Open Access
September 2008 A nonlinear test model for filtering slow-fast systems
Boris Gershgorin, Andrew Majda
Commun. Math. Sci. 6(3): 611-649 (September 2008).


A nonlinear test model for filtering turbulent signals from partial observations of nonlinear slow-fast systems with multiple time scales is developed here. This model is a nonlinear stochastic real triad model with one slow mode, two fast modes, and catalytic nonlinear interaction of the fast modes depending on the slow mode. Despite the nonlinear and non-Gaussian features of the model, exact solution formulas are developed here for the mean and covariance. These formulas are utilized to develop a suite of statistically exact extended Kalman filters for the slow-fast system. Important practical issues such as filter performance with partial observations, which mix the slow and fast modes, model errors through linear filters for the fast modes, and the role of observation frequency and observational noise strength are assessed in unambiguous fashion in the test model by utilizing these exact nonlinear statistics.


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Boris Gershgorin. Andrew Majda. "A nonlinear test model for filtering slow-fast systems." Commun. Math. Sci. 6 (3) 611 - 649, September 2008.


Published: September 2008
First available in Project Euclid: 29 September 2008

zbMATH: 1152.62065
MathSciNet: MR2455468

Primary: 60G35 , 60H10

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

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 3 • September 2008
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