Abstract
The general problem of determining the attitude deterministically, that is, directly without the optimization of a cost function, from measurements of arc lengths and directions is examined. While there is no continuous degeneracy for the solutions to this problem, because effectively three data are given, nonetheless, the attitude solution still has generally a discrete degeneracy which can be removed only by the addition of further data. The only case escaping the discrete degeneracy has an over-determined solution. Specific algorithms are developed for all cases, and the nature of the degeneracy is explored in detail.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
WERTZ, J. R. (ed.) Spacecraft Attitude Determination and Control, Kluwer Academic Publishers, Dordrecht, 1978.
BLACK, H. D. “A Passive System for Determining the Attitude of a Satellite,” AIAA Journal, Vol. 2, 1964, pp. 1350–1351.
SHUSTER, M. D. and OH, S. D. “Three-Axis Attitude Determination from Vector Observations,” Journal of Guidance and Control, Vol. 4, No. 1, January–February 1981, pp. 70–77.
SHUSTER, M. D. “In Quest of Better Attitudes,” Advances in the Astronautical Sciences, Vol. 108, December 2001, pp. 2089–2117.
MARKLEY, F. L. and MORTARI, D. “Quaternion Attitude Estimation Using Vector Observations,” The Journal of the Astronautical Sciences, Vol. 48, Nos. 2 and 3, April–September 2000, pp. 359–380.
SHUSTER, M. D. “A Survey of Attitude Representations,” The Journal of the Astronautical Sciences, Vol. 41, No. 4, October–December 1993, pp. 439–517.
WERTZ, J. R. (ed.) op. cit., Chapter 7.
SHUSTER, M. D. “Spacecraft Attitude Determination and Control,” in Pisacane, V. L. and Moore, R. C. (eds.) Fundamentals of Space Systems, Oxford University Press, New York and London, 1994.
SHUSTER, M. D. “Efficient Algorithms for Spin-Axis Attitude Estimation,” The Journal of the Astronautical Sciences, Vol. 31, No. 2, April–June 1983, pp. 237–249.
SHUSTER, M. D. “Maximum Likelihood Estimation of Spacecraft Attitude,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, January–March 1989, pp. 79–88.
SHUSTER, M. D. “A Broad Look at Deterministic Three-Axis, Attitude Determination,” presented as paper AIAA 2000-4239 at the AIAA/AAS Astrodynamics Specialists Conference, Denver, Colorado, August 14–17, 2000.
DAVENPORT, P.B. “Rotations about Nonorthogonal Axes,” AIAA Journal, Vol. 11, No. 6, June 1973, pp. 853–857.
SHUSTER, M. D. and MARKLEY, F. L. “Generalization of the Euler Angles,” The Journal of the Astronautical Sciences, Vol. 51, No. 2, April–June 2003, pp. 124–132.
SHUSTER, M. D. “The TRIAD Algorithm as Maximum Likelihood Estimator,” submitted to The Journal of the Astronautical Sciences.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sinister, M.D. Deterministic Three-Axis Attitude Determination. J of Astronaut Sci 52, 405–419 (2004). https://doi.org/10.1007/BF03546371
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03546371