Sparse gauss-hermite quadrature filter with application to spacecraft attitude estimation

Journal of Guidance, Control, and Dynamics

Volumn 34, Issue 2, 2011, Pages 367-379

  Jia, Bin ^a   Xin, Ming ^a   Cheng, Yang ^a  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN NETWORKS; GAUSSIAN DISTRIBUTION; NUMERICAL METHODS;

BAYESIAN ESTIMATION FRAMEWORK; COMPUTATIONALLY EFFICIENT; CUBATURE KALMAN FILTERS; GAUSS-HERMITE QUADRATURE; MULTIDIMENSIONAL NUMERICAL INTEGRATION; MULTIDIMENSIONAL PROBLEMS; SPACECRAFT ATTITUDE ESTIMATION; UNSCENTED KALMAN FILTER;

KALMAN FILTERS;

EID: 79952477215     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.52016     Document Type: Article

References (36)

1. 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. doi:10.2514/1.22452 (Pubitemid 46219868)
2. Cheng, Y., and Crassidis, J. L., "Particle Filtering for Attitude Estimation Using a Minimal Local-Error Representation," Journal of Guidance, Control, and Dynamics, Vol. 33, No. 4, 2010, pp. 1305-1310. doi:10.2514/1.47236
3. 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. doi:10.2514/2.5102
4. Jazwinski, A., Stochastic Processing and Filtering Theory, Academic Press, New York, 1970, pp. 93-347.
5. Gelb, A., Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974, pp. 182-202.
6. Julier, S., Uhlmann, J., and Durrant-Whyte, H. F., "A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators," IEEE Transactions on Automatic Control, Vol. 45, No. 3, 2000, pp. 477-482. doi:10.1109/9.847726
7. Julier, S. J., and Uhlmann, J. K., "Unscented Filtering and Nonlinear Estimation," Proceedings of the IEEE, Vol. 92, No. 3, 2004, pp. 401-422. doi:10.1109/JPROC.2003.823141 (Pubitemid 40890750)
8. Gordon, N. J., Salmond, D. J., and Smith, A. F. M., "Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation," IEE Proceedings. F, Communications, Radar, and Signal Processing, Vol. 140, No. 2, 1993, pp. 107-113. doi:10.1049/ip-f-2.1993.0015
9. Arulampalam, M. S., Maskell, S., Gordon, N., and Clapp, T., "ATutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking," IEEE Transactions on Signal Processing, Vol. 50, No. 2, 2002, pp. 174-185. doi:10.1109/78.978374 (Pubitemid 34291500)
10. 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. doi:10.2514/3.56190 (Pubitemid 13486954)
11. Shuster, M. D., "A Simple Kalman Filter and Smoother for Spacecraft Attitude," Journal of the Astronautical Sciences, Vol. 37, No. 1, 1989, pp. 89-106.
12. Psiaki, M. L., "Attitude-Determination Filtering via Extended Quaternion Estimation," Journal of Guidance, Control, and Dynamics, Vol. 23, No. 2, 2000, pp. 206-214. doi:10.2514/2.4540 (Pubitemid 30578276)
13. Oshman, Y., and Carmi, A., "Attitude Estimation from Vector Observations Using Genetic-Algorithm-Embedded Quaternion Particle Filter," Journal of Guidance, Control, and Dynamics, Vol. 29, No. 4, 2006, pp. 879-891. doi:10.2514/1.17951 (Pubitemid 44212621)
14. Carmi, A., and Oshman, Y., "Fast Particle Filtering for Attitude and Angular-Rate Estimation from Vector Observations," Journal of Guidance, Control, and Dynamics, Vol. 32, No. 1, 2009, pp. 70-78. doi:10.2514/1.36979
15. Ito, K., and Xiong, K., "Gaussian Filters for Nonlinear Filtering Problems," IEEE Transactions on Automatic Control, Vol. 45, No. 5, 2000, pp. 910-927. doi:10.1109/9.855552
16. Arasaratnam, I., Haykin, S., and Elliott, R. J., "Discrete-Time Nonlinear Filtering Algorithms Using Gauss-Hermite Quadrature," Proceedings of the IEEE, Vol. 95, No. 5, 2007, pp. 953-977. doi:10.1109/JPROC.2007.894705
17. Arasaratnam, I., and Haykin, S., "Cubature Kalman Filters," IEEE Transactions on Automatic Control, Vol. 54, No. 6, 2009, pp. 1254-1269. doi:10.1109/TAC.2009.2019800
18. Norgaard, M., Poulsen, N., and Ravn, O., "New Developments in State Estimation for Nonlinear Systems," Automatica, Vol. 36, No. 11, 2000, pp. 1627-1638. doi:10.1016/S0005-1098(00)00089-3
