Study on Efficient Sensor Node Selection for Observability Gramian Optimization⋆

Abstract

This study attempts a practical comparison of optimization methods for sensor node selection to efficiently monitor large-scale dynamical systems represented by linear time-invariant state space models. Sensor measurements are evaluated based on an observability measure, the matrix determinant of the observability Gramian. This study confirms the applicability of selection strategies, namely, a convex relaxation method using semidefinite programming, a greedy maximization and its approximation that considers the gradient of the observability measure. Examples based on numerical and real-world experiments illustrate the effectiveness of the selection algorithms in terms of their optimization measures and the run time for the selection.