Constraint in Attitude Estimation Part I: Constrained Estimation
Tóm tắt
A complete and careful foundation is presented for maximum-likelihood attitude estimation and the calculation of measurement sensitivity matrices with the intent of revealing heretofore undisclosed pitfalls associated with unconstrained quaternion estimation. Efficient formulas are developed for computing the measurement sensitivity matrix for any attitude representation for which an efficient formula for the inverse kinematic equation is known. In particular, it is shown that the measurement sensitivity matrix for the quaternion is ambiguous and may take on a wide range of values. Hence, estimates of a quaternion which do not take correct account of the norm constraint will be physically meaningless. It is shown also that within Maximum Likelihood Estimation the form of the Wahba cost function for attitude estimation is incorrect when the attitude constraint is relaxed. A simple physical example is presented for quaternion estimation from noise-free vector measurements which fails when the norm constraint on the quaternion is relaxed. Part I of this work provides the basis for more detailed investigations of unconstrained attitude estimation in Part II [1].
Tài liệu tham khảo
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.
SHUSTER, M. D. “The Quaternion in the Kaiman Filter,” Paper No. AAS-93–62, Proceedings, AAS/AIAA Astrodynamics Specialists Conference, Victoria, British Columbia, Canada, August 1993; printed as “The Quaternion in the Kaiman Filter,” Advances in the Astronautical Sciences, Vol. 85, pp. 25–37, 1993.
SHUSTER, M. D. “A Survey of Attitude Representations,” The Journal of the Astronautical Sciences, Vol. 41, No. 4, pp. 439–517, October–December 1993.
SORENSON, H. W. Parameter Estimation, Marcel Dekker, New York, 1980.
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.
FALLON, L. III and RIGTERINK, P. V. “Introduction to Estimation Theory,” in WERTZ, J. R. (ed.), Spacecraft Attitude Determination and Control, Kluwer Academic, Dordrecht, 1978, pp. 447–459.
SHUSTER, M. D., PITONE, D. S. and BIERMAN, G. J. “Batch Estimation of Spacecraft Sensor Alignments,” The Journal of the Astronautical Sciences, Vol. 39, No. 4, October–December 1991, Part I: pp. 519–546, Part II: pp. 547–571.
SHUSTER, M. D. “Kaiman Filtering of Spacecraft Attitude and the QUEST Model,” The Journal of the Astronautical Sciences Vol. 38, No. 3, July–September, 1990, pp. 377–393.
SHUSTER, M. D. “Erratum: Kaiman Filtering of Spacecraft Attitude and the QUEST Model,” The Journal of the Astronautical Sciences, Vol. 51, No. 3, July–September 2003.
MARKLEY, F. L. “Attitude Error Representations for Kaiman Filtering,” to appear, Journal of Guidance, Control and Dynamics.
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, September– October 1982, pp. 417–429.
BAR-ITZHACK, I. Y. and FEGLEY, K. A. “Orthogonalization Techniques of a Direction Cosine Matrix,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-5, September 1969, pp. 798–804.
BAR-ITZHACK, I. Y. “Iterative Optimal Orthogonalization of the Strapdown Matrix,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-11, January 1975, pp. 30–37.
BAR-ITZHACK, I. Y., MEYER, J., and FUHRMANN, P. A. “Strapdown Matrix Orthogonalization: the Dual Iterative Algorithm,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-12, January 1976, pp. 32–37.
BAR-ITZHACK, I. Y. and MEYER, J. “On the Convergence of Iterative Orthogonalization Processes,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-12, March 1976, pp. 146–151.
MEYER, J. and BAR-ITZHACK, I. Y. “Practical Comparison of Iterative Matrix Orthogonalization Algorithms,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-13, May 1977, pp. 230–235.
BROUCKE, R. A. “Equations of Motion of a Rotating Rigid Body,” Journal of Guidance, Control and Dynamics, Vol. 13, 1990, pp. 1150–1152.
SHUSTER, M. D. “Man, Like These Attitudes Are Totally Random!” Advances in the Astronautical Sciences, Vol. 108, December 2001, Part I: pp. 383–396, Part II: pp. 397–408.
SHUSTER, M. D. “Uniform Attitude Probability Distributions,” to appear, The Journal of the Astronautical Sciences, Vol. 51, No. 4, October–December 2003.
SHUSTER, M. D. and OH, S. D. “Three-Axis Attitude Determination from Vector Observations,” Journal of Guidance, Control and Dynamics, Vol. 4, No. 1, Jan.–Feb. 1981 pp. 70–77.
WAHBA, G. “A Least-Squares Estimate of Satellite Attitude,” Problem 65-1, SIAM Review, Vol. 7, No. 3, July 1965, p. 409.