An approach to the optimal scanning measurement problem using optimum experimental design

Abstract

We address the problem of activating discrete scanning sensors so as to maximize some quantitative observability measure for a given distributed parameter system. In contrast to the classical approach based on a direct application of non-linear programming algorithms, the key idea here is to operate on the density of sensors per unit area instead of the positions of individual sensors. Mathematically, this procedure involves searching for a family of "optimal" probability measures defined on subsets of the set of feasible measurement points. The method proposed for solving the problem so formulated, originates from an extremely efficient approach which is based on directly constrained design measures that are used in optimum experimental design theory. As a result, a fast iterative procedure is obtained whose each step reduces to replace less informative sensor locations with points which furnish more information about the system state.