Structural cost-optimal design of sensor networks for distributed estimation

TL;DR

This paper presents a cost-efficient design approach for sensor networks monitoring full-rank systems, utilizing structured systems theory to optimize sensing and networking costs with polynomial solutions and approximations.

Contribution

It introduces a novel framework that relaxes the cost optimization problem into two subproblems, providing polynomial solutions and a 2-approximation for large-scale systems.

Findings

Sensing cost optimization has a polynomial solution.

Networking cost optimization is NP-hard but solvable under certain conditions.

A 2-approximation relaxation is applicable for large-scale systems.

Abstract

In this letter we discuss cost optimization of sensor networks monitoring structurally full-rank systems under distributed observability constraint. Using structured systems theory, the problem is relaxed into two subproblems: (i) sensing cost optimization and (ii) networking cost optimization. Both problems are reformulated as combinatorial optimization problems. The sensing cost optimization is shown to have a polynomial order solution. The networking cost optimization is shown to be NP-hard in general, but has a polynomial order solution under specific conditions. A 2-approximation polynomial order relaxation is provided for general networking cost optimization, which is applicable in large-scale system monitoring.