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March 2010 Filtering a nonlinear slow-fast system with strong fast forcing
Boris Gershgorin, Andrew Majda
Commun. Math. Sci. 8(1): 67-92 (March 2010).


A three-mode nonlinear slow-fast system with fast forcing is studied here as a model for filtering turbulent signals from partial observations. The model describes the interaction of two externally driven fast modes with a slow mode through catalytic nonlinear coupling. The special structure of the nonlinear interaction allows for the analytical solution for the first and second order statistics even with fast forcing. These formulas are used for testing the exact Nonlinear Extended Kalman Filter for the slow-fast system with fast forcing. Various practical questions such as the influence of the strong fast forcing on the slowly varying wave envelope, the role of observations, the frequency and variance of observations, and the model error due to linearization are addressed here.


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Boris Gershgorin. Andrew Majda. "Filtering a nonlinear slow-fast system with strong fast forcing." Commun. Math. Sci. 8 (1) 67 - 92, March 2010.


Published: March 2010
First available in Project Euclid: 23 February 2010

zbMATH: 1202.62128
MathSciNet: MR2655901

Primary: 34A05 , 93E11

Keywords: extended Kalman filter , fast forcing , nonlinear model , slow-fast system

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 1 • March 2010
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