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 covariances of the state estimates. This work investigates the development of tractable algorithms to solve for the optimal and suboptimal sensor schedules. A condition on the non-optimality of an initialization of the schedule is developed. Using this condition, both an optimal and a suboptimal algorithm are devised to prune the search tree of all possible sensor schedules. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. The performance of the suboptimal algorithm is also investigated and an analytical error bound is provided. Numerical simulations are conducted to demonstrate the performance of the proposed algorithms, and the application of the algorithms in active robotic mapping is explored. (c) 2012 Elsevier Ltd. All rights reserved.