Computing point estimates from a non-Gaussian posterior distribution using a probabilistic k-means clustering approach |
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| Affiliation: | 1. Service d’Automatique, Université de Mons (UMONS), BioSys Center and Institute of Biosciences, B-7000 Mons, Belgium;2. Service de Thermodynamique et Physique mathématique, Université de Mons (UMONS), BioSys Center and Institute of Biosciences, B-7000 Mons, Belgium;3. Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstraße 1, 39106 Magdeburg, Germany;4. Otto-von-Guericke-Universität, Fakultät für Elektrotechnik und Informationstechnik Institut für Automatisierungstechnik, D-39106 Magdeburg, Germany;1. Process Dynamics and Operations Group, Technical University of Dortmund, Germany;2. Evonik Industries AG, Germany;1. Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea;2. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta 30332, GA, USA;3. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge 02139, MA, USA;4. Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver BC V6T1Z3, Canada |
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| Abstract: | The Kalman filter algorithm gives an analytical expression for the point estimates of the state estimates, which is the mean of their posterior distribution. Conventional Bayesian state estimators have been developed under the assumption that the mean of the posterior of the states is the ‘best estimate’. While this may hold true in cases where the posterior can be adequately approximated as a Gaussian distribution, in general it may not hold true when the posterior is non-Gaussian. The posterior distribution, however, contains far more information about the states, regardless of its Gaussian or non-Gaussian nature. In this study, the information contained in the posterior distribution is explored and extracted to come up with meaningful estimates of the states. The need for combining Bayesian state estimation with extracting information from the distribution is demonstrated in this work. |
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| Keywords: | Nonlinear Bayesian state estimation K-means clustering Ensemble Kalman filter Particle filter |
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