Optimal scheduling policy for spatio temporally dependent observation using age of information

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This paper proposes an optimal scheduling policy for a remote estimation problem, where sensor observations of two spatio-temporally correlated processes are broadcasted to two remote estimators. At each time instant only a single observation can be communicated. For this purpose, a system scheduler determines which sensor measurement is communicated. The scheduler cannot observe measurements, and exploits age-of-information (AoI) to calculate the expected estimation error. We derive an optimal scheduling policy, with AoI as state-variable, that minimizes the average mean squared error for an infinite time horizon. The obtained policy yields a periodic scheduling of the sensor measurements, and we show that the AoI for the process with the largest marginal variance does not exceed one.