﻿

#### Astronomical School’s Report, 2017, Volume 13, Issue 1, Pages 22–27

https://doi.org/10.18372/2411-6602.13.04
UDC 523.68; 520.373; 521.95; 521.96

# Application of statistical methods for processing of meteor TV observations

## Kozak P.M.

Astronomical Observatory of Taras Shevchenko National University of Kyiv, Observatorna str. 3, 04053 Kyiv, Ukraine

Abstract

Processing of two images of the same meteor registered simultaneously with the help of two cameras allows to calculate its complete kinematical characteristics, including trajectory parameters and orbital elements. This procedure generally consists of two stages: astrometric processing, where the calculated parameters are right ascensions and declinations of a range of meteor head points, and the trajectory and orbital elements themselves computation, which use the right ascensions and declinations as input parameters. The problem of this classic approach is unknown errors of calculated parameters. If we use the regression analysis for astrometric processing we calculate both the equatorial coordinates themselves of a meteor, and their standard deviations. As reduction models we usually use polynomial ones (linear, square, limited or entire cubic), or a method of arbitrary chosen optical center. Independently of the reduction model to be used we finally get a range of pairs (the value and standard deviation) for right ascensions and declinations of a meteor. If we suppose that the statistical distributions of calculation errors for right ascensions and declinations are completely described by two parameters – mean value and standard deviation – and determine the view of this distribution we will be able to use the Monte-Carlo method to generate random values of equatorial coordinated of the meteor head points on each step, and put them consecutively into all formulas for trajectory parameters and orbital elements calculation. Finally, we will get statistical distribution for each calculated parameter completely describing it as a random value. For publishing results one can present the standard deviations of each distribution as an error of calculated parameters, and average value of the distribution (or modal, median) as the mean value of them. The idea and examples of realization of the statistical approach for calculating kinematic parameters of a meteor from double station TV observations are proposed. The given approach includes the generation of random numbers in accordance with the statistical distributions of measured equatorial coordinates of the meteor, and allows to plot according distributions for all calculated kinematic parameters of the space particle. Obtained statistical distributions of kinematic characteristics of a meteor may be used not only for determination of errors of calculated parameters, but also for precising their average values.

Keywords: meteors; meteor kinematics; meteor TV observations; statistical data processing

References

1. Valeev S.G. (1991). Regressionnoe modelirovanie pri obrabotke nablyudeny. M.: Nauka. 272 p.
2. Deych A.N. (1965). K voprosu o reduktsii fotograficheskikh polozheny pri proizvol’nom opticheskom tsentre. Astronomichesky zhurnal, XLII, 5, 1114–1116.
3. Kozak P.N. (2002). Analiz metodov i tochnost’ opredeleniya ekvatorial’nykh koordinat pri tsifrovoy obrabotke televizionnykh nablyudeny meteorov. Kinematika i fizika nebesnykh tel, 18(5), 471–480.
4. Kozak P.N. (2003). Vektornyy metod opredeleniya parametrov traektorii i elementov geliotsentricheskoy orbity meteora dlya televizionnykh nablyudeny. Kinematika i fizika nebesnykh tel, 19(1), 62–76.
5. Kurs astrofiziki i zvezdnoy astronomii. T.1 / Pod red. A.A. Mikhaylova (1973). M.: Nauka. 608 p.
6. Cepleha Z. (1987). Geometric, dynamic, orbital, and photometric data on meteoroids from photographic fireball networks. Bull. Astron. Inst. Czech., 1987(38), 222–234.
7. Kozak P. (2008). “Falling Star”: Software for Processing of Double-Station TV Meteor Observations. Earth, Moon, and Planets, 102(1–4), 277–283. https://doi.org/10.1007/s11038-007-9223-x
8. Kozak P.M., Rozhilo A.A., Taranukha Y.G. (2001). Some features of digital kinematic and photometrical processing of faint TV meteors. Proc. Meteoroids 2001 Conf., Swedish institute of space physics, Kiruna, Sweden, 6–10 August 2001 (ESA SP-495, November 2001)., 337–342.