On the design of a stable adaptive filter for state estimation in high dimensional systems

Automatica

Volumn 37, Issue 3, 2001, Pages 341-359

  Hoang, H S ^a   Baraille, R ^b   Talagrand, O ^c  

^a CNES   (France)

^b SHOM/GRCS/CMO   (France)

^c LABORATOIRE DE MÉTÉOROLOGIE DYNAMIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; PARAMETER ESTIMATION; STATE ESTIMATION; STATISTICAL METHODS;

HIGH DIMENSIONAL SYSTEMS; PARAMETER UNCERTAINTY;

ADAPTIVE FILTERING;

EID: 0035284104     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(00)00175-8     Document Type: Article

References (41)

1. Albert R. Regression and the Moore-Penrose pseudoinverse. 1972;Academic Press, New York.
2. Anderson B.D.O., Liu Y. Controller reduction: Concepts and approaches. IEEE Transactions in Automatic Control. 34(7):1989;802-812.
3. Anderson B.D.O., Moore J.B. Optimal filtering. 1979;Prentice-Hall, Englewood Cliffs, NJ.
4. Anderson B.D.O., Moore J.B. Detectability and stabilizability of time-varying discrete time linear systems. SIAM Journal of Control and Optimization. 19(1):1981;20-32.
5. Baraille, R., & Filatoff, N. (1995). Modèle shallow-water multicouches isopycnal de Miami. Rapport d'études CMO, 03 / 95, EPSHOM / CMO, Brest, France.
6. Belanger P.R. Estimation of noise covariance matrices for a linear time-varying stochastic process. Automatica. 10:1974;267-275.
7. Bucy R.S. Global theory of the Riccati equation. Journal of Computer Systems Sciences. 1:1967;349-361.
8. Caines P.E., Mayne D.Q. On the discrete-time matrix Riccati equation of optimal control. International Journal of Control. 12:1970;785-794.
9. Chan S.W., Goodwin G.C., Sin K.S. Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems. IEEE Transactions on Automatic Control. AC-29(2):1984;110-118.
10. Chassignet E. Rings in numerical models of ocean general circulation: A statistical study. Journal of Geophysical Research. 97:1992;9479-9492.
11. Cohn S., Todling R. Approximate data assimilation schemes for stable and unstable dynamics. Journal of the Meteorological Society of Japan. 74(1):1996;63-75.
12. Dee D., Cohn S.E., Dalcher A., Ghil M. An efficient algorithm for estimating noise covariances in distributed systems. IEEE Transactions on Automatic Control. AC-30(11):1985;1057-1065.
13. De Mey P., Robinson A.R. Assimilation of altimeter eddy fields in a limited-area quasi-geostrophic model. JPO. 17:1987;2280-2293.
14. Fitzgerald R.R. Divergence of the Kalman filter. IEEE Transactions on Automatic Control. AC-16:1971;736-747.
15. Fukumori I., Malanotte-Rizzoli P. An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model. Journal of Geophysical Research. 100(C4):1995;6777-6793.
16. Germani A., Jetto L., Piccioni M. Galerkin approximation for optimal filtering of infinite dimensional linear systems. SIAM Journal of Control and Optimization. 26:1988;1287-1305.
17. Gibson J.S. An analysis of optimal model regulation: Convergence and stability. SIAM Journal of Control and Optimization. 19:1981;686-707.
18. Golub G.H., Van Loan C. Matrix Computation. 1993;Johns Hopkins University Press, Baltimore.
19. Haines K. A direct method for assimilating sea surface height data into ocean model with adjustments to the deep circulations. JPO. 21:1991;843-868.
20. Halevi Y. The optimal reduced-order estimator for systems with singular measurements noise. IEEE Transactions on Automatic Control. 34(7):1989;777-783.
21. Hautus M.L.J. Controllability and observability conditions of linear autonomous systems. Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen. Series A:1969;443-448.
22. Hoang, H. S., De Mey, P., & Talagrand, O. (1994). A simple algorithm of stochastic approximation type for system parameters and state estimation. Proceedings of the 33rd IEEE CDC, Florida, USA, 747-752.
23. Hoang H.S., Baraille R., Talagrand O., De Mey P., Carton X. Adaptive filtering: Application to satellite data assimilation in oceanography. Journal of Dynamics of Atmospheres and Oceans. 27:1997;257-281.
24. Hoang H.S., De Mey P., Talagrand O., Baraille R. A new reduced-order adaptive filter for state estimation in high dimensional systems. Automatica. 33(8):1997;1475-1498.
25. Hoang, H.S., Baraille, R., Cohn, S., Talagrand, O., & Carton, X. (1997c). A numerical method for estimation of the gain matrix in a stable reduced-order adaptive filter. Proceedings of IFAC conference' control of industrial systems. Belfort, France, June.
26. Jazwinski A.H. Stochastic processes and filtering theory. 1970;Academic Press, New York.
27. Kailath T. Linear systems. 1980;Prentice-Hall, Englewood Cliffs, NJ.
28. Kalman R.E. Contribution to the theory of optimal control. Boletin de Sociedade Matematica Mexicana. 5:1961;102-119.
29. Kunisch K. Approximation schemes for the linear-quadratic optimal control problem associated with delay equations. SIAM Journal of Control and Optimization. 20:1982;506-540.
30. LeDimet F.-X., Talagrand O. Variational algorithms for analysis and assimilation of metrological observations: Theoretical aspects. Tellus. 38A:1986;97-110.
31. Ljung L. System identification: Theory for the user. 1987;Prentice Hall, Englewood Cliffs, NJ.
32. Luenberger D.G. Observers for multivariable systems. IEEE Transactions on Automatic Control. AC-11:1966;190-197.
33. Mehra R. On the identification of variances and adaptive Kalman filtering. IEEE Transactions on Automatic Control. AC-15:1970;175-184.
34. Salamon D. Structure and stability of finite dimensional approximations for functional differential equations. SIAM Journal on Control and Optimization. 23:1982;928-951.
35. Tikhonov A.N., Arshenin V.la. Methods for solution of ill-posed problems. 1986;Nauka, Moskva.
36. Polyak B.T., Juditsky A.B. Acceleration of stochastic approximation by averaging. SIAM Journal on Control and Optimization. 30:1992;838-855.
37. Strejc V. State space theory of discrete linear control. 1981;Academia, Prague.
38. Verron J. Nudging satellite altimetry data into quasi-geostrophic ocean models. Journal of Geophysical Research. 97(C5):1992;7479-7491.
39. Vinter R.B. Filter stability for stochastic evolution equations. SIAM Journal on Control and Optimization. 15:1977;465-485.
40. Willems J.C., Mitter S.K. Controllability, observability, pole allocation, and state reconstruction. IEEE Transactions on Automatic Control. AC-16:1971;582-595.
41. Wonham W.M. On a matrix Riccati equation of stochastic control. SIAM Journal on Control. 6(4):1968;681-698.