Skip to main content
SpringerLink
Log in

The quest for better attitudes

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

This article is adapted from my Brouwer lecture of February 2001 [1]. It has been shortened by about one quarter and updated. Given the occasion (in 2001) I had thought it inappropriate to give a talk in my usual style, which is rich in equations and mathematical derivation. Instead, I attempted to give a talk rich in perspective and personal anecdotes (and maybe a few equations). Since the original lecture, my appreciation of the subject matter has grown and some addenda and corrigenda have become necessary.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. SHUSTER, M. D. “In Quest of Better Attitudes” (Dirk Brouwer Lecture), presented as paper No. AAS-01-250 at the 11th AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, California, February 11-14; 2001; reprinted in Advances in the Astronautical Sciences, Vol. 108, December 2001, pp. 2089-2117.

    Google Scholar 

  2. SHUSTER, M. D. “Approximate Algorithms for Fast Optimal Attitude Computation,” Paper No. 78–1249, Proceedings, AIAA Guidance and Control Conference, Palo Alto, California, August 1978, pp. 88–95.

    Google Scholar 

  3. 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.

    Article  MATH  Google Scholar 

  4. WERTZ, J. R. (ed.) Spacecraft Attitude Determination and Control, Springer, New York and Berlin, 1978.

    Google Scholar 

  5. BLACK, H. D. “A Passive System for Determining the Attitude of a Satellite,” AIAA Journal, Vol. 2, July 1964, pp. 1350–1351.

    Article  Google Scholar 

  6. SHUSTER, M. D. “A Survey of Attitude Representations,” The Journal of the Astronautical Sciences, Vol. 41, No. 4, October–December 1993, pp. 439–517.

    MathSciNet  Google Scholar 

  7. SORENSON, H. Parameter Estimation, Marcel Dekker, New York, 1980.

    MATH  Google Scholar 

  8. LERNER, G. M., HUANG, W. H., and SHUSTER, M. D. “Investigation of the AEM-A/HCMM Attitude Control System Performance,” presented as paper No. AAS-77-116 at the AAS/AIAA Astrodynamics Conference, Grand Teton National Park, Wyoming, September 1977.

    Google Scholar 

  9. POTEMRA, T. A., MOBLEY, F. F., and ECKARD, F. L. (eds.) The Johns Hopkins University APL Technical Digest—Special Issue on Magsat, Vol. 1, No. 3, 1980, pp. 162–248.

    Google Scholar 

  10. SHUSTER, M. D. “Spacecraft Attitude Determination and Control,” Chapter 5 in V. L. Pisacane and R. C. Moore, Fundamentals of Space Systems, Oxford University Press, New York and Oxford, 1994, pp. 245–336; second edition (with W. Dellinger): 2005, pp. 236-325.

    Google Scholar 

  11. WAHBA, G. “Problem 65-1: A Least Squares Estimate of Spacecraft Attitude,” SIAM Review, Vol. 7, No. 3, July 1965, p. 409.

    Article  Google Scholar 

  12. 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.

    Google Scholar 

  13. FALLON, L. III, HARROP, I. H., and STURCH, C. R. “Ground Attitude Determination and Gyro Calibration Procedures for the HEAO Missions,” Proceedings, AIAA 17th Aerospace Sciences Meeting, New Orleans, Louisiana, January 1979.

    Google Scholar 

  14. KEAT, J. “Analysis of Least Squares Attitude Determination Routine DOAOP,” Computer Sciences Corporation, CSC/TM-77/6034, February 1977.

    Google Scholar 

  15. DAVENPORT, P. R. “Attitude Determination and Sensor Alignment via Weighted Least Squares Affine Transformations,” NASA X-514-71-312, November 1965.

    Google Scholar 

  16. DAVENPORT, P. R. “A Vector Approach to the Algebra of Rotations with Applications,” NASA TN-D-4696, August 1968.

    Google Scholar 

  17. DIRAC, P.A.M. Principles of Quantum Mechanics, 4th ed., Oxford University Press, Oxford, 1958.

    MATH  Google Scholar 

  18. SHUSTER, M. D. “QUEST, a Longa História de um Algoritmo Rápido,” (in Portuguese) Plenary Talk, Primeiro Simpósio de Tecnologia Aeroespacial, São José dos Campos (SP), Brazil, August 1990; Instituto Nacional de Pesquisas Espaciais, São José dos Campos (SP), Brazil, NTI-002/91-DMC, December 1991.

    Google Scholar 

  19. SHUSTER, M. D. “Algorithms for Determining Optimal Attitude Solutions,” Computer Sciences Corporation, CSC/TM-78/6056, 1978.

    Google Scholar 

  20. SHUSTER, M. D. and FREESLAND, D. C. “The Statistics of TASTE and the Inflight Estimation of Sensor Precision,” Paper 56, Proceedings, Flight Mechanics Symposium 2005, NASA Goddard Space Flight Center, Greenbelt, Maryland, October 18–20, 2005.

    Google Scholar 

  21. MURRELL, J.W. “Precision Attitude Determination for Multimission Spacecraft,” Paper AIAA 78-1248, Proceedings, AIAA Guidance and Control Conference, Palo Alto, California, August 1978, pp. 70–87.

    Google Scholar 

  22. LEFFERTS, E. J., MARKLEY, F. L., and SHUSTER, M. D. “Kalman Filtering for Spacecraft Attitude Estimation,” Journal of Guidance, Control and Dynamics, Vol. 5, No. 5, September–October 1982, pp. 417–429.

