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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

—

Project

<a href="/en/project/GA13-34856S" target="_blank" >GA13-34856S: Advanced random field methods in data assimilation for short-term weather prediction</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

SIAM/ASA Journal on Uncertainty Quantification

ISSN

2166-2525

e-ISSN

—

Volume of the periodical

3

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

17

Pages from-to

1-17

UT code for WoS article

—

EID of the result in the Scopus database

—