19. Hao, R. Z., Huang, J. X., and Li, L. Q., "Target Tracking Algorithm Based on Gauss-Hermite Quadrature in Passive Sensor Array," The 9th International Conference on Signal Processing, IEEE Publ., Piscataway, NJ, Oct. 2008, pp. 2628-2631.
20. Cui, N., Hong, L., and Layne, J. R., "A Comparison of Nonlinear Filtering Approaches with an Application to Ground Target Tracking," Signal Processing, Vol. 85, No. 8, 2005, pp. 1469-1492. doi:10.1016/j.sigpro.2005.01. 010 (Pubitemid 40762447)
21. Zoeter, O., and Heskes, T., "Gaussian Quadrature Based Expectation Propagation," Proceedings of Artificial Intelligence and Statistics, Barbados, Soc. for Artificial Intelligence and Statistics, NJ, Jan. 2005, pp. 445-452.
22. Davis, P. J., and Rabinowitz, P., Methods of Numerical Integration, 2nd ed., Academic Press, New York, 1984.
23. Julier, S. J., and Uhlmann, J. K., "Reduced Sigma Point Filters for the Propagation of Means and Covariances Through Nonlinear Transformations, " Proceedings of the American Control Conference, Vol. 2, Anchorage, AK, IEEE Publ., Piscataway, NJ, May 2002, pp. 887-892.
24. Julier, S. J., "The Spherical Simplex Unscented Transformation, " Proceedings of American Control Conference, Denver, CO, IEEE Publ., Piscataway, NJ, Jun. 2003, pp. 2430-2434.
25. Lozano, J. G. C., Carrillo, L. R. G., Dzul, A., and Lozano, R., "Spherical Simplex Sigma-Point Kalman Filters: A Comparison in the Inertial Navigation of a Terrestrial Vehicle," Proceedings of American Control Conference, Seattle, WA, IEEE Publ., Piscataway, NJ, Jun. 2008, pp. 3536-3541.
26. Li, W. C., Wei, P., and Xiao, X. C., "A Novel Simplex Unscented Transform and Filter," Proceedings of the International Symposium on Communications and Information Technologies, Sydney, Australia, IEEE Publ., Piscataway, NJ, 2007, pp. 926-931.
27. Levesque, J. F., "Second-Order Simplex Sigma Points for Nonlinear Estimation," AIAA Guidance, Navigation, and Control Conference, Keystone, CO, AIAA Paper 2006-6093, Aug. 2006.
28. Van Zandt, J. R., "A More Robust Unscented Transform," Proceedings of the SPIE, Vol. 4473, SPIE, Bellingham, WA, July 2001. doi:10.1117/12.492745 (Pubitemid 35152666)
29. Sun, F. M., Ma,Y. H., andWang, J. L., "Extended Symmetric Sampling Strategy for Unscented Kalman Filter," International Conference on Control, Automation and Systems Engineering, IEEE Publ., Piscataway, NJ, July 2009, pp. 383-386.
30. Zhang,W., Liu, M., and Zhao, Z. G., "Accuracy Analysis of Unscented Transformation of Several Sampling Strategies," 10th ACIS International Conference on Software Engineering, Artificial Intelligences, Networking and Parallel/Distributed Computing, IEEE Publ., Piscataway, NJ, May 2009, pp. 377-380.
31. Dunik, J., Simandl, M., Straka, O., and Kral, L., "Performance Analysis of Derivative-Free Filters," The 44th IEEE Conference on Decision and Control and 2005 European Control Conference, IEEE Publ., Piscataway, NJ, Dec. 2005, pp. 1941-1946.
32. Smolyak, S. A., "Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions," Soviet Mathematics -Doklady Vol. 4, 1963, pp. 240-243.
33. Gerstner, T., and Griebel, M., "Numerical Integration Using Sparse Grids," Numerical Algorithms, Vol. 18, Nos. 3-4, 1998, pp. 209-232. doi:10.1023/A:1019129717644
34. Florian, H., and Viktor,W., "Likelihood Approximation by Numerical Integration on Sparse Grids," Journal of Econometrics, Vol. 144, No. 1, 2008, pp. 62-80. doi:10.1016/j.jeconom.2007.12.004
35. Gerstner, T., and Griebel, M., "Dimension-Adaptive Tensor-Product Quadrature," Computing, Vol. 71, No. 1, 2003, pp. 65-87. doi:10.1007/s00607-003-0015-5
36. Crassidis, J. L., and Junkins, J. L., Optimal Estimation of Dynamic Systems, CRC Press, Boca Raton, FL, 2004, pp. 419-430.