Particle Kalman Filtering: A Nonlinear Framework for Ensemble Kalman Filters

Ibrahim Hoteit, Xiaodong Luo, Dinh-Tuan Pham, Irene M. Moroz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Optimal nonlinear filtering consists of sequentially determining the conditional probability distribution functions (pdf) of the system state, given the information of the dynamical and measurement processes and the previous measurements. Once the pdfs are obtained, one can determine different estimates, for instance, the minimum variance estimate, or the maximum a posteriori estimate, of the system state. It can be shown that, many filters, including the Kalman filter (KF) and the particle filter (PF), can be derived based on this sequential Bayesian estimation framework. In this contribution, we present a Gaussian mixture-based framework, called the particle Kalman filter (PKF), and discuss how the different EnKF methods can be derived as simplified variants of the PKF. We also discuss approaches to reducing the computational burden of the PKF in order to make it suitable for complex geosciences applications. We use the strongly nonlinear Lorenz-96 model to illustrate the performance of the PKF.
Original languageEnglish (US)
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010
PublisherAIP Publishing
Pages1075-1079
Number of pages5
DOIs
StatePublished - Sep 20 2010

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