Abstract
This paper is concerned with improving the attitude estimation accuracy by implementing an adaptive Gaussian sum filter where the a posteriori density function is approximated by a sum of Gaussian density functions. Compared to the traditional Gaussian sum filter, this adaptive approach utilizes the Fokker-Planck-Kolmogorov residual minimization to update the weights associated with different components of the Gaussian mixture model. Updating the weights provides an accurate approximation of the a posteriori density function and thus superior estimates. Simulation results show that updating the weights during the propagation stage not only provides better estimates between the observations but also provides superior estimator performance where the measurements are ambiguous.
Similar content being viewed by others
References
Wertz, J.R. Spacecraft Attitude Determination and Control, Dordrecht: Kluwer Academic Publishers, 1978.
Sidi, J.M. Spacecraft Dynamics and Control, Cambridge, UK: Cambridge University Press, 1997.
Gerald, L.M. “Three-Axis Attitude Determination,” The Journal of the Astronautical Sciences, Vol. 45, April–June 1997, pp. 195–204.
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. 70–77.
Mortari, D. “ESOQ: A Closed-Form Solution to the Wahba Problem,” The Journal of the Astronautical Sciences, Vol. 45, April–June 1997, pp. 817–826.
Mortari, D. “Second Estimator of The Optimal Quaternion,” Journal of Guidance, Control and Dynamics, Vol. 23, September–October 2000, pp. 885–888.
Lefferts, E. J., Markley, F.L., and Shuster, M.D. “Kaiman Filtering For Spacecraft Attitude Estimation,” Journal of Guidance, Control and Dynamics, Vol. 5, Sept.–Oct. 1982, pp. 417–492.
Bar-Itzhack, I. Y. “REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination,” Journal of Guidance, Control and Dynamics, Vol. 19, No. 5,1996, pp. 1034–1038.
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.
Cheng, Y. and Crassidis, J.L. “Particle Filtering for Sequential Spacecraft Attitude Estimation,” presented as paper AIAA-2004-5337 at the AIAA Guidance, Navigation, and Control Conference, Providence, RI, 2004.
Crassidis, J.L., Markley, F.L., and Cheng, Y. “A Survey of Nonlinear Attitude Estimation Methods,” Journal of Guidance, Control and Dynamics, Vol. 30, No. 1,2007, pp. 12–28.
Jazwinski, A. H. Stochastic Processes and Filtering Theory, Academic Press, 1970.
Anderson, B.D. and Moore, J.B. Optimal Filtering, Prentice-Hall, 1979.
Gelb, A. Applied Optimal Estimation, MIT Press, 1974.
Doucet, A., Freitas, N.d., and Gordon, N. Sequential Monte-Carlo Methods in Practice, Springer-Verlag, April 2001.
Iyengar, R. N. and Dash, P. K. “Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique,” Journal of Applied Mechanics, Vol. 45, 1978, pp. 393–399.
Roberts, J.B. and Spanos, P.D. Random Vibration and Statistical Linearization, Wiley, 1990.
Lefebvre, T., Bruyninckx, H., and Schutter, J.D. “Kaiman Filters of Non-Linear Systems: A Comparison of Performance,” International Journal of Control, Vol. 77, No. 7, 2004, pp. 639–653.
Lefebvre, T., Bruyninckx, H., and Schutter, J.D. “Comment on A New Method for the Nonlinear Transformations of Means and Covariances in Filters and Estimators,” IEEE Transactions on Automatic Control, Vol. 47, No. 8, 2002.
Ristic, B., Arulampalam, S., and Gordon, N. Beyond the Kaiman Filter: Particle Filters for Tracking Applications, Artech House, 2004.
Daum, F. and Huang, J. “Curse of Dimensionality and Particle Filters,” Proceedings of the 2003 IEEE Aerospace Conference, Vol. 4, March 8–15, 2003, pp. 1979–1993.
Risken, H. The Fokker-Planck Equation: Methods of Solution and Applications, Springer, 1989.
Daum, F.E. “Exact Finite Dimensional Nonlinear Filters,” IEEE Transactions on Automatic Control, July 1986.
