Statement of the problem of assessing instability of passive quantum frequency standards in the presence of an error from the interaction

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.