Ensemble Kalman Estimation with Gaussian Mixture Models

• Author / Creator

  Li, Ruoxia

• The objective of this work is to study the problems that arise in state estimation for severely nonlinear systems. In practice, many processes are nonlinear, accompanied by uncertain parameters. The complexity of the model causes the probability density function (PDF) of the states to deviate from a Gaussian distribution. This presents a challenge for Kalman-based state estimators such as the extended Kalman filter, since they model the state PDF as Gaussian. In order to achieve more accurate estimation, the modeling of the state distribution needs to be improved. The first problem is to develop an estimator for the state PDF of arbitrary distribution. In this work, we develop an estimator based on a Gaussian mixture model (GMM) coupled with the ensemble Kalman filter (EnKF) specifically for estimation with multimodal state distributions.The second problem is that the conventional recursive state estimation procedures cannot handle inequality constraints on the states. Therefore, they might result in physically meaningless or non-convergent estimates, especially when the initial values are poor. The incorporation of constraints can help improve the estimation significantly. In this work, we develop a novel state estimation technique to incorporate inequality constraints for the case of Gaussian filters. Furthermore, we consider the constrained estimation for the case where the state PDF cannot be approximated with a Gaussian distribution. To this end, we develop a framework to incorporate the inequality constraints for the GMM based EnKF mentioned in the first problem.The filtering provides the estimates by assimilating the history data. Such estimation can be further improved by using the smoothing technique which assimilate all the available data. Therefore the third problem is to develop a smoothing framework for the systems whose state PDF is non-Gaussian. In this work, we extend the existing ensemble Kalman smoother (EnKS) to deal with non-Gaussian systems by combining it with the GMM model. The thesis focuses on three aspects in data assimilation problem. The first is filtering problems for non-Gaussian systems. The second is smoothing problems for non-Gaussian systems. The third is the incorporation of inequality constraints into estimation. The thesis provides the theoretical deduction of our proposed approaches as well as practical applications.

• Subjects / Keywords

  • Ensemble Kalman smoother
  • Ensemble Kalman filter
  • Inequality constraints
  • Gaussian mixture model

• Graduation date

  Fall 2018

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3H12VQ2B

• License

  Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.