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Youssef Marzouk. Mitra, Subhadeep Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2012-09-13T18:58:22Z 2012-09-13T18:58:22Z 2012 2012 http://hdl.handle.net/1721.1/72873 808372196 Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 131-138). Particle filtering is a technique used for state estimation from noisy measurements. In fluid dynamics, a popular problem called Lagrangian data assimilation (LaDA) uses Lagrangian measurements in the form of tracer positions to learn about the changing flow field. Particle filtering can be applied to LaDA to track the flow field over a period of time. As opposed to techniques like Extended Kalman Filter (EKF) and Ensemble Kalman Filter (EnKF), particle filtering does not rely on linearization of the forward model and can provide very accurate estimates of the state, as it represents the true Bayesian posterior distribution using a large number of weighted particles. In this work, we study the performance of various particle filters for LaDA using a two-dimensional point vortex model; this is a simplified fluid dynamics model wherein the positions of vortex singularities (point vortices) define the state. We consider various parameters associated with algorithm and examine their effect on filtering performance under several vortex configurations. Further, we study the effect of different tracer release positions on filtering performance. Finally, we relate the problem of optimal tracer deployment to the Lagrangian coherent structures (LCS) of point vortex system. by Subhadeep Mitra. S.M. 138 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Computation for Design and Optimization Program. Particle filtering with Lagrangian data in a point vortex model Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="647c6e7e-31fe-4fbd-bbb6-b2229868b4bc"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Particle filtering with Lagrangian data in a point vortex model</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2012</PublicationDate> <Authors> <Author> <DisplayName>Mitra, Subhadeep</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Computation for Design and Optimization Program.</Keyword> <Abstract>Particle filtering is a technique used for state estimation from noisy measurements. In fluid dynamics, a popular problem called Lagrangian data assimilation (LaDA) uses Lagrangian measurements in the form of tracer positions to learn about the changing flow field. Particle filtering can be applied to LaDA to track the flow field over a period of time. As opposed to techniques like Extended Kalman Filter (EKF) and Ensemble Kalman Filter (EnKF), particle filtering does not rely on linearization of the forward model and can provide very accurate estimates of the state, as it represents the true Bayesian posterior distribution using a large number of weighted particles. In this work, we study the performance of various particle filters for LaDA using a two-dimensional point vortex model; this is a simplified fluid dynamics model wherein the positions of vortex singularities (point vortices) define the state. We consider various parameters associated with algorithm and examine their effect on filtering performance under several vortex configurations. Further, we study the effect of different tracer release positions on filtering performance. Finally, we relate the problem of optimal tracer deployment to the Lagrangian coherent structures (LCS) of point vortex system.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>