# Worst-case Guarantees for Remote Estimation of an Uncertain Source

arXiv: https://arxiv.org/abs/1902.03339 · HTML: https://mlsanity.com/paper/1902.03339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2019.

## Built on by (most cited first, 1 of 1)

- [Approximate Information States for Worst-Case Control and Learning in Uncertain Systems](https://mlsanity.com/paper/2301.05089/) (2023)

## Abstract (arXiv)

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.