Attitude Filtering on SO(3)

F. Landis Markley1
1Guidance, Navigation and Control Systems Engineering Branch, NASA’s Goddard Space Flight Center, Greenbelt, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

CRASSIDIS, J. L. and JUNKINS, J. L. Optimal Estimation of Dynamic Systems, Chapman & Hall/ CRC, Boca Raton, FL, 2004, Chapters 2 and 5.

JAZWINSKI, A.H. Stochastic Processes and Filtering Theory, Academic Press, New York, 1970, Chapters 4–7.

SCHMIDT, S. F. “The Kalman Filter: Its Recognition and Development for Aerospace Applications,” Journal of Guidance and Control, Vol. 4, No. 1, 1981, pp. 4–7.

FARRELL, J. L. “Attitude Determination by Kalman Filtering,” Automatica, Vol. 6, 1970, pp. 419–430.

MURRELL, J.W. “Precision Attitude Determination for Multimission Spacecraft,” presented as paper AIAA-78-1248 at the AIAA Guidance and Control Conference, Palo Alto, CA, August 1978.

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, 1982, pp. 417–429.

MARKLEY, F. L. “Attitude Error Representations for Kalman Filtering,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 2, 2003, pp. 311–317.

STUELPNAGEL, J. “On the Parameterization of the Three-Dimensional Rotation Group,” SIAM Review, Vol. 6, No. 4, 1964, pp. 422–430.

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.

MARKLEY, F. L. “Attitude Estimation or Quaternion Estimation?” The Journal of the Astronautical Sciences, Vol. 52, No. 1/2, 2004, pp. 221–238.

JULIER, S. J., UHLMANN, J. K., and DURRANT-WHYTE, H. F. “A New Approach for Filtering Nonlinear Systems,” Proceedings of the American Control Conference, Seattle, WA, 1995, pp. 1628–1632.

WAN, E. A. and VAN DER MERWE, R. “The Unscented Kalman Filter,” Kalman Filtering and Neural Networks, ed. by S. S. Haykin, John Wiley & Sons, New York, 2001, Chapter 7.

NØRGAARD, M, POULSEN, N. K., and RAVN, O. “New Developments in State Estimation for Nonlinear Systems,” Automatica, Vol. 36, 2000, pp. 1627–1638.

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.

DOUCET, A., DE FREITAS, N., and GORDON, N., editors Sequential Monte Carlo Methods in Practice, Statistics for Engineering and Information Science, Springer, New York, 2001, Chapter 1.

ARULAMPALAM, M. S., MASKELL, S., GORDON, N., and CLAPP, T. “A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking,” IEEE Transactions on Signal Processing, Vol. 50, No. 2, 2002, pp. 174–188.

CRASSIDIS, J. L. and CHENG, Y. “Particle Filtering for Sequential Spacecraft Attitude Estimation,” presented as paper AIAA-2004-5337 at the AIAA Guidance and Control Conference, Providence, RI, August 2004.

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.

DAUM, F. E. “New Exact Nonlinear Filters,” Bayesian Analysis of Time Series and Dynamical Models, ed. by J. C. Spall, Marcel Dekker, New York, 1988, Chapter 8.

GARDINER, C.W. Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 3rd ed., Springer, Berlin, Heidelberg, New York, 2004, pp. 96–101.

LO, J. T.-H. “Optimal Estimation for the Satellite Attitude Using Star Tracker Measurements,” Automatica, Vol. 22, No. 4, 1986, pp. 477–482.

LO, J. T.-H. and ESHELMAN, L. R. “Exponential Fourier Densities on SO(3) and Optimal Estimation and Detection for Rotational Processes,” SIAM Journal on Applied Mathematics, Vol. 36, No. 1, 1979, pp. 73–82.

MARKLEY, F. L. “Attitude Filtering on SO(3),” The AAS Malcolm D. Shuster Astronautics Symposium, Advances in the Astronautical Sciences, Vol. 122, ed. by John L. Crassidis, F. Landis Markley, John L. Junkins, and Kathleen C. Howello, San Diego, CA, Univelt, Inc. 2006, pp. 149–174.

NACHBIN, L. The Haar Integral, D. van Nostrand Company, Inc., Princeton, 1965.

SHUSTER, M.D. “Maximum Likelihood Estimation of Spacecraft Attitude,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, 1989, pp. 79–88.

SHUSTER, M.D. “Uniform Attitude Probability Distributions,” The Journal of the Astronautical Sciences, Vol. 51, No. 4, 2003, pp. 451–475.

SHUSTER, M.D. “A Simple Kalman Filter and Smoother for Spacecraft Attitude,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, 1990, pp. 89–106.

SHUSTER, M.D. “Kalman Filtering of Spacecraft Attitude and the QUEST Model,” The Journal of the Astronautical Sciences, Vol. 38, No. 3, 1989, pp. 377–393.

PETER, F. and WEYL, H. “Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe,” Mathematische Annalen, Vol. 97, 1927, pp. 737–755.

TALMAN, J.D. Special Functions: A Group Theoretical Approach, Based on Lectures by Eugene P. Wigner, W. A. Benjamin, New York, 1968, Chapters 7 and 9.

GROSS, K. I. “On the Evolution of Noncommutative Harmonic Analysis,” American Mathematical Monthly, Vol. 85, 1978, pp. 525–548.

BIEDENHARN, L. C. and LOUCK, J.D. Angular Momentum in Quantum Physics, Vol. 8 of Encyclopedia of Mathematics and its Applications, Addison-Wesley, Reading, MA, 1981, Chapter 3.

MARKLEY, F. L. and MORTARI, D. “Quaternion Attitude Estimation Using Vector Observations,” The Journal of the Astronautical Sciences, Vol. 28, No. 2/3, 2000, pp. 359–380.

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.

HORN, R.A. and JOHNSON, C. R. Matrix Analysis, Cambridge University Press, Cambridge, 1985, pp. 411–420, 18, 20.

MARKLEY, F. L. “Attitude Determination and Parameter Estimation Using Vector Observations: Theory,” The Journal of the Astronautical Sciences, Vol. 37, No. 1, 1989, pp. 41–58.

MARKLEY, F. L. “Attitude Determination and Parameter Estimation Using Vector Observations: Application,” The Journal of the Astronautical Sciences, Vol. 39, No. 3, 1991, pp. 367–381.

PSIAKI, M. “Attitude-Determination Filtering via Extended Quaternion Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 2, 2000, pp. 206–214.

CRASSIDIS, J. L. and MARKLEY, F. L. “New Algorithm for Attitude Determination Using Global Positioning System Signals,” Journal of Guidance, Control, and Dynamics, Vol. 20, No. 5, 1997, pp. 891–896.

ARNOLD, L. Stochastic Differential Equations: Theory and Practice, Wiley-Interscience, New York, 1974, pp. 163–175.

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.

ANDREWS, S. F. and BILANOW, S. “Recent Flight Results of the TRMM Kalman Filter,” presented as paper AIAA-2002-5047 at the AIAA Guidance and Control Conference, Monterey, CA, August 5–8, 2002.

PLETT, M. “Magnetic Field Models,” Spacecraft Attitude Determination and Control, ed. by J. R. Wertz, D. Reidel, Dordrecht, Holland, 1978, pp. 782, 783.

SEDLAK, J. and HASHMALL, J. “Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise,” Flight Mechanics Symposium 1997, NASA Conference Publication 3345, Greenbelt, MD, 1997, pp. 83–87.