Sensor Network Design for Parameter Estimation of Distributed Systems Using Nonsmooth Optimality Criteria

A computational procedure is presented for designing configurations of a measurement network consisting of a large number of stationary sensors collecting data for parameter estimation of a distributed system. Two widely used minimax criteria defined on the Fisher information matrix, namely those of MV-and E-optimality, are considered here as the measures of the estimation accuracy. The approach applied here is to impose constraints on the sensor density in a given spatial domain and to replace the worst-case criteria by their convex smooth approximations. As a result, a fast iterative procedure is obtained whose each step reduces to replacing less informative sensor locations with points which furnish more informaton about the parameters. This planning algorithms is verified by a numerical example on a two-dimensional heat equation.