Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Battin, R.H.: 1964,Astronautical Guidance, McGraw Hill, New York, pp. 338–339.
Bierman, G.J.: 1977, Factorization Methods for Discrete Sequential Estimation, Academic Press, New York.
Bierman,G.J., and C.L.Thornton: 1977, ‘Numerical Comparison of Kalman Filter Algorithms Orbit Determination Case Study’, Automautica
Bryson,A.E., and Y.C.Ho: 1969, Applied Optimal Control, Blaisdell, Waltham Mass.
Garlson,N.A.: 1983, ‘Fast Triangular Formulation of the Square Root Filter’, AIAA Journal, 11, No.9, p. 1259.
Chodas,P.: 1981, ‘Application of the Extended Kalman Filter to Several Formulations of Orbit Determination’, UTIAS Technical Note, No.224.
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.
Deutsch,R.: 1963, Orbital dynamics of Space Vehicles, Prentice Hall.
Escobal,P.R.: 1965, Methods of Orbit Determination, John Wiley and Sons, New York.
Fitzgerald,R.J.: 1969, ‘Divergence of the Kalman Filter’, IEEE Automatic Control, vol.AC14, No.4, pp. 359–367.
Fuchs,A.J.: 1981, ‘Present Status and Future Trends in Near Earth Satellite Orbit Determination’, Proc. Int. Sym. Space Craft Flight Dynamics, Darmstadt, FRG.
Herrick,S.: 1972, Astrodynamics, Vol.2,Von Nostrand,Reinhold, London.
Jazvinsky,A.H.: 1970, Stochastic Processes and Filtering Theory,Academic Press.
Kalman,R.E.: 1960, ‘A New Approach to Linear Filtering and Prediction Problem’, Jour.Basic Engineering,vol.82D, pp. 35–45.
Maybeck,P.S.: 1979, Stochastic Models Estimation and Control, vol.1, Academic Press, New York.
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.
Schlee,F.H., et al. :1967, ‘Divergence in the Kalman Filter’, AIAA Jour., vol.5, No.5, pp. 1114–1120.
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.
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.
Sorenson,H.W.: 1970, ‘Least Squares Estimation from Gauss to Kalman’, IEEE Spectrum, pp. 63–68.
Sorenson,H.W.: 1980, ‘Parameter Estimation’, Control and Systems Theory, vol. 9.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 D. Reidel Publishing Company
About this paper
Cite this paper
Raju, D.S.R., Rao, C.S., Shrivastava, S.K. (1986). Early Orbit Determination Using U-D Covariance Propagation Filter. In: Bhatnagar, K.B. (eds) Space Dynamics and Celestial Mechanics. Astrophysics and Space Science Library, vol 127. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4732-0_29
Download citation
DOI: https://doi.org/10.1007/978-94-009-4732-0_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8603-5
Online ISBN: 978-94-009-4732-0
eBook Packages: Springer Book Archive