A nonlinear test model for filtering slow-fast systems

Boris Gershgorin, Andrew Majda

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)611-649
Number of pages39
JournalCommunications in Mathematical Sciences
Volume6
Issue number3
StatePublished - 2008

Fingerprint

Slow-fast System
Filtering
Partial Observation
Multiple Time Scales
Linear Filter
Model Error
Model
Nonlinear Interaction
Kalman Filter
Extended Kalman filters
Nonlinear Systems
Exact Solution
Filter
Statistics

Keywords

  • Extended Kalman filter
  • Nonlinear model
  • Slow-fast system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A nonlinear test model for filtering slow-fast systems. / Gershgorin, Boris; Majda, Andrew.

In: Communications in Mathematical Sciences, Vol. 6, No. 3, 2008, p. 611-649.

Research output: Contribution to journalArticle

Gershgorin, B & Majda, A 2008, 'A nonlinear test model for filtering slow-fast systems', Communications in Mathematical Sciences, vol. 6, no. 3, pp. 611-649.
Gershgorin, Boris ; Majda, Andrew. / A nonlinear test model for filtering slow-fast systems. In: Communications in Mathematical Sciences. 2008 ; Vol. 6, No. 3. pp. 611-649.
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