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Consider a remote estimation problem where a sensor wants to communicate thestate of an uncertain source to a remote estimator over a finite time horizon.The uncertain source is modeled as an autoregressive process with boundednoise. Given that the sensor has a limited communication budget, the sensormust decide when to transmit the state to the estimator who has to producereal-time estimates of the source state. In this paper, we consider the problemof finding a scheduling strategy for the sensor and an estimation strategy forthe estimator to jointly minimize the worst-case maximum instantaneousestimation error over the time horizon. This leads to a decentralized minimaxdecision-making problem. We obtain a complete characterization of optimalstrategies for this decentralized minimax problem. In particular, we show thatan open loop communication scheduling strategy is optimal and the optimalestimate depends only on the most recently received sensor observation.

Worst-case Guarantees for Remote Estimation of an Uncertain Source