Dirac mixture approximation of multivariate Gaussian densities

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 3851-3858

  Hanebeck, Uwe D ^a   Huber, Marco F ^a   Klumpp, Vesa ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

MIXTURES; NONLINEAR DYNAMICAL SYSTEMS;

CONTINUOUS DOMAIN; CUMULATIVE DISTRIBUTION; DETERMINISTIC APPROXIMATION; DIRAC DISTRIBUTION; DISTANCE MEASURE; NOISY MEASUREMENTS; OPTIMAL APPROXIMATION; SYSTEMATIC METHOD;

GAUSSIAN DISTRIBUTION;

EID: 77950798678     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400649     Document Type: Conference Paper

References (14)

1. S. J. Julier and J. K. Uhlmann, "A New Extension of the Kalman Filter to Nonlinear Systems," in International Symposium on Aerospace/Defence Sensing, Simulation and Control, 1997.
2. D. Tenne and T. Singh, "The Higher Order Unscented Filter," in Proceedings of the American Control Conference, June 2003, pp. 2441-2446.
3. M. F. Huber and U. D. Hanebeck, "Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation," in Proceedings of the 17th IFAC World Congress (IFAC), Seoul, Korea, Jul. 2008.
4. J. H. Kotecha and P. M. Djurić, "Gaussian Particle Filtering," IEEE Transactions on Signal Processing, vol.51, no.10, pp. 2592-2601, 2003.
5. K. Ito and K. Xiong, "Gaussian Filters for Nonlinear Filtering Problems," IEEE Transactions on Automatic Control, vol.45, no.5, pp. 910-927, May 2000.
6. O. C. Schrempf, D. Brunn, and U. D. Hanebeck, "Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering," in Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006), San Diego, California, Dec. 2006.
7. U. D. Hanebeck and O. C. Schrempf, "Greedy Algorithms for Dirac Mixture Approximation of Arbitrary Probability Density Functions," in Proceedings of the 2007 IEEE Conference on Decision and Control (CDC 2007), New Orleans, Louisiana, Dec. 2007, pp. 3065-3071.
8. U. D. Hanebeck and V. Klumpp, "Localized Cumulative Distributions and a Multivariate Generalization of the Cramér-von Mises Distance," in Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), Seoul, Republic of Korea, Aug. 2008, pp. 33-39.
9. D. D. Boos, "Minimum Distance Estimators for Location and Goodness of Fit," Journal of the American Statistical Association, vol.76, no.375, pp. 663-670, 1981.
10. R. H. Byrd, P. Lu, and J. Nocedal, "A Limited Memory Algorithm for Bound Constrained Optimization," SIAM Journal on Scientific and Statistical Computing, vol.16, no.5, pp. 1190-1208, 1995.
11. D. Guo and X. Wang, "Quasi-Monte Carlo Filtering in Nonlinear Dynamic Systems," IEEE Transactions on Signal Processing, vol.54, pp. 2087-2098, 2006.
12. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992.
13. J. Hartinger and R. Kainhofer, "Non-uniform Low-discrepancy Sequence Generation and Integration of Singular Integrands," in Monte Carlo and Quasi-Monte Carlo Methods 2004, H. Niederreiter and D. Talay, Eds. Springer, 2006.
14. G. Pagès and J. Printems, "Optimal Quadratic Quantization for Numerics: The Gaussian Case," Monte Carlo Methods and Applications, vol.9, no.2, pp. 135-166, 2003.