Journal ArticleDOI
Interactive Kaiman filtering
Gerd Bürger,Mark A. Cane +1 more
TLDR
A key feature of the filter is replaced with a principle that uses a more global approach through the utilization of a set of preselected regimes, and a compromise between the different error models is found through the use of a weighting function that reflects the 'closeness' of the error model to the correct model.Abstract:
Data assimilation via the extended Kalman filter can become problematic when the assimilating model is strongly nonlinear, primarily in connection with sharp, "switchlike" changes between different regimes of the system. The filter seems too inert to follow those switches quickly enough, a fact that can lead to a complete failure when the switches occur often enough. In this paper we replace the key feature of the filter, the use of local linearity for the error model update, with a principle that uses a more global approach through the utilization of a set of preselected regimes. The method uses all regime error models simultaneously. Being mutually incompatible, a compromise between the different error models is found through the use of a weighting function that reflects the 'closeness' of the error model to the correct model. To test the interactive Kalman filter a series of numerical experiments is performed using the double-well system and the well-known Lorenz system, and the results are compared to the extended Kalrnan filter. It turns out that, depending on the set of preselected regimes, the performance is worse than, comparable to, or better than that of the extended Kalman filter.read more
Citations
More filters
Journal ArticleDOI
An Introduction to Estimation Theory (gtSpecial IssueltData Assimilation in Meteology and Oceanography: Theory and Practice)
Journal ArticleDOI
A Note on the Particle Filter with Posterior Gaussian Resampling
TL;DR: In this paper, a particle filter with Gaussian resampling (PFGR) method is proposed to generate the posterior analysis ensemble in an effective and efficient way, which can approximate more accurately the Bayesian analysis.
Book ChapterDOI
The Oceanographic Data Assimilation Problem: Overview, Motivation and Purposes
TL;DR: In this article, a brief non-technical overview is given of the data assimilation problem in oceanography and a historical perspective is presented that illustrates its main motivations and discusses the objectives of combining fully complex ocean general circulation models and oceanographic data.
Journal ArticleDOI
Solving for the Generalized Inverse of the Lorenz Model (gtSpecial IssueltData Assimilation in Meteology and Oceanography: Theory and Practice)
Geir Evensen,Nabil Fario +1 more
Journal ArticleDOI
Application of neural network collocation method to data assimilation
TL;DR: The method makes use of the flexibility of a neural network for constructing an arbitrary mapping function and can solve an assimilation problem even if the model differential equations do not express the observed phenomena exactly.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Stochastic Processes and Filtering Theory
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.