Geodesic
The optimal measurements theory as a new paradigm in the metrology
Journal of computational and engineering mathematics, Tome 7 (2020) no. 1, pp. 3-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is an overview and contains a brief history of the theory of optimal dynamic measurements as one of the paradigms in Metrology. The introduction contains the main provisions of the paradigmatic concept of T. Kuhn and its criticism by P. Feyerabend from anarchist point of view. The conclusion about the coexistence of conflicting paradigms within the same science is made. In the first part, a mathematical model of measuring transducer is described and the conditions for the existence of a unique precise optimal dynamic measurement are given. In the second part, various approximate optimal measurements are proposed and the conditions for convergence of the sequence of approximate dynamic measurements to the precise optimal measurement are specified. The third part contains an approach to the study of a stochastic mathematical model of a measuring transducer based on the Nelson – Gliklikh derivative of the stochastic process. In the conclusion, the ways of further possible research are outlined. The list of publications contains all available sources related to the issue.
Keywords: deterministic mathematical model of measurement transducer, stochastic mathematical model of measurement transducer, precise optimal dynamic measurement, approximate optimal measurement, degenerate flow, stochastic optimal measurement, Nelson – Gliklikh derivative, Wiener process, "white noise"'. 
@article{JCEM_2020_7_1_a0,
     author = {A. L. Shestakov and A. V. Keller and A. A. Zamyshlyaeva and N. A. Manakova and S. A. Zagrebina and G. A. Sviridyuk},
     title = {The optimal measurements theory as a new paradigm in the metrology},
     journal = {Journal of computational and engineering mathematics},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a0/}
}
TY  - JOUR
AU  - A. L. Shestakov
AU  - A. V. Keller
AU  - A. A. Zamyshlyaeva
AU  - N. A. Manakova
AU  - S. A. Zagrebina
AU  - G. A. Sviridyuk
TI  - The optimal measurements theory as a new paradigm in the metrology
JO  - Journal of computational and engineering mathematics
PY  - 2020
SP  - 3
EP  - 23
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a0/
LA  - en
ID  - JCEM_2020_7_1_a0
ER  - 
%0 Journal Article
%A A. L. Shestakov
%A A. V. Keller
%A A. A. Zamyshlyaeva
%A N. A. Manakova
%A S. A. Zagrebina
%A G. A. Sviridyuk
%T The optimal measurements theory as a new paradigm in the metrology
%J Journal of computational and engineering mathematics
%D 2020
%P 3-23
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a0/
%G en
%F JCEM_2020_7_1_a0
A. L. Shestakov; A. V. Keller; A. A. Zamyshlyaeva; N. A. Manakova; S. A. Zagrebina; G. A. Sviridyuk. The optimal measurements theory as a new paradigm in the metrology. Journal of computational and engineering mathematics, Tome 7 (2020) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a0/