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

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 4, pp. 481-491

Résumé

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.

Détail

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

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