Early Orbit Determination Using U-D Covariance Propagation Filter

  • D. Sita Rama Raju
  • Ch. Sreehari Rao
  • S. K. Shrivastava
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 127)


The problem of short arc orbit determination with the data from a single station during the early orbital phase of a launch vehicle mission poses challenges. In this paper after a review of various methods an efficient U-D covariance factorization filtering algorithm is adopted for early orbit determination with limited data. It exhibits improved numerical characteristics particularly in ill conditioned problems. The early orbit determination algorithm considers data over a duration of 150 sec from a single tracking station at one sample per sec and computes the orbit sequentially. As an illustration a nominal 400 km circular orbit is considered. Keplerian model is used. Range, azimuth and elevation data combination results in best orbit estimate. The reduction in position error is very rapid. However, the velocity error reduces gradually. The algorithm converges for very large uncertainty in initial state.


Kalman Filter Orbit Determination Covariance Factorization Velocity Error Tracking Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Battin, R.H.: 1964,Astronautical Guidance, McGraw Hill, New York, pp. 338–339.Google Scholar
  2. Bierman, G.J.: 1977, Factorization Methods for Discrete Sequential Estimation, Academic Press, New York.zbMATHGoogle Scholar
  3. Bierman,G.J., and C.L.Thornton: 1977, ‘Numerical Comparison of Kalman Filter Algorithms Orbit Determination Case Study’, Automautica Google Scholar
  4. Bryson,A.E., and Y.C.Ho: 1969, Applied Optimal Control, Blaisdell, Waltham Mass.Google Scholar
  5. Garlson,N.A.: 1983, ‘Fast Triangular Formulation of the Square Root Filter’, AIAA Journal, 11, No.9, p. 1259.Google Scholar
  6. Chodas,P.: 1981, ‘Application of the Extended Kalman Filter to Several Formulations of Orbit Determination’, UTIAS Technical Note, No.224.Google Scholar
  7. Curkendal,D.W., and C.T. Leondes: 1973–74, ‘Sequential Filter Design for Precision Orbit Determination and Physical Constant Refinement’, Celes.Mech., vol. 8, p.481.CrossRefGoogle Scholar
  8. Deutsch,R.: 1963, Orbital dynamics of Space Vehicles, Prentice Hall.Google Scholar
  9. Escobal,P.R.: 1965, Methods of Orbit Determination, John Wiley and Sons, New York.Google Scholar
  10. Fitzgerald,R.J.: 1969, ‘Divergence of the Kalman Filter’, IEEE Automatic Control, vol.AC14, No.4, pp. 359–367.Google Scholar
  11. Fuchs,A.J.: 1981, ‘Present Status and Future Trends in Near Earth Satellite Orbit Determination’, Proc. Int. Sym. Space Craft Flight Dynamics, Darmstadt, FRG.Google Scholar
  12. Herrick,S.: 1972, Astrodynamics, Vol.2,Von Nostrand,Reinhold, London.Google Scholar
  13. Jazvinsky,A.H.: 1970, Stochastic Processes and Filtering Theory,Academic Press.Google Scholar
  14. Kalman,R.E.: 1960, ‘A New Approach to Linear Filtering and Prediction Problem’, Jour.Basic Engineering,vol.82D, pp. 35–45.Google Scholar
  15. Maybeck,P.S.: 1979, Stochastic Models Estimation and Control, vol.1, Academic Press, New York.Google Scholar
  16. Mayers,K.A.: 1973, ‘Filtering Theory Methods and Applications to the Orbit Determination Problem for Near Earth Satellites’, Applied Mech-anics Research Lab. ,The Univ. of Texas at Austin, AMRI.,1058.Google Scholar
  17. Schlee,F.H., et al. :1967, ‘Divergence in the Kalman Filter’, AIAA Jour., vol.5, No.5, pp. 1114–1120.Google Scholar
  18. Schmidt,S.F.: 1981, ‘The Kalman Filter its Recognition and Development for Aerospace Applications’, Jour, of Guidance, Control and Dynamics, vol.4, No.1, pp. 4–7.Google Scholar
  19. Shrivastava,S,K.: 1979, ‘Some factors influencing Accuracy of Orbit Determination’, Jour, of Aeronautical Society of India, vol.31, No.1–4, pp. 21–29.Google Scholar
  20. Sorenson,H.W.: 1970, ‘Least Squares Estimation from Gauss to Kalman’, IEEE Spectrum, pp. 63–68.Google Scholar
  21. Sorenson,H.W.: 1980, ‘Parameter Estimation’, Control and Systems Theory, vol. 9.Google Scholar
  22. Tapley,B.D.: 1973, ‘Statistical Orbit Determination Theory’, Recent Advances in Dynamical Astronomy, B.D. Tapley and V. Szebehely (eds.), D. Reidel Publishing Company, Dordrecht, Holland, pp. 396–425.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • D. Sita Rama Raju
    • 1
  • Ch. Sreehari Rao
    • 1
  • S. K. Shrivastava
    • 1
  1. 1.ISTRAC, SHAR CentreIndian Space Research OrganisationSriharikotaIndia

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