Scaled unscented transform Gaussian sum filter: Theory and application

Handle URI:
http://hdl.handle.net/10754/561455
Title:
Scaled unscented transform Gaussian sum filter: Theory and application
Authors:
Luo, Xiaodong; Moroz, Irene M.; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to Lorenz and Emanuel (1998) [27]. We will present the details of implementing the SUT-GSF and examine the effects of filter parameters on the performance of the SUT-GSF. © 2010 Elsevier B.V. All rights reserved.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Fluid Modeling and Prediction Group
Publisher:
Elsevier BV
Journal:
Physica D: Nonlinear Phenomena
Issue Date:
May-2010
DOI:
10.1016/j.physd.2010.01.022
ARXIV:
arXiv:1005.2665
Type:
Article
ISSN:
01672789
Additional Links:
http://arxiv.org/abs/arXiv:1005.2665v1
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLuo, Xiaodongen
dc.contributor.authorMoroz, Irene M.en
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2015-08-02T09:11:48Zen
dc.date.available2015-08-02T09:11:48Zen
dc.date.issued2010-05en
dc.identifier.issn01672789en
dc.identifier.doi10.1016/j.physd.2010.01.022en
dc.identifier.urihttp://hdl.handle.net/10754/561455en
dc.description.abstractIn this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to Lorenz and Emanuel (1998) [27]. We will present the details of implementing the SUT-GSF and examine the effects of filter parameters on the performance of the SUT-GSF. © 2010 Elsevier B.V. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1005.2665v1en
dc.subjectData assimilationen
dc.subjectEnsemble Kalman filteren
dc.subjectGaussian sum filteren
dc.subjectScaled unscented Kalman filteren
dc.titleScaled unscented transform Gaussian sum filter: Theory and applicationen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Fluid Modeling and Prediction Groupen
dc.identifier.journalPhysica D: Nonlinear Phenomenaen
dc.contributor.institutionMath Inst, Oxford OX1 3LB, Englanden
dc.contributor.institutionUniv Oxford, Oxford Man Inst, Oxford OX2 6ED, Englanden
dc.identifier.arxividarXiv:1005.2665en
kaust.authorLuo, Xiaodongen
kaust.authorHoteit, Ibrahimen
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