Polynomial extended Kalman filter

IEEE Transactions on Automatic Control

Volumn 50, Issue 12, 2005, Pages 2059-2064

  Germani, Alfredo ^a   Manes, Costanzo ^a   Palumbo, Pasquale ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b CNR   (Italy)

Author keywords

Extended Kalman filtering; Nonlinear stochastic systems; Polynomial filtering

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; POLYNOMIALS; STATE ESTIMATION; STOCHASTIC CONTROL SYSTEMS;

EXTENDED KALMAN FILTERING; NONLINEAR STOCHASTIC SYSTEMS; POLYNOMIAL FILTERING;

KALMAN FILTERING;

EID: 30344462326     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.860256     Document Type: Article

References (29)

1. D. L. Alspace and H. W. Sorenson, "Nonlinear Bayesian estimation using Gaussian sum approximation," IEEE Trans. Autom. Control, vol. AC-17, no. 4, pp. 439-448, Aug. 1972.
2. B. D. O. Anderson and J. B. Moore, Optimal Filtering. Upper Saddle. River, NJ: Prentice-Hall, 1979.
3. M. L. A. Netto, L. Gimeno, and M. J. Mendes, "On the optimal and suboptimal nonlinear filtering problem for discrete-time systems," IEEE Trans. Autom. Control, vol. AC-23, no. 6, pp. 1062-1067, Dec. 1978.
4. Z. Bai, "Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems," Appl. Numer. Math., vol. 43, pp. 9-44, 2002.
5. J. Baras, A. Bensoussan, and M. R. James, "Dynamic observers as asymptotic limits of recursive filters: Special cases," SIAM J. Appl. Math., vol. 48, pp. 1147-1158, 1993.
6. M. Bontayeb, H. Rafarlaky, and M. Darouach, "Covergence analysis of the extended Kalman filter used as an observer for nonlinear discrete-time systems," IEEE Trans. Autom. Control, vol. 42, no. 4, pp. 581-586, Apr. 1997.
7. C. Bruni, G. Di Pillo, and G. Koch, "Bilinear systems: An appealing class of nearly linear systems in theory and applications," IEEE Trans. Autom. Control, vol. AC-19, no. 4, pp. 334-348, Aug. 1974.
8. R. Bucy and P. Joseph, Filtering for Stochastic Processes With Applications to Guidance. New York: Wiley, 1968.
9. R. Bucy, "Linear and nonlinear filtering," Proc. IEEE, vol. 58, no. 6, Jun. 1970.
10. F. Carravetta, A. Germani, and M. Raimondi, "Polynomial filtering for linear discrete-time non-Gaussian systems," SIAM J. Control Optim., vol. 34, no. 5, pp. 1666-1690, 1996.
11. F. Carravetta, A. Germani, and M. Raimondi, "Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise," IEEE Trans. Autom. Control, vol. 42, no. 8, pp. 1106-1126, Aug. 1997.
12. A. Germani, C, Manes, and P. Palumbo, "Polynomial extended Kalman filtering for discrete-time nonlinear stochastic systems," in Proc. 42nd IEEE Conf. Decision and Control, vol. 1, Maui, HI, Dec. 2003, pp. 886-891.
13. C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications. New York: Springer-Verlag, 1987.
14. A. Gelb, Applied Optimal Estimation. Cambridge, MA: MIT Press, 1984.
15. G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.
16. K. Ito and K. Xiong, "Gaussian filters for nonlinear filtering problems," IEEE Trans. Autom. Control, vol. 45, no. 5, pp. 910-927, May 2000.
17. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic, 1970.
18. S. J. Julier and J. K. Uhlmann, "Unscented filtering and nonlinear estimation," Proc. IEEE, vol. 92, no. 3, pp. 401-422, Mar. 2004.
19. Y. Kleyman and I. Mochalov, "Identification of nonstationary systems," Autom. Rem. Control, vol. 55, pp. 149-163, 1994.
20. K. Kowalski and W. H. Steeb, Nonlinear Dynamical Systems and Carleman Linearization. Singapore: World Scientific, 1991.
21. L. Ljung, "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems," IEEE Trans. Autom. Control, vol. AC-24, no. 1, pp. 36-50, Jan. 1979.
22. K. Reif, S. Günther, E. Yaz, and R. Unbehauen, "Stochastic stability of the discrete-time extended Kalman filter," IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 714-728, Apr. 1999.
23. M. G. Safonov, Stability and Robustness of Multivariable Feedback Systems. Cambridge, MA: MIT Press, 1980.
24. M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, "A tutorial on particle filters for online nonlinear/non-Gaussian bayesian tracking," IEEE Trans. Signal Process., vol. 50, no. 2, pp. 174-188, Feb. 2002.
25. S. Sastry, Nonlinear Systems: Analysis, Stability and Control. New York: Springer-Verlag, 1999.
26. S. Svoronos, G. Stephanopoulos, and R. Aris, "Bilinear approximation of general nonlinear dynamic systems with linear inputs," Int. J. Control, vol. 31, no. 1, pp. 109-126, 1980.
27. J. T.-H. Lo, "Global bilinearization of systems with control appearing linearly," SIAM J. Control Optim., vol. 13, no. 4, pp. 879-885, 1975.
28. W. S. Wong and S. T. Yau, "The estimation algebra of nonlinear filtering systems," in Mathematical Control Theory, J. Baillieul and J. C. Willems, Eds. New York: Springer-Verlag, 1999, pp. 33-65.
29. N. van de Wouw, H. Nijmeijer, and D. H. van Campen, "Statistical bilinearization in stochastic nonlinear dynamics," in Proc. 2nd Int. Conf. on Control of Oscillations and Chaos, vol. 3, 2000, pp. 394-399.