We investigate possibilities of choosing an activation policy of discrete scanning sensors in such a way as to maximize the accuracy of parameter estimation of a distributed system defined in a given multidimensional domain. A general functional defined on the Fisher information matrix is used as the design criterion. The setting examined here corresponds to situations where one has many sensors and activates only some of them during a given time interval, or alternatively, has several sensors which are mobile. The proposed approach, which has been suggested by Fedorov’s idea of directly constrained design measures, consists in imposing constraints on the sensor density in a given spatial domain. As a result, an extremely fast iterative procedure is obtained whose each step reduces to replacing less informative sensor locations with points which furnish more informaton about the parameters. The performance of the proposed algorithm is evaluated by numerical experiments.