    Article  Google Scholar 

  23. CHENG, Y. and SHUSTER, M. D. “QUEST and The Anti-QUEST: Good and Evil Attitude Estimation,” The Journal of the Astronautical Sciences, Vol. 53, No. 3, July–September 2005, pp. 337–351.

    Google Scholar 

  24. VAROTTO, S. E. C., ORLANDO, V., and LOPES, R.V. F. “Um procedimento para determinação da atitude de satélites artificiais utilizando técnicas de estimação ótima estática e dinâmica,” Atas, Congresso Brasileiro de Automática, Belo Horizonte, 1986, pp. 946–951.

    Google Scholar 

  25. FISHER, H. L., SHUSTER, M. D., and STRIKWERDA, T. E. “Attitude Determination for the Star-Tracker Mission,” paper No. AAS-89-365, AAS/AIAA Astrodynamics Specialists Conference, Stowe, Vermont, August 7–-10, 1989; Advances in the Astronautical Sciences, Vol. 71, 1990, pp. 138–150.

    Google Scholar 

  26. SHUSTER, M. D. “Kalman Filtering of Spacecraft Attitude and the QUEST Model,” The Journal of the Astronautical Sciences, Vol. 38, No. 3, July–September 1990, pp. 377–393; Erratum: Vol. 51, No. 3, July–September 2003, p. 359.

    Google Scholar 

  27. JAZWINSKI, A. H. Stochastic Processes and Filtering Theory, Academic Press, New York and Orlando, 1970.

    MATH  Google Scholar 

  28. SHUSTER, M. D., CHITRE, D. K., and NIEBUR, D. P. “Inflight Estimation of Spacecraft Attitude-Sensor Accuracy and Alignments,” Journal of Guidance, Control and Dynamics, Vol. 5, No. 4, July–August 1982, pp. 339–343.

    Article  Google Scholar 

  29. SHUSTER, M. D., PITONE, D. S., and BIERMAN, G. J. “Batch Estimation of Spacecraft Sensor Alignments, I. Relative Alignment Estimation,” The Journal of the Astronautical Sciences, Vol. 39, No. 4, October–December 1991, pp. 519–546.

    Google Scholar 

  30. SHUSTER, M. D. and PITONE, D. S. “Batch Estimation of Spacecraft Sensor Alignments, II. Absolute Alignment Estimation,” The Journal of the Astronautical Sciences, Vol. 39, No. 4, October–December 1991, pp. 547–571.

    Google Scholar 

  31. 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.

    Google Scholar 

  32. SHUSTER, M. D. “A Simple Kalman Filter and Smoother for Spacecraft Attitude,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, January–March 1989, pp. 89–106.

    Google Scholar 

  33. SEDLAK, J. and CHU, D. “Kalman Filter Estimation of Attitude and Gyro Bias with the QUEST Observation Model,” Paper AAS-93-297, AAS/GSFC International Symposium on Space Flight Dynamics, NASA Goddard Space Flight Center, April 26–30, 1993; Advances in the Astronautical Sciences, Vol. 84, 1993, pp. 683–696.

    Google Scholar 

  34. MARKLEY, F. L. “Attitude Determination Using Vector Observations and the Singular Value Decomposition,” The Journal of the Astronautical Sciences, Vol. 36, No. 3, July–September 1988, pp. 245–258.

    Google Scholar 

  35. MARKLEY, F. L. “Attitude Determination Using Vector Observations: a Fast Optimal Matrix Algorithm,” The Journal of the Astronautical Sciences, Vol. 41, No. 2, April–June 1993, pp. 261–280.

    MathSciNet  Google Scholar 

  36. MORTARI, D. “Second Estimator for the Optimal Quaternion,” Journal of Guidance, Control and Dynamics, Vol. 23, No. 4, September–October 2000, pp. 885–888.

    Article  Google Scholar 

  37. BRUCCOLERI, C. and MORTARI, D. “MRAD: Modified Rodrigues Vector Attitude Determination,” The Journal of the Astronautical Sciences, Vol. 54, Nos. 3 and 4, July–December 2006, pp. 383–390.

    Article  MathSciNet  Google Scholar 

  38. CHENG, Y. and SHUSTER, M. D. “Robustness and Accuracy of the QUEST Algorithm,” presented as paper AAS-07-102 at the AAS/AIAA 17th Space Flight Mechanics Meeting, Sedona, Arizona, January 28–February 2, 2007; Advances in the Astronautical Sciences, Vol. 127, 2007, pp. 41-61.

    Google Scholar 

  39. CHENG, Y. and SHUSTER, M. D. “The Speed of Attitude Estimation,” presented as paper AAS-07-105 at the AAS/AIAA 17th Space Flight Mechanics Meeting, Sedona, Arizona, January 28–February 2, 2007; Advances in the Astronautical Sciences, Vol. 127, 2007, pp. 101-116.

    Google Scholar 

  40. SHUSTER, M. D. and NATANSON, G.A. “Quaternion Computation from a Geometric Point of View,” The Journal of the Astronautical Sciences, Vol. 41, No. 4, October–December 1993, pp. 545–556.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Acme Spacecraft Company, 13017 Wisteria Drive, Box 328, Germantown, MD, 20874, USA

    Malcolm D. Shuster (Director of Research)

Authors
  1. Malcolm D. Shuster
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Malcolm D. Shuster.

Additional information

This article is dedicated also to the memory of Roger D. Werking (1941–2006), who was a strong force behind the development of QUEST.

For Paul Davenport, who showed the way

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shuster, M.D. The quest for better attitudes. J of Astronaut Sci 54, 657–683 (2006). https://doi.org/10.1007/BF03256511

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03256511

Keywords

Search

Navigation