Identification of linear relations from noisy data: Geometrical aspects

The problem of determining linear models from data corrupted by noise has been revisited by several authors in recent years. With reference to the Frisch scheme, this work presents some geometrical aspects regarding the sets of solutions obtained in the identification procedure. An analysis is made on how these sets vary as the amount of noise on the data varies; the existence of particular solutions for data linked by a number of linear relations greater than one, is also shown.