Mean-square filter design for nonlinear polynomial systems with Poisson noise

Proceedings of the American Control Conference

Volumn , Issue , 2011, Pages 612-617

  Basin, Michael ^a   Maldonado, Juan J ^a  

^a UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; POISSON EQUATION; POLYNOMIALS; STOCHASTIC SYSTEMS;

EXPLICIT CLOSED FORM; FILTERING PROBLEMS; GENERAL EXPRESSION; LINEAR OBSERVATIONS; NONLINEAR POLYNOMIAL SYSTEMS; POLYNOMIAL FILTERS; POLYNOMIAL SYSTEMS; WHITE GAUSSIAN NOISE;

GAUSSIAN NOISE (ELECTRONIC);

EID: 80053146797     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2011.5991082     Document Type: Conference Paper

References (38)

1. H.J. Kushner, On differential equations satisfied by conditional probability densities of Markov processes, SIAM J. Control, vol.12, pp.106-119, 1964.
2. R.E. Kalman and R.S. Bucy, New results in linear filtering and prediction theory, ASME Trans., Part D (J. of Basic Engineering), vol.83, pp.95-108, 1961.
3. W.M. Wonham, Some applications of stochastic differential equations to nonlinear filtering, SIAM J. Control, vol.2, pp.347-369, 1965.
4. V.E. Benes, Exact finite-dimensional filters for certain diffusions with nonlinear drift, Stochastics, vol.5, pp.65-92, 1981. (Pubitemid 12424272)
5. S.S.T. Yau, Finite-dimensional filters with nonlinear drift I: A class of filters including both Kalman-Bucy and Benes filters, J. Math. Systems, Estimation, and Control, vol.4, pp.181-203, 1994.
6. ∞ filtering, Automatica 32, 1195-1199.
7. ∞ filtering, Systems and Control Letters 29, 233-240.
8. Shi, P. (1998) Filtering on sampled-data systems with parametric uncertainty, IEEE Transactions on Automatic Control, 43, 1022-1027.
9. Fleming, W.H., McEneaney, W.M. (2001) Robust limits of risk sensitive nonlinear filters, Mathematics of Control, Signals and Systems, 14, 109-142. (Pubitemid 32837903)
10. Yaz, E., Yaz, Y. (2001) State estimation of uncertain nonlinear systems with general criteria, Applied Mathematics Letters, 14, 605-610. (Pubitemid 33675381)
11. ∞ filtering for a class of nonlinear systems with state delay and parameter uncertainty, Int. J. Control, 75, 766-774.
12. Wang, Z., Lam, J., Liu, X. (2003) Nonlinear filtering for state delayed systems with Markovian switching, IEEE Transactions on Signal Processing, 51, 2321-2328.
13. M. Mahmoud and P. Shi, Robust Kalman filtering for continuous timelag systems with Markovian jump parameters, IEEE Trans. on Circuits and Systems, vol.50, pp.98-105, 2003.
14. ∞ filtering for uncertain discrete-time state-delayed systems, IEEE Transactions on Signal Processing, 52, 1631-1640.
15. ∞ filtering for nonlinear stochastic systems, IEEE Transactions on Signal Processing, 53, 589-598.
16. J. Sheng, T. Chen and S.L. Shah, Optimal filtering for multirate systems, IEEE Trans. on Circuits and Systems, vol.52, pp.228-232, 2005. (Pubitemid 40589997)
17. ∞-filtering for polytopic discrete-time systems, IEEE Transactions on Signal Processing, 53, 3183-3192.
18. Zhang, H., Basin, M.V., Skliar, M. (2007) Ito-Volterra optimal state estimation with continuous, multirate, randomly sampled, and delayed measurements, IEEE Transactions on Automatic Control, 52, 401-416.
19. ∞ estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control, 52, 2070-2084.
20. ∞ infinity filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 1268-1277.
21. ∞ infinity control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica, 45, 684-691.
22. Wei, G., Wang, Z., Shu, H. (2009) Robust filtering with stochastic nonlinearities and multiple missing measurements, Automatica, 45, 836-841.
23. ∞ infinity filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays, Automatica, 45, 1032-1037.
24. R.S. Liptser and A.N. Shiryayev, Theory of Martingales, Springer, 1989.
25. V.S. Pugachev and I.N. Sinitsyn, Stochastic Systems: Theory and Applications. World Scientific, 2001.
26. H. Lu, Z. Liang and D. Chen, A combined transformation of ordering SPECT sinograms for signal extraction from measurements with Poisson noise, SPIE Proc.,vol. 4322, pp. 1431-1438, 2001.
27. I. Kolmanovsky and T.L. Maizenberg, Optimal containment control for a class of stochastic systems perturbed by Poisson and Wiener processes, Proc. 2002 American Control Conf., pp. 322-327, 2002.
28. P. Hannequin and J. Mas, Statistical and heuristic image noise extraction (SHINE): A new method for processing Poisson noise in scintigraphic images, Phys. Med. Biol. vol. 47, pp. 4329-4344, 2002. (Pubitemid 36113414)
29. I. Kolmanovsky and T. Maizenberg, Optimal containment control for a class of stochastic systems perturbed by Poisson and Wiener processes, IEEE Trans. on Automatic Control, vol.47, no.12, pp. 1641-1645, 2002.
30. B. Zhang, M.J. Fadili, J.-L. Starck and S.W. Dige, Fast Poisson noise removal by biorthogonal haar domain hypothesis testing, Statistical Methodology, vol. 5, pp. 387-396, 2008.
31. F.X. Dupé, M.J. Fadili and J.-L. Starck, Image deconvolution under Poisson noise using sparse representations and proximal thresholding iteration, Proc. IEEE ICASSP - Int. Conf. on Acoustics, Speech, and Signal Processing, pp.761-764, 2008.
32. B. Zhang, M.J. Fadili and J.-L. Starck, Wavelets, ridgelets, and curvelets for Poisson noise removal, IEEE Trans. on Image Processing, vol.17, no.7, pp.1093-1108, 2008.
33. M.V. Basin, J. Perez and M. Skliar, Optimal filtering for polynomial system states with polynomial multiplicative noise, Int. J. Robust and Nonlinear Control, vol.16, pp.287-298, 2006.
34. M.V. Basin, New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems. Springer, 2008.
35. M.V. Basin, D. A. Calderon-Alvarez and M. Skliar, Optimal filtering for incompletely measured polynomial states over linear observations, Int. J. Adaptive Control and Signal Processing, vol.22, pp.482-494, 2008.
36. K.J. A&rinström, Introduction to Stochastic Control Theory, Academic Press, 1970.
37. A.H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970.
38. M. V. Basin, M. A. Alcorta-Garcia and D. Peña, Simulation and optimal filtering for linear systems with Poisson white noises, Dynamics of Continuous, Discrete and Impulsive Systems. Series B, vol.14, pp.221-231, 2007.