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 we seek to optimize the a posteriori error covariance over an infinite time horizon. 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. We also show that the error will die out exponentially for any detectable LTI system. Finally, we provide simulations to compare the performance of the algorithm against other known techniques.