Non-Linear Continuous-Discrete Smoothing by Basis Function Expansions of Brownian Motion

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorTronarp, Filipen_US
dc.contributor.authorSärkkä, Simoen_US
dc.contributor.departmentDepartment of Electrical Engineering and Automationen_US
dc.date.accessioned2019-02-25T08:40:57Z
dc.date.available2019-02-25T08:40:57Z
dc.date.issued2018-09-05en_US
dc.description.abstractThis paper is concerned with inferring the state of a Itô stochastic differential equation (SDE) from noisy discrete-time measurements. The problem is approached by considering basis function expansions of Brownian motion, that as a consequence give approximations to the underlying stochastic differential equation in terms of an ordinary differential equation with random coefficients. This allows for representing the latent process at the measurement points as a discrete time system with a non-linear transformation of the previous state and a noise term. The smoothing problem can then be solved by sigma-point or Taylor series approximations of this non-linear function, implementations of which are detailed. Furthermore, a method for interpolating the smoothing solution between measurement instances is developed. The developed methods are compared to the Type III smoother in simulation examples involving (i) hyperbolic tangent drift and (ii) the Lorenz 63 system where the present method is found to be better at reconstructing the smoothing solution at the measurement points, while the interpolation scheme between measurement instances appear to suffer from edge effects, serving as an invitation to future research.en
dc.description.versionPeer revieweden
dc.format.extent8
dc.format.extent1114-1121
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationTronarp , F & Särkkä , S 2018 , Non-Linear Continuous-Discrete Smoothing by Basis Function Expansions of Brownian Motion . in Proceedings of the 21st International Conference on Information Fusion, FUSION 2018 . , 8455493 , IEEE , pp. 1114-1121 , International Conference on Information Fusion , Cambridge , United Kingdom , 10/07/2018 . https://doi.org/10.23919/ICIF.2018.8455493en
dc.identifier.doi10.23919/ICIF.2018.8455493en_US
dc.identifier.isbn9780996452762
dc.identifier.otherPURE UUID: 13863ff1-1837-4738-9af0-4521a443dd79en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/13863ff1-1837-4738-9af0-4521a443dd79en_US
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85054091403&partnerID=8YFLogxKen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/31575329/ELEC_Tronarp_Sarkka_Non_Linear_Continuous_Discrete_FUSION_2018.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/36650
dc.identifier.urnURN:NBN:fi:aalto-201902251807
dc.language.isoenen
dc.relation.ispartofInternational Conference on Information Fusionen
dc.relation.ispartofseriesProceedings of the 21st International Conference on Information Fusion, FUSION 2018en
dc.rightsopenAccessen
dc.subject.keywordbasis expansionen_US
dc.subject.keywordBrownian motionen_US
dc.subject.keywordNon-linear continuous-discrete smoothingen_US
dc.subject.keywordstochastic differential equationen_US
dc.titleNon-Linear Continuous-Discrete Smoothing by Basis Function Expansions of Brownian Motionen
dc.typeConference article in proceedingsfi
dc.type.versionacceptedVersion
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