On the Limited Communication Analysis and Design for Decentralized Estimation

TL;DR

This paper analyzes and designs decentralized estimation schemes with limited scalar communication, providing necessary and sufficient conditions for their operation, and formulates the minimal communication cost as an integer programming problem.

Contribution

It extends previous work to a more general setup, offering conditions for sensor communication and addressing cost-efficient network design for decentralized estimation.

Findings

Necessary and sufficient conditions for sensor communication are derived.

Finite-time state estimation is achieved with scalar exchanges.

The minimal communication graph is formulated as an integer programming problem.

Abstract

This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation~schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.