Density approximation based on dirac mixtures with regard to nonlinear estimation and filtering

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 1709-1714

  Schrempf, Oliver C ^a   Brunn, Dietrich ^a   Hanebeck, Uwe D ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GAUSSIAN DISTRIBUTION; NONLINEAR SYSTEMS; OPTIMIZATION; PROBABILITY DENSITY FUNCTION;

DENSITY APPROXIMATION; DIRAC MIXTURES; OPTIMALITY;

NONLINEAR FILTERING;

EID: 39649083575     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.376759     Document Type: Conference Paper

References (15)

1. D. L. Alspach and H. W. Sorenson, "Nonlinear Bayesian Estimation Using Gaussian Sum Approximation," IEEE Transactions on Automatic Control, vol. AC-17, no. 4, pp. 439-448, 1972.
2. S. Challa, Y. Bar-Shalom, and V Krishnamurthy, "Nonlinear Filtering via Generalized Edgeworth Series and Gauss-Hermite Quadrature," IEEE Transactions on Signal Processing, vol. 48, no. 6, pp. 1816-1820, 2000.
3. D. Brigo, B. Hanzon, and F. LeGland, "A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter," IEEE Transactions on Automatic Control, vol. 42, no. 2, pp. 247-252, 1998.
4. N. Oudjane and S. Rubenthaler, "Stability and Uniform Particle Approximation of Nonlinear Filters in Case of non-Ergodic Signal," Prépublication, Laboratoire de Probabilités et Modèles Aléatoires, Université de Paris VI, Tech. Rep. PMA786, January 2003. [Online]. Available: http://www.proba.jussieu.fr/mathdoc/textes/PMA-786. pdf
5. S. Arulampalam, S. Maskell, N. Gordon, and T Clapp, "A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking," IEEE Transactions of Signal Processing, vol. 50, no. 2, pp. 174-188, 2002.
6. E. Bølviken, P J. Acklam, N. Christophersen, and J.-M. Størdal, "Monte Carlo Filters for Non-Linear State Estimation," Automatica, vol. 37, pp. 177-183, 2001.
7. A. Doucet, S. Godsill, and C. Andrieu, "On Sequential Monte Carlo Sampling Methods for Bayesian Filtering," Statistics and Computing, vol. 10, no. 3, pp. 197-208, 2000.
8. E. Bølviken and G. Storvik, "Deterministic and Stochastic Particle Filters in State Space Models," in Sequential Monte Carlo Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon, Eds. Springer Series of "Statistics for Engineering and Information Science", 2001.
9. S. Kullback and R. A. Leibler, "On Information and Sufficiency," Annals of Mathematical Statistics, vol. 22, no. 2, pp. 79-86, 1951.
10. M. D. Weber, L. M. Leemis, and R. K. Kincaid, "Minimum Kolmogorov-Smirnov Test Statistic Parameter Estimates," Journal of Statistical Computation and Simulation, vol. 76, no. 3, pp. 196-206, 2006.
11. W. H. Press, B. P Flannery, S. A. Teukolsky, and W. T Vetterling, "Kolmogorov-Smirnov Test," in Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 1992, pp. 623-628.
12. D. A. Darling, "The Kolmogorov-Smirnov, Cramér-von Mises Tests," The Annals of Mathematical Statistics, vol. 28, no. 4, pp. 823-83, 1957.
13. 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.
14. O. C. Schrempf, D. Brunn, and U. D. Hanebeck, "Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramérvon Mises Distance," in Proceedings of the International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Heidelberg, Germany, September 2006, pp. 512-517.
15. U. D. Hanebeck and O. Feiermann, "Progressive Bayesian Estimation for Nonlinear Discrete-Time Systems: The Filter Step for Scalar Measurements and Multidimensional States," in Proceedings of the 2003 IEEE Conference on Decision and Control (CDC'03), Maui, Hawaii, 2003, pp. 5366-5371.