The study of selenophysical parameters with the use of the noise-immune method of robust estimates

Yu.A. Nefedyev^∗ , A.O. Andreev^∗∗ , N.Yu. Demina^∗∗∗

Kazan Federal University, Kazan, 420008 Russia

E-mail: ^∗star1955@yandex.ru, ^∗∗alexey-andreev93@mail.ru, ^∗∗∗vnu357@mail.ru

Received May 25, 2020

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DOI: 10.26907/2541-7746.2020.4.481-491

For citation: Nefedyev Yu.A., Andreev A.O., Demina N.Yu. The study of selenophysical parameters with the use of the noise-immune method of robust estimates. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 4, pp. 481–491. doi: 10.26907/2541-7746.2020.4.481-491. (In Russian)

Abstract

This work is dedicated to the issues of reducing long-period series of astronomical observations. Such series contain both unequal and erroneous observations. Determination of the desired parameters from such observations is, thus, a rather complicated task. The main challenge is fair assessment of the accuracy of results produced. There are a number of methods for solving this problem, but the most suitable one for determining noise-immune estimates is the Huber M-estimator method (NIHEM). The selenophysical parameters were found by the analysis of measurements of the Mösting A crater from the Kaguya and Apollo lunar missions and from the heliometric observations. Such observations have a complex internal structure, and their analysis with the use of the method of least squares makes it impossible to either assess and eliminate erroneous measurements or take into account the unequal accuracy of the observations taken. Hence, to derive the desired selenophysical parameters, the NIHEM approach was used. As a result, the values and estimates of the Mösting A crater’s radius-vector, its selenographic longitude and latitude, lunar obliquity, values of harmonics in the expansion of physical libration into longitude, and corrections to the mean radius of the Moon were obtained.

Keywords: M-estimator method, noise-immune robust analysis, selenographic observations, planetary parameters

Acknowledgments. The study was supported in part by the Russian Science Foundation (project no. 20-12-00105 – the method of data analysis was developed and numerical calculations were performed), as well as by the Russian Foundation for Basic Research (project no. 19-32-90024), and Theoretical Physics and Mathematics Advancement Foundation “BASIS”. The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University.

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