Fuller, A.T. “Analysis of Nonlinear Stochastic Systems by Means of the Fokker-Planck Equation,” International Journal of Control, Vol. 9, 1969, p. 6.
Kumar, M., Singla, P., Chakravorty, S., and Junkins, J.L. “A Multi-Resolution Approach for Steady State Uncertainty Determination in Nonlinear Dynamical Systems,” Proceedings of the 38th Southeastern Symposium on System Theory, 2006.
Kumar, M., Singla, P., Chakravorty, S., and Junkins, J.L. “The Partition of Unity Finite Element Approach to the Stationary Fokker-Planck Equation,” Proceedings of the 2006 AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Keystone, CO, Aug. 21–24,2006.
Muscolino, G., Ricciardi, G., and Vasta, M. “Stationary and Non-Stationary Probability Density Function for Non-Linear Oscillators,” International Journal of Non-Linear Mechanics, Vol. 32,1997, pp. 1051–1064.
Paola, M. D. and Sofi, A. “Approximate Solution of the Fokker-Planck-Kolmogorov Equation,” Probabilistic Engineering Mechanics, Vol. 17, 2002, pp. 369–384.
Markley, F.L. “Attitude Filtering on SO(3),” presented as paper AAS-05-460 at the AAS Malcolm D. Shuster Astronautics Symposium, Grand Island, NY, June 2005.
Sorenson, H.W. and Alspach, D.L. “Recursive Bayesian Estimation using Gaussian Sums,” Automatica, Vol. 7, 1971, pp. 465–479.
Alspach, H. and Sorenson, D. “Nonlinear Bayesian Estimation using Gaussian Sum Approximations,” IEEE Transactions on Automatic Control, Vol. 17, No. 4, 1972, pp. 439–448.
Ito, K. and Xiong, K. “Gaussian Filters for Nonlinear Filtering Problems,” IEEE Transactions on Automatic Control, Vol. 45, No. 5, 2000, pp. 910–927.
Terejanu, G., Singla, P., Singh, T., and Scott, P.D. “A Novel Gaussian Sum Filter Method for Accurate Solution to Nonlinear Filtering Problem,” The 11th International Conference on Information Fusion, Cologne, Germany, June 2008.
Singla, P. and Singh, T. “A Gaussian function Network for Uncertainty Propagation through Nonlinear Dynamical System,” Proceedings of the 18th AAS/AIAA Spaceflight Mechanics Meeting, Galveston, TX, Jan. 27–31, 2008.
Terejanu, G., Singla, P., Singh, T., and Scott, P.D. “Uncertainty Propagation for Nonlinear Dynamical Systems using Gaussian Mixture Models,” Journal of Guidance, Control, and Dynamics, Vol. 31, 2008, pp. 1623–1633.
Singla, P., Griffith, T. D., and Junkins, J. L. “Attitude Determination and On-Orbit Autonomous Calibration of Star Tracker For GIFTS Mission,” Proceedings of the AAS/AIAA Space Flight Mechanics Meeting (K. T. Alfriend, B. Neta, K. Luu, and C. A. H. Walker, eds.), Advances in Aerospace Sciences, Vol. 112, 2002, pp. 19-38.
Shuster, M.D. “A Survey of Attitude Representations,” The Journal of the Astronautical Sciences, Vol. 41, October–December 1993, pp. 439–517.
Junkins, J. L. and Singla, P. “How Nonlinear Is It? A Tutorial on Nonlinearity of Orbit and Attitude Dynamics,” The Journal of Astronautical Sciences, Vol. 52, No. 1–2, 2004, pp. 7–60.
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented at the F. Landis Markley Astronautics Symposium, Cambridge, Maryland, June 29–July 2, 2008.
Rights and permissions
About this article
Cite this article
George, J., Terejanu, G. & Singla, P. Spacecraft Attitude Estimation Using Adaptive Gaussian Sum Filter. J of Astronaut Sci 57, 31–45 (2009). https://doi.org/10.1007/BF03321492
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321492