Fourier-Hermite Kalman filter

IEEE Transactions on Automatic Control

Volumn 57, Issue 6, 2012, Pages 1511-1515

  Sarmavuori, Juha ^a   Särkkä, Simo ^b  

^a NOKIA SIEMENS NETWORKS   (Finland)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Extended Kalman filtering (EKF); Fourier Hermite series; nonlinear KF; statistical linearization

Indexed keywords

EXTENDED KALMAN FILTERING; FIRST ORDER; FOURIER-HERMITE SERIES; GAUSSIAN FILTERS; NONLINEAR FUNCTIONS; NONLINEAR KF; STATISTICAL LINEARIZATION;

EXTENDED KALMAN FILTERS;

FOURIER SERIES;

EID: 84861722884     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2174667     Document Type: Article

References (26)

1. R. E. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME, J. Basic Eng., vol. 82, pp. 35-45, Mar. 1960.
2. J. L. Maryak, J. C. Spall, and B. D. Heydon, "Use of the Kalman filter for inference in state-space models with unknown noise distribution," IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 87-90, Jan. 2004.
3. R. L. Stratonovich, Conditional Markov Processes and Their Application to the Theory of Optimal Control. New York: American Elsevier Publishing Co., 1968.
4. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic Press, 1970.
5. A. Gelb, Ed., Applied Optimal Estimation. Cambridge, MA: The MIT Press, 1974.
6. S. J. Julier, J. K. Uhlmann, and H. F. Durrant-Whyte, "A new method for the nonlinear transformation of means and covariances in filters and estimators," IEEE Trans. Autom. Control, vol. 45, no. 3, pp. 477-482, Mar. 2000.
7. K. Ito and K. Xiong, "Gaussian filters for nonlinear filtering problems," IEEE Trans. Autom. Control, vol. 45, no. 5, pp. 910-927, May 2000.
8. Y.Wu,D. Hu, M.Wu, and X. Hu, "A numerical-integration perspective on Gaussian filters," IEEE Trans. Signal Processing, vol. 54, no. 8, pp. 2910-2921, Aug. 2006. (Pubitemid 44131746)
9. I. Arasaratnam and S. Haykin, "Cubature Kalman filters," IEEE Trans. Autom. Control, vol. 54, no. 6, pp. 1254-1269, Jun. 2009.
10. R. van der Merwe, "Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models," Ph.D. dissertation, OGI School Sci. Eng., Oregon Health & Sci. Univ., Portland, OR, 2004.
11. T. Lefebvre, H. Bruyninckx, and J. D. Schutter, "Comment on 'a new method for the nonlinear transformation of means and covariances in filters and estimators'," IEEE Trans. Autom. Control, vol. 47, no. 8, pp. 1406-1409, Aug. 2002.
12. T. Lefebvre, H. Bruyninckx, and J. D. Schutter, "Kalman filters for nonlinear systems: A comparison of performance," Int. J. Control, vol. 77, 7, pp. 639-653, 2004.
13. R. van der Merwe and E. Wan, "Sigma-point Kalman filters for probabilistic inference in dynamic state-space models," in Proc. Workshop Adv. Machine Learning, 2003, [CD ROM].
14. S. Lototsky, R. Mikulevicius, and B. Rozovskii, "Nonlinear filtering revisited: A spectral approach," SIAM J. Control Optim., vol. 35, pp. 435-461, 1997. (Pubitemid 127577128)
15. R. Mikulevicius and B. L. Rozovskii, "Fourier-Hermite expansions for nonlinear filtering," Theory Probab. Appl., vol. 44, pp. 606-612, 2000.
16. S. V. Lototsky, "Chaos approach to nonlinear filtering," in The Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovskii, Eds. London, U.K.: Oxford Univ. Press, 2011, pp. 231-264.
17. H. Singer, "Generalized Gauss-Hermite filtering," AStA Adv. Stat. Anal., vol. 92, no. 2, pp. 179-195, 2008.
18. H. Singer, "Moment equations and Hermite expansion for nonlinear stochastic differential equations with application to stock price models," Comput. Stat., vol. 21, 3, pp. 385-397, 2006. (Pubitemid 44876291)
19. S. Challa, Y. Bar-Shalom, and V. Krishnamurthy, "Nonlinear filtering via generalized edgeworth series and Gauss-Hermite quadrature," IEEE Trans. Signal Processing, vol. 48, no. 6, pp. 1816-1820, Jun. 2000.
20. P. Maybeck, Stochastic Models, Estimation and Control. New York: Academic Press, 1982, vol. 2.
21. A. Gelb and W. V. Vander, Multiple-Input Describing Functions and Nonlinear System Design. New York: McGraw Hill, 1968.
22. Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation. New York: Wiley Interscience, 2001.
23. W. Luo, "Wiener chaos Expansion and Numerical Solutions of Stochastic Partial Differential Equations," Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2006.
24. J. P. Boyd, Chebyshev and Fourier Spectral Methods. New York: Dover, 2000.
25. P. Malliavin, Stochastic Analysis. New York: Springer, 1997.
26. P. I. Kuznetsov, R. L. Stratonovich, and V. I. Tikhonov, "Quasi-moment functions in the theory of random processes," Theory Prob. Appl., vol. 1, pp. 80-97, 1960.