Abstract
This paper is organized around three themes that have interested me over my career: covariance analysis, constrained estimation, and angular momentum. Both analytical and numerical approaches to covariance analysis are discussed. The section on constraints begins with general considerations arising from the nature of the rotation group before moving to Wahba’s Problem and quaternion Kaiman filters. The discussion of angular momentum includes its use in attitude determination and control as well as in the detection and diagnosis of spacecraft anomalies. Relevant illustrative examples are included.
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Markley, F. L. “Humble Problems,” presented as paper AAS 06-238 at the 2006 AAS/AIAA Space Flight Mechanics Meeting, San Diego, CA, 2006; Advances in the Astronautical Sciences, Vol. 124, Part II, 2006, pp. 2205–2222.
Crassidis, J.L. and Junkins, J.L. Optimal Estimation of Dynamic Systems, Chapman & Hall/CRC, Boca Raton, FL, 2004, Chapter 5.
Farrenkopf, R. L. “Analytic Steady-State Accuracy Solutions for Two Common Spacecraft Attitude Estimators,” Journal of Guidance and Control, Vol. 1, No. 4, 1978, pp. 282–284.
Murrell, J. W. “Precision Attitude Determination for Multimission Spacecraft,” presented as paper AIAA 78-1248 at the 1978 AIAA Guidance and Control Conference, Palo Alto, CA, August 1978, pp. 70–87.
Lefferts, E. J., Markley, F. L., and Shuster, M. D. “Kaiman Filtering for Spacecraft Attitude Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 5, No. 5, 1982, pp. 417–429.
Fallon, III, L. “Gyroscope Models,” in Spacecraft Attitude Determination and Control, J. R. Wertz, ed., D. Reidel, Dordrecht, Holland, 1978, pp. 266–270.
Markley, F. L. and Reynolds, R. R. “Analytic Steady-State Accuracy of a Spacecraft Attitude Estimator,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 6, 2000, pp. 1065–1067.
Markley, F. L., Seidewitz, E., and Deutschmann, J. “Attitude Determination Error Analysis: General Model and Specific Application,” Mécanique Spatiale: Space Dynamics, Cepadues-Editions, Toulouse, France, 1989, pp. 251–266.
Markley, F.L. and Carpenter, J.R. “Generalized Linear Covariance Analysis,” The Journal of the Astronautical Sciences, Vol. 57, Nos. 1 & 2, 2009. (this issue)
Bauer, F. H., Femiano, M. D., and Mosier, G. E. “Attitude Control System Conceptual Design for the X-Ray Timing Explorer,” presented as paper AIAA 92-4334 at the 1992 AIAA Guidance, Navigation, and Control Conference, Hilton Head Island, SC, August 1992, pp. 236–250.
Sedlak, J. and Hashmall, J. “Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise,” Proceedings of the 1997 Flight Mechanics Symposium, NASA Conference Publication 3345, Greenbelt, MD, 1976, pp. 83–87.
Andrews, S.F. and Bilanow, S. “Recent Flight Results of the TRMM Kaiman Filter,“ presented as paper AIAA 2002-5047 at the 2002 AIA A Guidance, Navigation, and Control Conference, Monterey, CA, August 2002.
Markley, F. L. and Bar-Itzhack, I. Y. “Unconstrained Optimal Transformation Matrix,” IEEE Transactions on Aerospace and Electronic System, Vol. 34, No. 1, 1998, pp. 338–340.
Markley, F.L. “Equations of Motion,” in Spacecraft Attitude Determination and Control, J. R. Wertz, ed., D. Reidel, Dordrecht, Holland, 1978, pp. 510–523.
Shuster, M.D. “A Survey of Attitude Representations,” The Journal of the Astronautical Sciences, Vol. 41, No. 4,1993, pp. 439–517.
Markley, F. L. “Parameterization of the Attitude,” in Spacecraft Attitude Determination and Control, J. R. Wertz, ed., D. Reidel, Dordrecht, Holland, 1978, pp. 410–420.
Stuelpnagel, J. “On the Parameterization of the Three-Dimensional Rotation Group,” SIAM Review, Vol. 6, No. 4, 1964, pp. 422–430.
Wahba, G. “A Least Squares Estimate of Spacecraft Attitude,” SIAM Review, Vol. 7, No. 3, 1965, p. 409.
Horn, R. A. and Johnson, C. R. Matrix Analysis, Cambridge, UK, Cambridge University Press, 1985.
Golub, G.H. and Van Loan, C.F. Matrix Computations, Baltimore, MD, The Johns Hopkins University Press, 1983.
Lerner, G.M. “Three-Axis Attitude Determination,” in Spacecraft Attitude Determination and Control, J.R. Wertz, ed., D. Reidel, Dordrecht, Holland, 1978, pp. 420–428.
Shuster, M.D. and Oh, S.D. “Three-Axis Attitude Determination from Vector Observations,” Journal of Guidance and Control, Vol. 4, No. 1, 1981, pp. 10–11.
Markley, F.L. “Attitude Determination Using Vector Observations and the Singular Value Decomposition,” The Journal of the Astronautical Sciences, Vol. 36, No. 3,1988, pp. 245–258.
Markley, F.L. “Attitude Determination Using Vector Observations: a Fast Optimal Matrix Algorithm,” The Journal of the Astronautical Sciences, Vol. 41, No. 2, 1993, pp. 261–280.
Mortari, D. “ESOQ: A Closed-Form Solution to the Wahba Problem,” The Journal of the Astronautical Sciences, Vol. 45, No. 2, 1997, pp. 195–204.
Mortari, D. “Second Estimator of the Optimal Quaternion,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 5, 2000, pp. 885–888.
