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| Titel |
On the Kalman Filter error covariance collapse into the unstable subspace |
| VerfasserIn |
A. Trevisan, L. Palatella |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 18, no. 2 ; Nr. 18, no. 2 (2011-03-28), S.243-250 |
| Datensatznummer |
250013898
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| Publikation (Nr.) |
 copernicus.org/npg-18-243-2011.pdf |
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| Zusammenfassung |
| When the Extended Kalman Filter is applied to a
chaotic system, the rank of the error covariance matrices, after a
sufficiently large number of iterations, reduces to N+ + N0 where
N+ and N0 are the number of positive and null Lyapunov
exponents. This is due to the collapse into the unstable and neutral
tangent subspace of the solution of the full Extended Kalman Filter.
Therefore the solution is the same as the solution obtained by confining
the assimilation to the space spanned by the Lyapunov vectors with
non-negative Lyapunov exponents. Theoretical arguments and numerical
verification are provided to show that the asymptotic state and covariance
estimates of the full EKF and of its reduced form, with assimilation in
the unstable and neutral subspace (EKF-AUS) are the same.
The consequences of these findings on applications of Kalman type Filters
to chaotic models are discussed. |
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