Optimal Scheduling of Multiple Spatiotemporally Dependent Observations for Remote Estimation Using Age of Information

This article proposes an optimal scheduling policy for a system where spatiotemporally 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 transmits observations, and design scheduling schemes that minimize mean squared error (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 MSE 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.