Markley, F. L. and Mortari, D. “Quaternion Attitude Estimation Using Vector Observations,” The Journal of the Astronautical Sciences, Vol. 48, No. 2/3, 2000, pp. 359–380.
Markley, F.L. “Attitude Estimation or Quaternion Estimation?” The Journal of the Astronautical Sciences, Vol. 52, No. 1/2, 2004, pp. 221–238.
Oshman, Y. and Carmi, A. “Attitude Estimation from Vector Observations Using a Genetic-Algorithm-Embedded Quaternion Particle Filter,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 4, 2006, pp. 879–891.
Shuster, M.D. “Maximum Likelihood Estimate of Spacecraft Attitude,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, 1989, pp. 79–88.
Markley, F.L. “Attitude Filtering on SO(3),” The Journal of the Astronautical Sciences, Vol. 54, No. 3/4, 2006, pp. 391–413.
Shuster, M.D. “Constraint in Attitude Estimation Part I: Constrained Estimation,” The Journal of the Astronautical Sciences, Vol. 51, No. 1, 2003, pp. 51–74.
Shuster, M.D. “Constraint in Attitude Estimation Part II: Unconstrained Estimation,” The Journal of the Astronautical Sciences, Vol. 51, No. 1, 2003, pp. 75–101.
Pittelkau, M. E. “An Analysis of the Quaternion Attitude Determination Filter,” The Journal of the Astronautical Sciences, Vol. 51, No. 1, 2003, pp. 103–120.
Markley, F. L. “Attitude Error Representations for Kaiman Filtering,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 2, 2003, pp. 311–317.
Zanetti, R., Majji, M., Bishop, R.H., and Mortari, D. “Norm Constrained Kaiman Filtering,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 5, 2009, pp. 1458–1465.
Calise, A. J. “Enforcing an Algebraic Constraint in Extended Kaiman Filter Design,” presented as paper AIAA 2007-6515 at the 2007 AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, August 2007.
Carmi, A. and Oshman, Y. “Asymptotic Behavior of the Estimation Error Covariance of Quaternion Estimators,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 6, 2008, pp. 1665–1676.
Crassidis, J. L. and Markley, F. L. “Unscented Filtering for Spacecraft Attitude Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4, 2003, pp. 536–542.
Reynolds, R.G. “Asymptotically Optimal Attitude Filtering with Guaranteed Convergence,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 1, 2008, pp. 114–122.
Morton, H.S., Jr., JUNKINS, J.L., and BLANTON, J.N. “Analytical Solutions for Euler Parameters,” Celestial Mechanics, Vol. 10, 1974, pp. 287–301.
Kraige, L. G. and JUNKINS, J. L. “Perturbation Formulations for Satellite Attitude Dynamics,” Celestial Mechanics, Vol. 13, 1976, pp. 39–64.
Markley, F.L. “New Dynamic Variables for Momentum-Bias Spacecraft,” The Journal of the Astronautical Sciences, Vol. 41, No. 4, 1993, pp. 557–567.
Sedlak, J.E. “Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation and Results,” Proceedings of the 2005 Flight Mechanics Symposium, Goddard Space Flight Center, Greenbelt, MD, NASA Conference Publication NASA/CP-2005-212789, October 2005.
Markley, F.L. and Sedlak, J.E. “Kaiman Filter for Spinning Spacecraft Attitude Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 6, 2008, pp. 1750–1760.
Kuznik, F. “Satellite Saviors,” AIR & SPACE/Smithsonian, Vol. 6, No. 3, 1991, pp. 66–70.
Flatley, T. W., Forden, J.K., Henretty, D. A., Lightsey, E. G., and Markley, F.L. “Onboard Attitude Determination and Control Algorithms for SAMPEX,” Proceedings of the 1990 Flight Mechanics/ Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, MD, NASA Conference Publication 3102, May 1990, pp. 379–398.
Mccullough, J.D., Flatley, T. W., Henretty, D. A., Markley, F.L., and San, J.K. “Testing of the Onboard Attitude Determination and Control Algorithms for SAMPEX,” Proceedings of the 1992 Flight Mechanics/ Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, MD, May 1992, NASA Conference Publication 3186, pp. 55–68.
Markley, F.L., Flatley, T.W. and Leoutsakos, T. “SAMPEX Special Pointing Mode,” Proceedings of the 1995 Flight Mechanics/Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, MD, May 1995, NASA Conference Publication 3299, pp. 201–215.
Tsai, D.C., Markley, F.L., and Watson, T.P. “SAMPEX Recovery to Spin Stabilized Mode,” SpaceOps 2008, Heidelberg, Germany, May 12–16, 2008.
Markley, F. L. and Nelson, J. D. “Zero-Gyro Safemode Controller for the Hubble Space Telescope,” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 4, 1994, pp. 815–822.
Markley, F. L., Kennedy, K. R., Nelson, J.D., and Moy, E. W. “Autonomous Spacecraft Gyro Failure Detection Based on Conservation of Angular Momentum,” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 6, 1994, pp. 1385–1
Markley, F.L., Andrews, S.F., O’Donnell, J.R., Jr., and Ward, D.K. “Attitude Control System of the Wilkinson Microwave Anisotropy Probe,” Journal of Guidance, Control, and Dynamics, Vol. 28, No. 3, 2005, pp. 385–397.
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Presented at the F. Landis Markley Astronautics Symposium, Cambridge, Maryland, June 29–July 2, 2008.
This paper is dedicated to Eugene J. Lefferts.
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Markley, F.L. Lessons Learned. J of Astronaut Sci 57, 3–29 (2009). https://doi.org/10.1007/BF03321491
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DOI: https://doi.org/10.1007/BF03321491