THE THEORY OF OPTIMAL LINEAR-ESTIMATION FOR CONTINUOUS FIELDS OF MEASUREMENTS

The main problem of linear estimation theory in infinite dimensional s paces is presented and its typical difficulties are illustrated. The u se of Wiener measures to represent continuous observation equations is carefully analysed in relation to the physical description of measure ments and to the mathematical limit when the number of observations gr ows to infinity. The overdetermined problem is solved by applying the Wiener principle of minimizing the mean square estimation error; the s olution is proved to exist and to be unique under very general conditi ons on the observation operators. Examples coming from space geodesy, potential theory and image analysis are presented to prove the effecti veness of the method and its applicability in different contexts.