A parallel algorithm for optimum monitoring network design in parameter estimation of distributed systems

The design of a network of observation nodes in a spatial domain is addressed. The observations are to be used to estimate unknown parameters of a distributed parameter system. Given a finite number of possible sites at which to locate a sensor, the problem is formulated as the selection of the gauged sites so as to minimize a convex criterion defined on the Fisher information matrix associated with the estimated parameters. The search for an optimal solution to this binary optimization problem is performed through solving a relaxed problem in which a constrained discrete probability distribution on the set of all allowable sites is sought. The main contribution here consists in properly parallelizing this solution using the parallel variable distribution approach. As a result, each processor minimizes a convex function subject to linear constraints through the use of a simplicial decomposition algorithm. The resulting individual solutions are then synchronized by finding their optimal convex combination.