The aim of this research is to develop a method for a posteriori control over the stability of observation conditions in modern high-precise absolute measurements of the acceleration of the Earth's gravity on the basis of methods of the non-classical error theory (NET). These measurements are carried out in a complicated metrological situation, which is continuously broken under the influence of various causes: trends of the frequency spectrum and energy of microseisms, geological, atmospheric, tidal, and other space factors, including uncontrolled effects of the place of observation and possible malfunctions in the work of the gravimeter. Through such control, it is necessary to obtain such distributions of observation errors that provide effective, or, at least, admissible arithmetic mean estimates of the Galilean acceleration. The methodology of achieving this aim is provided by the NET algorithms, which are created to control the form of empirical distributions of errors of high-precise multiple large-scale observations based on the principles of the Neumann-Pearson hypothesis testing theory. The basic result of the study is the development of a method for diagnosing the metrological situation, which was in the course of observing, on the basis of the NET methods. These methods are based on the use of the posteriori estimates of statistical cumulates in the form of empirical distributions of errors with the further application of the χ2-criterion to control the significance of its deviations from the established norms. In accordance with the principles of the NET, such norms are the laws of: Gauss or Pearson-Jeffreys, since they provide the non-singularity of the weight function of observations, and therefore the possibility of estimates, in the mathematical processing of observations. The scientific novelty of this investigation: the NET procedures are used for the first time to improve the current absolute high-precise observations of Galilean acceleration, which are performed in complicated metrological conditions, simultaneously taking into account the number of non-stationary sources of systemic errors. Practical significance of the study: the development of an algorithm for controlling the form of the empirical distribution of errors in order to improve the realization of high-precise ballistic measurements of Galilean acceleration based on the axiomatics of the NET. The study of the reasons for the deviation of distribution of errors from the normal law has long been a necessary element of the theory of production accuracy and control over the stability of the operation of various aggregates. The introduction of such approaches, started by Kolmogorov and his school, has long been at the heart of the strategy, which ensures metrological literacy of the measurement process and ways of improving their accuracy.
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