation time of the suboptimal algorithm by using results from a low complexity solution to further prune the tree. Numerical simulations are performed to demonstrate the performance of the proposed algorithms.