Show simple item record

hal.structure.identifierCommonwealth Scientific and Industrial Research Organisation [Canberra] [CSIRO]
dc.contributor.authorBISHOP, Adrian
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierUniversity of New South Wales [Sydney] [UNSW]
dc.contributor.authorPATHIRAJA, Sahani
dc.date.accessioned2024-04-04T03:08:44Z
dc.date.available2024-04-04T03:08:44Z
dc.date.issued2017-01-21
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193552
dc.description.abstractEnThe purpose of this work is to analyse the effect of various perturbations and projections of Kalman-Bucy semigroups and Riccati equations. The original motivation was to understand the behaviour of various regulation methods used in ensemble Kalman filtering (EnKF). For example, covariance inflation-type methods (perturbations) and covariance localisation methods (projections) are commonly used in the EnKF literature to ensure well-posedness of the sample covariance (e.g. sufficient rank) and to 'move' the sample covariance closer (in some sense) to the Riccati flow of the true Kalman filter. In the limit, as the number of samples tends to infinity, these methods drive the sample covariance toward a solution of a perturbed, or projected, version of the standard (Kalman-Bucy) differential Riccati equation. The behaviour of this modified Riccati equation is investigated here. Results concerning continuity (in terms of the perturbations), boundedness, and convergence of the Riccati flow to a limit are given. In terms of the limiting filters, results characterising the error between the perturbed/projected and nominal conditional distributions are given. New projection-type models and ideas are also discussed within the EnKF framework; e.g. projections onto so-called Bose-Mesner algebras. This work is generally important in understanding the limiting bias in both the EnKF empirical mean and covariance when applying regularisation. Finally, we note the perturbation and projection models considered herein are also of interest on their own, and in other applications such as differential games, control of stochastic and jump processes, and robust control theory, etc.
dc.language.isoen
dc.title.enPerturbations and Projections of Kalman-Bucy Semigroups Motivated by Methods in Data Assimilation
dc.typeRapport
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1701.05798
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.type.institutionArxiv
bordeaux.type.reportrr
hal.identifierhal-01593872
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01593872v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2017-01-21&rft.au=BISHOP,%20Adrian&DEL%20MORAL,%20Pierre&PATHIRAJA,%20Sahani&rft.genre=unknown


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record