Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system

DOI10.1063/1.2909862zbMath1307.34064arXiv0711.3741OpenAlexW3099637575WikidataQ31161585 ScholiaQ31161585MaRDI QIDQ5179182

Anna Trevisan, Alberto Carrassi, Francesco Uboldi, Michael Ghil

Publication date: 19 March 2015

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3741

Mathematics Subject Classification ID

Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Meteorology and atmospheric physics (86A10) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (11)

Projected Shadowing-Based Data Assimilation ⋮ Mathematical foundations of hybrid data assimilation from a synchronization perspective ⋮ Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems ⋮ Reduced-order autodifferentiable ensemble Kalman filters ⋮ Resource-Constrained Model Selection for Uncertainty Propagation and Data Assimilation ⋮ Accuracy and stability of filters for dissipative PDEs ⋮ Accuracy of Some Approximate Gaussian Filters for the Navier--Stokes Equation in the Presence of Model Error ⋮ On instabilities in data assimilation algorithms ⋮ Observability of laminar bidimensional fluid flows seen as autonomous chaotic systems ⋮ Kalman filter data assimilation: Targeting observations and parameter estimation ⋮ Degenerate Kalman Filter Error Covariances and Their Convergence onto the Unstable Subspace

Cites Work

• Data assimilation with an extended Kalman filter for impact-produced shock-wave dynamics
• Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter
• Stochastic processes and filtering theory
• Conditioning of the Stable, Discrete-Time Lyapunov Operator
• Observability of Discretized Partial Differential Equations
• Controlling chaos
• Deterministic Nonperiodic Flow

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