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

The main problem of linear estimation theory in infinite dimensional spaces is The use of Wiener measures to represent continuous observation equations is carefully analysed in relation to the physical description of measurements and to the mathematical limit when the number of observations grows to infinity. The overdetermined problem is solved by applying the Wiener principle of minimizing the mean square estimation error; the solution is proved to exist and to be unique under very general conditions on the observation operators. Examples coming from space geodesy, potential theory and image analysis are presented to prove the effectiveness of the method and its applicability in different contexts.