Degenerate Kalman Filter Error Covariances and Their Convergence onto the Unstable Subspace

DOI10.1137/16M1068712zbMath1365.93497arXiv1604.02578OpenAlexW3106129013WikidataQ57764199 ScholiaQ57764199MaRDI QIDQ5269865

Marc Bocquet, Alberto Carrassi, Christopher K. R. T. Jones, Karthik S. Gurumoorthy, Amit Apte, Colin J. Grudzien

Publication date: 28 June 2017

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.02578

zbMATH Keywords

covariance matrixKalman filtercontrol theorylinear dynamicsdata assimilationLyapunov vectors

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Linear systems in control theory (93C05) Signal detection and filtering (aspects of stochastic processes) (60G35) Observability (93B07) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (7)

Mathematical foundations of hybrid data assimilation from a synchronization perspective ⋮ Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems ⋮ Asymptotic properties of linear filter for deterministic processes ⋮ Asymptotic Forecast Uncertainty and the Unstable Subspace in the Presence of Additive Model Error ⋮ Online learning of both state and dynamics using ensemble Kalman filters ⋮ Stability of non-linear filter for deterministic dynamics ⋮ Strong detectability and observers for linear time-varying systems

Uses Software

• EnKF

Cites Work

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• Kalman Filtering with Random Coefficients and Contractions
• Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model—multiscale effects, geometric degeneracy, and error dynamics
• Asymptotic Forecast Uncertainty and the Unstable Subspace in the Presence of Additive Model Error
• Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system
• Rank Deficiency of Kalman Error Covariance Matrices in Linear Time-Varying System With Deterministic Evolution
• Data Assimilation
• Matrix theory. Basic results and techniques

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