This paper considers a remote state estimation problem, where a sensor measures the state of a linear discrete-time system. The sensor has computational capability to implement a local Kalman filter. The sensor-to-estimator communications are scheduled intentionally over a finite time horizon to obtain a desirable tradeoff between the state estimation quality and the limited communication resources. Compared with the literature, we adopt a Gaussianity-preserving event-based sensor schedule bypassing the nonlinearity problem met in threshold event-based polices. We derive the closed-form of minimum mean-square error (MMSE) estimator and show that, if communication is triggered, the estimator cannot do better than the local Kalman filter, otherwise, the associated error covariance, is simply a sum of the estimation error of the local Kalman filter and the performance loss due to the absence of communication, We further design the scheduler's parameters by solving a dynamic programming (DP) problem. The computational overhead of the DP problem is less sensitive to the system dimension compared with that of existing algorithms in the literature. (C) 2016 Elsevier Ltd. All rights reserved.