Worst-case Guarantees for Remote Estimation of an Uncertain Source

Consider a remote estimation problem where a sensor wants to communicate the state of an uncertain source to a remote estimator over a finite-time horizon. The uncertain source is modeled as an autoregressive process with bounded noise. Given that the sensor has a limited communication budget, the sensor must decide when to transmit the state to the estimator who has to produce real-time estimates of the source state. In this article, we consider the problem of finding a scheduling strategy for the sensor and an estimation strategy for the estimator to jointly minimize the worst-case maximum instantaneous estimation error over the time horizon. This leads to a decentralized minimax decision-making problem. We obtain a complete characterization of optimal strategies for this decentralized minimax problem. In particular, we show that an open-loop communication scheduling strategy is optimal and the optimal estimate depends only on the most recently received sensor observation.