This paper studies a remote sensing system where multiple wireless sensors generate possibly noisy information updates of various surveillance fields and delivering these updates to a control center over a wireless network. The control center needs a sufficient number of recently generated information updates to have an accurate estimate of the current system status, which is critical for the control center to make appropriate control decisions. The goal of this work is then to design the optimal policy for scheduling the transmissions of information updates. Through Brownian approximation, we demonstrate that the control center's ability to make accurate real-time estimates depends on the averages and temporal variances of the delivery processes. We then formulate a constrained optimization problem to find the optimal means and variances. We also develop a simple online scheduling policy that employs the optimal means and variances to achieve the optimal system-wide performance. Simulation results show that our scheduling policy enjoys fast convergence speed and better performance when compared to other state-of-the-art policies.