Particle filtering with Lagrangian data in a point vortex model

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2012

Author dc:creator

• Mitra, Subhadeep

Advisor dc:contributor.advisor

• Youssef Marzouk.

• Computation for Design and Optimization Program.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/72873

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/72873