In this paper we study the problem of scheduling sensors to estimate the state of a linear dynamical system. The estimator is a Kalman filter and our objective is to optimize the a posteriori error covariance over an infinite time horizon. We focus on the case where a fixed number of sensors are selected at each time step, and we characterize the exact conditions for the existence of a schedule with uniformly bounded estimation error covariance, Using this result, we construct a scheduling algorithm that guarantees that the error covariance will be bounded if the existence conditions are satisfied. We call such an algorithm complete. Finally, we provide simulations to compare the performance of the algorithm against other known techniques. (C) 2017 Elsevier Ltd. All rights reserved.