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A comparison between numerical differentiation and Kalman filtering for a LEO satellite velocity determination

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The kinematic orbit is a time series of position vectors generally obtained from GPS observations. Velocity vector is required for satellite gravimetry application. It cannot directly be observed and should be numerically determined from position vectors. Numerical differentiation is usually employed for a satellite’s velocity, and acceleration determination. However, noise amplification is the single obstacle to the numerical differentiation. As an alternative, velocity vector is considered as a part of the state vector and is determined using the Kalman filter method. In this study, velocity vector is computed using the numerical differentiation (e.g., 9-point Newton interpolation scheme) and Kalman filtering for the GRACE twin satellites. The numerical results show that Kalman filtering yields more accurate results than numerical differentiation when they are compared with the intersatellite range-rate measurements.
Rocznik
Strony
103--110
Opis fizyczny
Bibliogr. 20 poz., rys., tab.
Twórcy
  • Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Enghelab Ave., P.O. Box 11365-4563, Tehran, Iran
autor
  • Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Enghelab Ave., P.O. Box 11365-4563, Tehran, Iran
autor
  • Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Enghelab Ave., P.O. Box 11365-4563, Tehran, Iran
Bibliografia
  • [1] L. Richard, J. Burden, F. Douglas, Numerical Analysis (7th Ed), Brooks, Cole, 2000.
  • [2] T. Reubelt, G. Asusten, E.W. Grafarend, Harmonic analysis of the Earth’s gravitational field by means of semi-continuous ephemerides of a low Earth orbiting GPS-tracked satellite. Case study: CHAMP. J Geod 77 (2003) (5-6):257-278. DOI : 10.1007/s00190- 003-0322-9.
  • [3] L. Foldvary, D. Svehla, Ch. Gerlach, M. Wermuth, Th Gruber, R. Rummel, M. Rothacher, B. Frommknecht, Th. Peters, P. Steigenberger, Gravity model TUM-2sp based on the energy balance approach and kinematic CHAMP orbits, Earth Observation with CHAMP - Results from Three Years in Orbit (Ed. Reigber Ch, Lühr H, Schwintzer P et al.), Springer, Berlin, 13-18, 2004.
  • [4] M. Hanke, O. Scherzer, Inverse problems light: numerical differentiation. Amer. Math. Monthly, 108 (2001) 512-5211.
  • [5] P.S. Maybeck, Stochastic Models, Estimation, and Control. Volume 1, Academic Press, Inc, 1979.
  • [6] A. Gelb, Applied Optimal Estimation. MIT Press, Cambridge, MA, 1974.
  • [7] R.G. Brown, P.Y.C Hwang, Introduction to Random Signals and Applied Kalman Filtering: With MATLAB Exercises and Solutions, 3rd ed., Wiley, New York, 1997.
  • [8] L. Foldavary, Analysis of Numerical Differentiation methods Applied for Determination of Kinematic Velocities for LEOs, Per. Pol. Civil Eng., 51/1 17-24, 2007.
  • [9] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed, Cambridge University Press, Cambridge, 1992.
  • [10] R.E. Kalman, A new approach to linear filtering and prediction problems. Transactions of the ASME, Ser. D, Journal of Basic Engineering, 82 (1960) 34-45.
  • [11] D.A. Vallado, Fundamentals of Astrodynamics and Applications. Third Edition. Published Jointly By Microcosm and Springer, New York, 2007.
  • [12] B.D. Tapley, B.E. Schutz, G.H. Born, Statistical Orbit Determination. Elsevier Academic Press, New York, 2004.
  • [13] F.G. Lemoine, et al., The development of the joint NASA GSFC and the National Imagery Mapping Agency (NIMA) geopotential model EGM96. NASA Technical Report NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, Maryland, 1998.
  • [14] M. Chapront-Touze, J. Chapront, The lunar ephemeris ELP 2000, Astronomy and Astrophysics, 190 (1988) 342-352.
  • [15] O. Montenbruck, Practical Ephemeris Calculations, Springer Verlag, Heidelberg, 1989.
  • [16] J.M. Picone, A.E. Hedin, D.P. Drob, A.C. Aikin, NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues. J. Geophys. Res., 107 (2002). doi:10.1029/2002JA009430, 2002.
  • [17] O. Montenbruck, E. Gill, Satellite orbits-models, methods, and applications. Springer, Berlin, 2000.
  • [18] D.D. McCarthy, G. Petit, IERS Conventions, IERS Tech. Note, vol. 32. Verlag des Bundesamts fur Kartogr. und Geod., Frankfurt am Main, Germany, 2004. Available at: http://www.iers.org/iers/publications/tn/tn32
  • [19] Z. Kang, B. Tapley, S. Bettadpur, J. Ries, P. Nagel, R. Pastor, Precise orbit determination for the GRACE mission using only GPS data, J. Geod 80 (2006)322-331.
  • [20] K. Case, G. Kruizinga, S. Wu, GRACE level 1B Data Product User Handbook Version 1.2, 2004.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2692dfbb-d43c-4f42-b76e-d9b3fd4825e6
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