  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 paper, 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.
