| Title:
|
Approximation approach for nonlinear filtering problem with time dependent noises. I. Conditionally optimal filter in the minimum mean square sense (English) |
| Author:
|
Hoang, S. |
| Author:
|
Nguyen, T. L. |
| Author:
|
Baraille, R. |
| Author:
|
Talagrand, O. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
409-425 |
| . |
| Category:
|
math |
| . |
| MSC:
|
93C10 |
| MSC:
|
93C55 |
| MSC:
|
93C99 |
| MSC:
|
93E11 |
| MSC:
|
93E25 |
| idZBL:
|
Zbl 0910.93077 |
| idMR:
|
MR1471386 |
| . |
| Date available:
|
2009-09-24T19:10:14Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124888 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/125394 |
| . |
| Reference:
|
[1] A. Albert: Regression and the Moore-Penrose Pseudoinverse.Academic Press, New York 1972. Zbl 0253.62030, MR 0331659 |
| Reference:
|
[2] D. L. Alspach, H. W. Sorenson: Nonlinear Bayesian estimation using Gaussian sum approximations.IEEE Trans. Automat. Control AC-17 (1972), 4, 439-448. Zbl 0264.93023 |
| Reference:
|
[3] B. D. O. Anderson, J. B. Moore: Optimal Filtering.Prentice-Hall, Englewood Cliffs, NJ 1979. Zbl 0688.93058 |
| Reference:
|
[4] G. P. Box, G. M. Jenkins: Time Series Analysis.Holden-Day, San Francisco 1970. Zbl 0249.62009 |
| Reference:
|
[5] R. S. Bucy, al: An Engineer's Guide to Building Nonlinear Filters.F. J. Seiler Research Lab., Project 7904-00-37, May 1972. |
| Reference:
|
[6] G. Chavent: On the uniqueness of local minima for general abstract nonlinear least squares problems.Inverse Problems 4 (1988), 417-433. Zbl 0658.65055, MR 0954901 |
| Reference:
|
[7] G. C. Goodwin, K. S. Sin: Adaptive Filtering and Control.Prentice-Hall, Englewood Cliffs, NJ 1984. |
| Reference:
|
[8] S. Hoang R. Baraille O. Talagrand L. Nguyen, P. DeMey: Approximation approach for nonlinear filtering problem with time dependent noises. Part II: Stable nonlinear filters.Kybernetika 33 (1997), No. 5 (to appear). MR 1603969 |
| Reference:
|
[9] S. Hoang P. DeMey O. Talagrand, R. Baraille: A new reduced-order adaptive filter for state estimation in high dimensional systems.In: Proc. IFAC Internat. Symp. Adaptive Systems in Control and Signal Processings (Cs. Banyasz, ed.), Budapest 1995, pp. 153-158, to appear in Automatica 33 (1997), No. 8. MR 1470055 |
| Reference:
|
[10] P. J. Huber: Robust Statistics.Wiley, New York 1981. Zbl 0536.62025, MR 0606374 |
| Reference:
|
[11] A. H. Jazwinski: Stochastic Processes and Filtering Theory.Academic Press, New York 1970. Zbl 0203.50101 |
| Reference:
|
[12] V. V. Kondrachev, A. A. Kocheshkov: Filtering and analysis of linear sample-data control systems with nonparametric specification of correlated noises.Avtomat. i Telemekh. (1985), No. 6, 67-76. (In Russian.) |
| Reference:
|
[13] A. Kowalski, D. Szynal: Filtering in discrete-time systems with state and observation noises correlated on a finite time interval.IEEE Trans. Automat. Control AC-31 (1986), 4, 381-384. Zbl 0592.93062 |
| Reference:
|
[14] I. E. Kazakov, X. V. Malchikov: Approximate design of Pugachev's filters of specified complexity.Automat. Remote Control 42 (1981), 1309. |
| Reference:
|
[15] F. L. Lewis: Optimal Estimation.Wiley, New York 1986. Zbl 0665.93065, MR 0832681 |
| Reference:
|
[16] C. J. Masreliez, D. Martin: Robust Bayesian estimation for the linear model and robustifying the Kalman filter.IEEE Trans. Automat. Control AC-22 (1977), 3, 361-371. Zbl 0354.93054, MR 0453124 |
| Reference:
|
[17] T. L. Nguyen, S. Hoang: On optimal filtering with correlated noises and singular correlation matrices.Automat. Remote Control 43 (1982), 5 (2), 660-669. MR 0687118 |
| Reference:
|
[18] T. L. Nguyen, S. Hoang: Optimal adaptive smoothing with correlated noises.Automat. Remote Control 43 (1982), 7 (1), 887-895. |
| Reference:
|
[19] T. L. Nguyen, S. Hoang: On one model of non-Markovian random process and its application to optimal estimation theory.Automat. Remote Control 43 (1982), 8 (1), 1021-1032. MR 0688867 |
| Reference:
|
[20] T. L. Nguyen, S. Hoang: On solution of ill-posed optimal linear filtering with correlated noises.Automat. Remote Control 44 (1983), 4 (1), 453-466. |
| Reference:
|
[21] B. T. Polyak, Ja. Z. Tsypkin: Robust identification.Automatica 16 (1980), 1, 53-63. MR 0571554 |
| Reference:
|
[22] V. S. Pugachev: Estimation of variables and parameters in discrete-time nonlinear systems.Automat. Remote Control 40 (1979), 512-521. Zbl 0421.93068, MR 0545519 |
| Reference:
|
[23] V. S. Pugachev: Conditionally optimal estimation in stochastic differential systems.Automatica 18 (1982), 685-696. Zbl 0526.60054, MR 0693492 |
| Reference:
|
[24] V. S. Pugachev: Probability Theory and Mathematical Statistics for Engineers.Pergamon Press, New York 1984. Zbl 0533.60001, MR 0746794 |
| Reference:
|
[25] V. S. Pugachev I. N. Sinitsyn, V. I. Shin: A software method of normal approximation in analysis of nonlinear stochastic systems.Avtomat. i Telemekh. (1987), No. 2, 62-67. (In Russian.) MR 0893520 |
| Reference:
|
[26] G. T. Schmidt: Linear and nonlinear filtering techniques.In: Control and Dynamical Systems (C. T. Leondes, ed.), Academic Press, New York 1976. Zbl 0331.93060, MR 0398580 |
| Reference:
|
[27] H. W. Sorenson: Survey on filtering techniques and stochastic control in dynamical systems.In: Control and Dynamical Systems (C. T. Leondes, ed.), Academic Press, New York 1976. MR 0398635 |
| Reference:
|
[28] J. Sternby: On consistency for the method of least squares using martingale theory.IEEE Trans. Automat. Control AC-22 (1977), 3, 346-352. Zbl 0354.93062, MR 0456844 |
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