Abstract
Construction of modern measuring complexes of the coordinate-time support system of Ukraine is impossible without improving mathematical models of quantum standards of frequency (QSF) used in group standards. This work is devoted to the analysis of methods for the stable solution of direct and inverse problems (methods for solving ill-posed problems) in models of the interaction of passive QSF in the process of their comparisons. The priority task is to use these methods for the numerical solution of problems in the design of group QSF and parallel quantum generators of random numbers. Methods for solving such problems are in demand, since they make it possible to create mathematical models of group QSF interaction. These models will enable the design of efficient parallel quantum random number generation devices for high-tech areas of cybersecurity.
 Varieties of methods such as the method of least squares or the method of the Moore-Penrose pseudo-inverse matrix are used, as a rule when evaluating the metrological parameters of QSF.Robust methods of regularization or filtering, for example, the Kalman or Wiener filter method, are used in the algorithms of group standards, due to the instability of the solution.However, these methods do not work in the presence of an error from the interaction of QSF in the process of their functioning in a group standard or in comparisons.
 The aim of this work is to analyze and substantiate the formulation of the problem of assessing the potential accuracy characteristics of passive QSF in the presence of an error from the interaction. Regularization parameters when determining the state vector of the group standard are found using signals transmitted by global navigation satellite systems such as GPS\GLONASS in the local differential correction mode.
Highlights
IntroductionThis discovery led to the emergence of a new branch of technical physics, namely, quantum electronics
Based on the results of the analysis of the influence of various external destabilizing factors on the characteristics of the output signals of the quantum standards of frequency (QSF) and methods for their compensation, the following main tasks of further research can be formulated: 1. To develop a method for identifying stochastic processes caused by the error from the interaction of the QSF in a group on the basis of a stochastic model of coupled oscillators, and to develop a method for measuring quantum noise by methods of group standardization
To conduct a study of the behavior of the resonant frequency of a quantum discriminator in a nonstationary fluctuating temperature field of a thermostat and develop a method for compensating for fluctuations in the frequency of a signal generated by a passive QSF caused by fluctuations in the temperature of a thermostat
Summary
This discovery led to the emergence of a new branch of technical physics, namely, quantum electronics In this area of outwardly traditional research, the issues of the theory of interaction of a radio-frequency field with matter and the elements of the theory of quantum amplifiers and generators have been sufficiently well studied. As a result of such a radical expansion of the range of problems, the issues of the influence of the error from the interaction on the estimation of the frequency instability of passive quantum standards of frequency (QSF) are still poorly understood. This is due to the laboriousness of this measuring task associated with the involvement of complex and expensive equipment. The standard frequency separation requirement does not apply, since all frequency measures used have practically the same frequency of oscillation
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