Structural Cost-Optimal Design of Sensor Networks for Distributed Estimation

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: first, sensing cost optimization; and second, 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.