# On the Optimal Solutions of the Infinite-Horizon Linear Sensor Scheduling Problem

arXiv: https://arxiv.org/abs/1312.0157 · HTML: https://mlsanity.com/paper/1312.0157/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2013.

## Built on by (most cited first, 3 of 3)

- [Deep Learning for Wireless Networked Systems: a joint Estimation-Control-Scheduling Approach](https://mlsanity.com/paper/2210.00673/) (2022)
- [Deep Reinforcement Learning for Wireless Scheduling in Distributed Networked Control](https://mlsanity.com/paper/2109.12562/) (2021)
- [PLATE: A perception-latency aware estimator,](https://mlsanity.com/paper/2401.13596/) (2024)

## Abstract (arXiv)

This paper studies the infinite-horizon sensor scheduling problem for linear Gaussian processes with linear measurement functions. Several important properties of the optimal infinite-horizon schedules are derived. In particular, it is proved that under some mild conditions, both the optimal infinite-horizon average-per-stage cost and the corresponding optimal sensor schedules are independent of the covariance matrix of the initial state. It is also proved that the optimal estimation cost can be approximated arbitrarily closely by a periodic schedule with a finite period. Moreover, it is shown that the sequence of the average-per-stage costs of the optimal schedule must converge. These theoretical results provide valuable insights into the design and analysis of various infinite-horizon sensor scheduling algorithms.