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Adaptive Filter for High Dimensional Inverse Engineering Problems: From Theory to Practical Implementation
HOM, SHOM, Toulouse, France
HOM, SHOM, Toulouse, France
- 1 HOM, SHOM, Toulouse, France
- 2 HOM, SHOM, Toulouse, France
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Abstract
The inverse engineering problems approach is a discipline that is growing very rapidly. The inverse problems we consider here concern the way to determine the state and/or parameters of the physical system of interest using observed measurements. In this context the filtering algorithms constitute a key tool to offer improvements of our knowledge on the system state, its forecast … which are essential, in particular, for oceanographic and meteorologic operational systems. The objective of this paper is to give an overview on how one can design a simple, no time-consuming Reduced-Order Adaptive Filter (ROAF) to solve the inverse engineering problems with high forecasting performance in very high dimensional environment.
KeywordsDynamical SystemsAdaptive FilteringStabilityReal Schur DecompositionStochastic ApproximationNumerical PredictionData Assimilation
- S. Haykin, “Adaptive Filter Theory,” Prentice Hall, Upper Saddle River, 2002.
- M. Ghil and P. Manalotte-Rizzoli, “Data Assimilation in Meteorology and Oceanography,” Advances in Geophysics, Vol. 33, 1991, pp. 141-266. doi:10.1016/S0065-2687(08)60442-2
- B. D. O. Anderson and J. B. Moore, “Optimal Filtering,” Prentice-Hall, Inc., Englewood Cliffs, 1979.
- H. S. Hoang, P. De Mey, O. Talagrand and R. Baraille, “A New Reduced-Order Adaptive Filter for State Estimation in High Dimensional Systems,” Automatica, Vol. 33, No. 8, 1997, pp. 1475-1498. doi:10.1016/S0005-1098(97)00069-1
- C. S. Spall, “An Overview of the Simultaneous Perturbation Method for Efficient Optimization, Johns Hopkins APL Technical Digest, Vol. 19, No. 4, 1998, pp. 482-492.
- F. X. Le Dimet and O. Talagrand, “Variational Algorithms for Analysis and Assimilation of Meteorological Observations: Theoretical Aspects,” Tellus, Vol. 37A, 1983, pp. 309-327.
- H. S. Hoang, O. Talagrand and R. Baraille, “On the Design of a Stable Filter for State Estimation in High Dimensional Systems,” Automatica, Vol. 37, No. 8, 2001, pp. 341-359. doi:10.1016/S0005-1098(00)00175-8
- H. S. Hoang, O. Talagrand and R. Baraille, “On the Stability of a Reduced-Order Filter Based on Dominant Singular Value Decomposition of the Systems Dynamics,” Automatica, Vol. 45, No. 10, 2009, pp. 2400-2405. doi:10.1016/j.automatica.2009.06.032
- G. H. Golub and C. F. Van Loan, “Matrix Computations,” 2nd Edition, Johns Hopkins, 1993.
- H. S. Hoang and R. Baraille, “Prediction Error Sampling Procedure Based on Dominant Schur Decomposition. Application to State Estimation in High Dimensional Oceanic Model,” Applied Mathematics and Computation, Vol. 218, No. 7, 2011, pp. 3689-3709. doi:10.1016/j.amc.2011.09.012
- H. S. Hoang and R. Baraille, “On Gain Initialization and Optimization of Reduced-Order Adaptive Filter,” IAENG International Journal of Applied Mathematics, Vol. 42, No. 1, 2011, pp. 19-33.
- E. N. Lorenz, “Deterministic Non-Periodic Flow,” Journal of the Atmospheric Sciences, Vol. 20, No. 2, 1963, pp. 130-141. doi:10.1175/1520-0469(1963)020 2.0.CO;2
- G. A. Kivman, “Sequential Parameter Estimation for Stochastic Systems,” Nonlinear Processes in Geophysics, Vol. 10, 2003, pp. 253-259. doi:10.5194/npg-10-253-2003
- G. Evensen, “The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,” Ocean Dynamics, Vol. 53, No. 4, 2003, pp. 343-367. doi:10.1007/s10236-003-0036-9