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Ensemble filtering for state space models

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Title: Ensemble filtering for state space models
Author(s): Yun, Jong Hyun
Director of Research: Chen, Yuguo
Doctoral Committee Chair(s): Chen, Yuguo
Doctoral Committee Member(s): Marden, John I.; Martinsek, Adam T.; Shao, Xiaofeng
Department / Program: Statistics
Discipline: Statistics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Nonlinear filtering Sequential Monte Carlo Particle filter Ensemble Kalman filter State space model Target tracking Augmented particle filter Localized augmented particle filter Particle Monte Carlo Markov chain Lorenz model Particle filtering with independent batches.
Abstract: The state space model has been widely used in various fields including economics, finance, bioinformatics, oceanography, and tomography. The goal of the filtering problem is to find the posterior distribution of the hidden state given the current and past observations. The first part of my thesis focuses on designing efficient proposal distributions for particle filters. I propose a new approach named the augmented particle filter (APF), which combines two sets of particles from the observation and state equations. The APF can be applied to general state space models, and it does not require special structures of the model or any approximation to the target or proposal distribution. I find through simulation studies that the APF performs similarly to or better than other filtering algorithms in the literature. The convergence of the augmented particle filter has been established. The second part of my thesis develops the localization methods for particle filters in high dimensional state space models. Under high dimensional state space models, the computational constraints prevent us from having a large number of particles to avoid the degeneracy problem of the importance weights. When the dimension of the state vector is high, it is common that only a few components of the state vector are dependent on any single component or a set of a few components of the observation vector. In filtering problems, the concept of localization is to use the information in the components of the observation vector to update only the corresponding a few components of the hidden state vector. I propose the localized augmented particle filter. This new approach divides state vectors into small blocks, and it updates each block of the state vectors through state dynamics and observations. By considering blocks, the influence of observations in updating state vectors is restricted to a few blocks of the state vectors, so the localized augmented particle filter allows constructing the proposal distribution in a lower dimension than the original model. The localized augmented particle filter can outperform many other methods in the literature. The convergence of the localized augmented particle filter has been proved for some class of models. The method to improve particle filters by dividing the particles into independent batches is presented. The development of the method is motivated by the particle Markov chain Monte Carlo method proposed by Andrieu et al. (2010). Often, the combination of particle filters in batches outperforms the standard particle filter. Parallel computing techniques can be easily adapted to make the implementation fast. The convergence property of the batched particle filter has been established. As the number of batches goes to infinity, the estimate based on the combination of batches converges to the target.
Issue Date: 2012-09-18
URI: http://hdl.handle.net/2142/34574
Rights Information: Copyright 2012 by Jong Hyun Yun. All rights reserved.
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08
 

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