This paper proposes an optimal scheduling policy for a system where spatio-temporally dependent sensor observations are broadcast to remote estimators over a resource-limited broadcast channel. We consider a system with a measurement-blind network scheduler that transmit observations, and design scheduling schemes that minimize MSE by determining a subset of sensor observations to be broadcast based on their information freshness, as measured by their age-of-information (AoI). By modeling the problem as a finite state-space Markov decision process (MDP), we derive an optimal scheduling policy, with AoI as a state-variable, minimizing the average mean squared error for an infinite time horizon. The resulting policy has a periodic pattern that renders an efficient implementation with low data storage. We further show that for any policy that minimizes the overall AoI, the estimation accuracy depends on how the scheduling order relates to the sensor’s intrinsic spatial correlation. Consequently, the estimation accuracy varies from worse than a randomized scheduling approach to near-optimal. Thus, we present an additional age-minimizing policy with optimal scheduling order. We also present alternative policies for large state spaces that are attainable with less computational effort. Numerical results validate the presented theory.