Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00439569" target="_blank" >RIV/67985807:_____/15:00439569 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/140965363" target="_blank" >http://dx.doi.org/10.1137/140965363</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/140965363" target="_blank" >10.1137/140965363</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit

Popis výsledku v původním jazyce

Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior) ensemble witha prescribed mean and covariance, consistent with the Kalman update. This includes several filters used in practice, such as the ensemble transform Kalman filter, the ensemble adjustment Kalman filter, and a filter by Whitaker and Hamill. We show that at every time index, as the number of ensemble members increases to infinity, the mean and covariance of an unbiased ensemble square root filter converge to those of the Kalman filter, in the case of a linear model and an initial distribution of which allmoments exist. The convergence is in all $L^p$, $1/leq p</infty$, with the usual rate $1//sqrt{N}$, and the constant does not depend on the model or the data dimensions. The result holds in infinite-dimensional separable Hilbert spaces a

Název v anglickém jazyce

Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit

Popis výsledku anglicky

Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior) ensemble witha prescribed mean and covariance, consistent with the Kalman update. This includes several filters used in practice, such as the ensemble transform Kalman filter, the ensemble adjustment Kalman filter, and a filter by Whitaker and Hamill. We show that at every time index, as the number of ensemble members increases to infinity, the mean and covariance of an unbiased ensemble square root filter converge to those of the Kalman filter, in the case of a linear model and an initial distribution of which allmoments exist. The convergence is in all $L^p$, $1/leq p</infty$, with the usual rate $1//sqrt{N}$, and the constant does not depend on the model or the data dimensions. The result holds in infinite-dimensional separable Hilbert spaces a

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-34856S" target="_blank" >GA13-34856S: Pokročilé metody náhodných polí v asimilaci dat pro krátkodobou předpověď počasí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM/ASA Journal on Uncertainty Quantification

ISSN

2166-2525

e-ISSN

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Svazek periodika

3

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

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EID výsledku v databázi Scopus

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