Statistical Separation of Fluctuations and Measurement Errors of the Controlled Parameter in the Joint Processing of Data from Two Independent Recording Systems

Abstract

We present a solution of the inverse problem in measurement theory. From statistical data of the observed superposition of a recorded random parameter and the error of the device, the distributions of the unobserved components of this sum are calculated. The processing of empirical data uses the apparatus of characteristic functions, cumulant decompositions, and asymptotic estimates in the form of a truncated Edgeworth series.