Construction of confidence regions in problem on probabilistic study into motion of minor bodies of the solar system
Tóm tắt
Different approaches to constructing regions of possible motions of minor bodies are examined. An economical approach to the minimization of the number of points of the initial region by means of defining this region with its boundary surface is offered, and the estimations of its efficiency are given. The methods for estimating the admissibility of the linear approach are considered. For this purpose, simple methods for calculating the nonlinear factors are offered, which makes it possible to classify a problem to be solved as either strongly or weakly nonlinear. Recommendations are given on the possibility of reducing the concrete estimation problem to a weakly nonlinear one, where the more economical linear approach can be used. The combined method of mapping the initial region in time is also offered which unites the linear and nonlinear approaches. By example of two asteroids, the area of applicability of linear mappings is estimated.
Tài liệu tham khảo
Avdyushev, V.A., A New Method for the Statistical Simulation of the Virtual Values of Parameters in Inverse Orbital Dynamics Problems, Solar Syst. Res., 2009, vol. 43, no. 6, p. 543.
Avdyushev, V.A., Chislennoe modelirovanie orbit (Orbits Numerical Simulation), Tomsk: Izd. NTL, 2010.
Avdyushev, V.A., Nonlinear Methods of Statistic Simulation of Virtual Parameter Values for Investigating Uncertainties in Orbits Determined from Observations, Celest. Mech. Dyn. Astr., 2011, vol. 110, no. 4, pp. 369–388.
Bard, Y., Nonlinear Parameter Estimation, New York: Acad. Press., 1974; Moscow: Statistika, 1979.
Bates, D.M. and Watts, D.G., Relative Curvature Measures of Nonlinearity, J. Roy. Stat. Soc., 1980., vol. 42, no. 1, pp. 1–25.
Beale, E.M.L., Confidence Regions in Non-Linear Estimation, J. Roy. Stat. Soc., 1960, vol. 22, pp. 41–88.
Chernitsov, A.M., Analysis of Some Simplified Estimation Schemes for Determining Parameters of Celestial Bodies Motion, Astron. Geodez., 1975, issue 5, pp. 6–19.
Chernitsov, A.M., Baturin, A.P., and Tamarov, V.A., An Analysis of Some Methods for the Determination of the Probabilistic Evolution of Motion of the Solar System’s Small Bodies, Astron. Vestn., 1998, vol. 32, no. 5, p. 405.
Chernitsov, A.M., Tamarov, V.A., and Baturin, A.P., Nonlinear Problems for Estimating the Covariance Error Matrixes for Initial Parameters of Motion of Small Bodies, in Trudy GAISh MGU (Works of Sternberg Astronomical Institute of Moscow State University), vol. 75: Tezisy dokladov Vseross. konf. VAK-2004 “Gorizonty Vselennoi” (Proc. Int. Conf. VAK-2004 “Universe Horizons”), Moscow, 2004, p. 216.
Chernitsov, A.M., Dubas, O.M., and Tamarov, V.A., Ways to Decrease the Least-Squares Problem Nonlinearity for Generating the Ares of Asteroid Possible Motion, Izv. Vyssh. Uchebn. Zaved. Fiz., 2006, vol. 49, no. 2, pp. 44–51.
Chernitsov, A.M., Dubas, O.M., and Tamarov, V.A., Modeling of Regions of Asteroid Possible Motion, Odessa Astron. Publ., 2007a, vol. 20,pt. 1, pp. 36–39.
Chernitsov, A.M., Tamarov, V.A., and Dubas, O.M., How the Setting Errors of Weighting Matrixes Influence onto Confidence Region Determination Accuracy of Asteroids Motion, Izv. Vyssh. Uchebn. Zaved. Fiz., 2007b, vol. 50,no. 12/2, pp. 52–59.
Draper, N.R. and Smith, H., Applied Regression Analysis, New York: Wiley, 1966; Moscow: Finansy i statistika, 1986, book 1.
Dubas, O.M., Chernitsov, A.M., Tamarov, V.A., and Baturin, A.P., Nonlinearity of Finite Element Method Problem under Generating Possible Areas of Motion for Asteroids Observed Once, Tezisy dokladov mezhd. konf. “Okolozemnaya astronomiya-2005” (Proc. Int. Conf. “Near-Earth Astronomy-2005”), Kazan: INASAN, Sept. 19–24, 2005, pp. 43–44.
Ivashkin, V.V. and Stikhno, K.A., To the Problem of Orbit Correction for (99942) Apophis Asteroid at the Time of Its Encounting with the Earth, Dokl. Akad. Nauk, 2008, vol. 419, no. 5, pp. 624–627.
Ivashkin, V.V. and Stikhno, K.A., On the Prevention of a Possible Collision of Asteroid Apophis with the Earth, Solar Syst. Res., 2009, vol. 43, no. 6, pp. 483.
Muinonen, K., Virtanen, J., Granvik, M., and Laakso, T., Asteroid Orbits Using Phase-Space Volumes of Variation, Mon. Notic. Roy. Astron. Soc., 2006, vol. 368, pp. 809–818.
Scheffe, H., The Analysis of Variance, New York: Wiley, 1959; Moscow: Nauka, 1980.
Ventsel’, E.S. and Ovcharov, L.A., Teoriya veroyatnostei i ee inzhenernye prilozheniya (Probability Theory and Its Engineering Applications), Moscow: Vysshaya shkola, 2000.
Zabotin, A.S. and Medvedev, Yu.D., The Way to Determine the Orbits and Ellipsoid of Scattering for Asteroids which Are Potentially Dangerous for the Earth, Trudy IPA RAN, 2008, issue 19, pp. 68–78.
Zabotin, A.S. and Medvedev, Yu.D., On the Accuracy of the Orbit of Asteroid (99942) APOPHIS at the Time of Its Encounter with the Earth in 2029, Astron. Lett., 2009, vol. 35, no. 4, p. 278.
ftp://ftp.lowell.edu/pub/elgb/astorb.dat