http://www.cnr.it/ontology/cnr/individuo/prodotto/ID198121
On the Kalman Filter error covariance collapse into the unstable subspace (Articolo in rivista)
- Type
- Label
- On the Kalman Filter error covariance collapse into the unstable subspace (Articolo in rivista) (literal)
- Anno
- 2011-01-01T00:00:00+01:00 (literal)
- Alternative label
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Trevisan A. and Palatella L. (literal)
- Rivista
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Titolo
- On the Kalman Filter error covariance collapse into the unstable subspace (literal)
- Abstract
- When the Extended Kalman Filter is applied to
a chaotic system, the rank of the error covariance matri-
ces, after a sufficiently large number of iterations, reduces
to N + + N 0 where N + and N 0 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 assimila-
tion to the space spanned by the Lyapunov vectors with non-
negative Lyapunov exponents. Theoretical arguments and
numerical verification are provided to show that the asymp-
totic state and covariance estimates of the full EKF and of
its reduced form, with assimilation in the unstable and neu-
tral subspace (EKF-AUS) are the same. The consequences
of these findings on applications of Kalman type Filters to
chaotic models are discussed. (literal)
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- Autore CNR
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