Approximation approach for nonlinear filtering problem with time dependent noises. II. Stable nonlinear filters
Kybernetika, Tome 33 (1997) no. 5, pp. 557-576
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Classification : 93C99, 93E11, 93E25
@article{KYB_1997_33_5_a6,
     author = {Hoang, S. and Baraille, R. and Talagrand, O. and Nguyen, T. L. and De Mey, P.},
     title = {Approximation approach for nonlinear filtering problem with time dependent noises. {II.} {Stable} nonlinear filters},
     journal = {Kybernetika},
     pages = {557--576},
     year = {1997},
     volume = {33},
     number = {5},
     mrnumber = {1603969},
     zbl = {0910.93078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1997_33_5_a6/}
}
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Hoang, S.; Baraille, R.; Talagrand, O.; Nguyen, T. L.; De Mey, P. Approximation approach for nonlinear filtering problem with time dependent noises. II. Stable nonlinear filters. Kybernetika, Tome 33 (1997) no. 5, pp. 557-576. http://geodesic.mathdoc.fr/item/KYB_1997_33_5_a6/

[1] R. Albert: Regression and the Moore-Penrose Pseudoinverse. Academic Press, New York 1972. | MR | Zbl

[2] A. Bryson, Ho-Yu-Chi: Applied Optimal Control. Ginn and Co., Waltham, Mass. 1969.

[3] P. D. Crutko: The Lyapunov Functions in Inverse Problems for Dynamical Controlled Systems. Scalar Models. Izv. Akad. Nauk SSSR Tekhn. Kibernet. (1983), No. 4.

[4] P. D. Crutko: The Lyapunov Functions in Inverse Problems for Dynamical Controlled Systems. Multidimensional models. Izv. Akad. Nauk SSSR Tekhn. Kibernet. (1984), No. 4.

[5] P. D. Crutko: Invesion of Direct Lyapunov Method in Control Problems for Dynamical Systems. Izv. Akad. Nauk SSSR Tekhn. Kibernet. (1989), No. 3.

[6] D. P. Dee: Simplification of the Kalman filter for meteorological data assimilation. Quart. J. Roy. Meteorol. Soc. 117 (1991), 365-384.

[7] R. J. Fitzgerald: Divergence of the Kalman filter. IEEE Trans. Automat. Control AC-16 (1971), 736-747.

[8] M. Ghil, P. Malanotte-Rizzoli: Data assimilation in meteorology and oceanography. Adv. in Geophysics 33 (1991), 141-266.

[9] R. E. Griffin, A. P. Sage: Sensitivity analysis of discrete filtering and smoothing algorithms. In: AIAA Guidance, Control and Flight Dynamics Conf., Pasadena, California 1988, Paper No. 68-824.

[10] H. Heffes: The effect of erroneous models on the Kalman filter response. IEEE Trans. Automat. Control AC-11 (1966), 541-543.

[11] H. S. Hoang P. De Mey, O. Talagrand: A simple algorithm of stochastic approximation type for system parameter and state estimation. In: 33rd IEEE CDC, Florida 1994, pp. 447-452.

[12] H. S. Hoang R. Baraille O. Talagrand P. De Mey, X. Carton: On the design of a stable adaptive filter. In: Proc. 35th IEEE CDC, Kobe 1996, Vol. 3, pp. 3543-3544.

[13] H. S. Hoang P. De Mey O. Talagrand, R. Baraille: A new reduced-order adaptive filter for high dimensional systems. In: Proc. of IFAC Internat. Symp. Adaptive Systems in Control and Signal Processing (Cs. Banyasz, ed.), Budapest 1995, pp. 153-158. Also: Automatica 33 (1997), 8, 1475-1498. | MR

[14] H. S. Hoang, T. L. Nguyen: Time-stable non-linear filters: Stochastic Lyapunov function approach. In: Recent Advances in Mathematical Theory of Systems and Control, Networks and Signal Processing (H. Kimura and S. Kodama, eds.), Mita Press, Tokyo 1992, pp. 653-658. | MR

[15] S. Hoang L. Nguyen R. Baraille, O. Talagrand: Approximation approach for nonlinear filtering problem with time dependent noises. Part I: Conditionally optimal filter in the minimum mean square sense. Kybernetika 33 (1997), 4, 409-425. | MR

[16] H. S. Hoang, O. Talagrand: On regularization approach to parameter estimation and application to design of stable filters. In: IFAC 12th World Congress, V-4, Sydney 1993, pp. 213-218.

[17] A. H. Jazwinski: Stochastic Processes and Filtering Theory. Academic Press, New York 1970. | Zbl

[18] R. E. Kalman, R. S. Bucy: New results in linear filtering and prediction theory. In: Trans. ASME, J. Basic Eng., 1961, 83D, pp. 95-108. | MR

[19] R. S. Liptser, A. N. Shiryaev: Statistics of Random Processes. Nauka, Moscow 1974. | MR

[20] L. Ljung, T. Sodestrom: Theory and Practice of Recursive Identification. Academic Press, New York 1983. | MR

[21] R. K. Mehra: On the identification of variances and adaptive Kalman filtering. IEEE Trans. Automat. Control AC-15 (1970), 175-184. | MR

[22] V. I. Meleshko, S. S. Sekt: Regularized estimates in problems with singular variance matrices. Automat. Remote Control 3 (1988), 293-297. | MR | Zbl

[23] T. L. Nguyen, H. S. Hoang: On solution of ill-posed optimal linear filtering problem with correlated noises. Automat. Remote Control 4 (1983), 1, 453-466. | MR

[24] V. S. Pugachev: Recursive estimation of variables and characteristics in the stochastic systems described by the difference equations. Dokl. Acad. Nauk USSR 243 (1976), 5. | MR

[25] S. Safonov, M. Athans: On stability theory. In: Proc. IEEE CDC, San Diego 1979. | MR | Zbl

[26] G. Sewell: The numerical Solution of Ordinary and Partial Differential Equations. Academic Press, New York 1988. | MR | Zbl

[27] L. M. Silverman: Discrete Riccati equations: Algorithms, asymptotic properties and system theory interpretation. In: Filtering and Stochastic Control in Dynamical Systems (C. T. Leondes, ed.), Mir, Moscow 1980.

[28] H. W. Sorenson: On the error behavior in linear minimum variance estimation problems. IEEE Trans. Automat. Control AC-12 (1967), 557-562.

[29] O. Talagrand, P. Courtier: Variational assimilation of meteorological observations with the Adjoint vorticity equations. I. Theory. Quart. J. Roy. Meteorol. Soc. 113 (1987), 1311-1328.

[30] J. Verron: Nudging satellite altimetry data into quasi-geostrophic models. J. Geophys. Research 97 (1992), 7479-7491.

[31] V. I. Zubov: On theory of analytic design of regulators. Automat. Remote Control (1963), No. 8.