Determination of linear relations from real data in the Frisch scheme context

Deriving linear relations from data affected by additive noise is a problem of high practical relevance in many fields. All available procedures are based on sets of assumptions concerning the noise process; the results obtained from their use depend, consequently, from the distance between the actual process and the specific assumptions. The Frisch scheme introduces less a priori assumptions than other commonly used methods like, for instance, Least Squares, but leads to a whole family of models compatible with a set of noisy data so that its use is impractical in most cases. This paper introduces, on the basis of definitions and properties previously described, a robust and consistent procedure to extract a single model from two independent sets of noisy data in the context of the Frisch scheme. This allows the use of this approach also in all practical cases requiring a single model to describe the process behind the data.