Adaptive gaussian sum filters for space surveillance

IEEE Transactions on Automatic Control

Volumn 56, Issue 8, 2011, Pages 1777-1790

  Horwood, Joshua T ^a   Poore, Aubrey B ^a  

^a NUMERICA CORPORATION   (United States)

Author keywords

Adaptive Gaussian sum filter; covariance consistency; Gaussian mixture; metrics; space surveillance; Uncertainty consistency

Indexed keywords

COVARIANCE CONSISTENCY; GAUSSIAN MIXTURE; GAUSSIAN SUM FILTER; METRICS; UNCERTAINTY CONSISTENCY;

CLUSTERING ALGORITHMS; MONITORING; NONLINEAR CONTROL SYSTEMS; SPACE SURVEILLANCE; UNCERTAINTY ANALYSIS;

GAUSSIAN DISTRIBUTION;

EID: 80051510190     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2142610     Document Type: Article

References (22)

1. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Dover, 1970.
2. S. J. Julier, J. K. Uhlmann, and H. F. Durant-Whyte, "A new method for the nonlinear transformation of means and covariances in filters and estimators," IEEE Trans. Autom. Control, vol. 55, no. 3, pp. 477-482, Mar. 2000.
3. S. J. Julier and J. K. Uhlmann, "Unscented filtering and nonlinear estimation," Proc. IEEE, vol. 92, no. 3, pp. 401-422, Mar. 2004. (Pubitemid 40890750)
4. S. Särkkä, "On unscented Kalman filtering for state estimation of continuous-time nonlinear systems," IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1631-1641, Sep. 2007. (Pubitemid 47456073)
5. B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications. Boston, MA: Artech House, 2004.
6. D. Alspach and H. Sorenson, "Nonlinear Bayesian estimation using Gaussian sum approximations," IEEE Trans. Autom. Control, vol. T-AC 17, no. 4, pp. 439-448, Aug. 1972.
7. O. Montenbruck and E. Gill, Satellite Orbits: Models, Methods, and Applications. Berlin, Germany: Springer, 2000.
8. P. McCullagh, Tensor Methods in Statistics. London, U.K.: Chapman and Hall, 1987.
9. A. Genz and B. D. Keister, "Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight," J. Comput. Appl. Math., vol. 71, pp. 299-309, 1996. (Pubitemid 126380866)
10. K. Ito and K. Xiong, "Gaussian filters for nonlinear filtering problems," IEEE Trans. Autom. Control, vol. 45, no. 5, pp. 910-927, May 2000.
11. W. I. Tam, K. N. Plataniotis, and D. Hatzinakos, "An adaptive Gaussian sum algorithm for radar tracking," Signal Process., vol. 77, pp. 85-104, 1999.
12. W. I. Tam, "Tracking Filters for Radar Systems,"Master's Thesis, University of Toronto, Toronto, ON, , 1997.
13. Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation. New York: Wiley, 2001.
14. R. Fletcher, Practical Methods of Optimization. New York: Wiley, 1991.
15. D. A. Vallado, Fundamentals of Astrodynamics and Applications. New York: Springer, 2007.
16. G. Terejanu, P. Singla, T. Singh, and P. D. Scott, "Uncertainty propagation for nonlinear dynamic systems using Gaussian mixture models," J. Guid. Control Dyn., vol. 31, no. 6, pp. 1623-1633, 2008.
17. R. Van Der Merwe and E. A. Wan, "The square-root unscented Kalman filter for state and parameter estimation," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process (ICASSP), 2001, vol. 6, pp. 3461-3464. (Pubitemid 32838365)
18. J. P. Royston, "Some techniques for assessing multivariate normality based on the Shapiro-Wilk W," Appl. Statist., vol. 32, no. 2, pp. 121-133, 1983. (Pubitemid 14641387)
19. K. V. Mardia, "Measures of multivariate skewness and kurtosis with applications," Biometrika, vol. 57, no. 3, pp. 519-530, 1970.
20. P. J. Olver, Classical Invariant Theory. Cambridge, MA: Cambridge Univ. Press, 1999.
21. R. A. Broucke and P. J. Cefola, "On the equinoctial orbit elements," Celest. Mech., vol. 5, pp. 303-310, 1972.
22. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1970.