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This paper is concerned with the design of transmission scheduler and estimator for linear discrete-time stochastic systems to reduce the number of measurements to be transmitted from sensor to estimator. To this purpose, both controllable and uncontrollable scheduling schemes are considered, respectively. A controllable scheduler is designed as a deterministic function of system measurements, and sequentially decides the transmission of each element of a measurement vector to the estimator. We derive an approximate minimum mean square error (MMSE) estimator. On the other hand, an uncontrollable scheduler means that the transmission of the measurement vector is driven by a random process which is independent of system evolution. The MMSE estimator under this scheduler is cast as the Kalman filtering with intermittent observations. Some stability conditions are established for both the estimators. Finally, illustrative examples are included to validate the theoretical results.