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We consider scheduling two Gauss-Markov systems. Two sensors, each measuring the state of one of the two systems, compute and report their local state estimates to a central remote estimator, respectively. Due to the bandwidth constraint, at each time, only one of the sensors is allowed to communicate its estimate with the remote estimator. Upon receiving the data from the sensors, the remote estimator computes the minimum mean squared error estimate of each system's state. We provide an explicit construction of an optimal schedule, which is periodic (hence allows simple and efficient practical implementation) and minimizes the sum of the average estimation error covariance of each system.