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Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems

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Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems. / Ala-Luhtala, Juha; Särkkä, Simo; Piche, Robert.

julkaisussa: Signal Processing, Vuosikerta 111, 06.2015, s. 124-136.

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Ala-Luhtala, Juha ; Särkkä, Simo ; Piche, Robert. / Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems. Julkaisussa: Signal Processing. 2015 ; Vuosikerta 111. Sivut 124-136.

Bibtex - Lataa

@article{f48a8dbdcbc241e88eee31b2eeaf892e,
title = "Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems",
abstract = "The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and sigma-point methods to approximate the intractable Gaussian expectations in the variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix.",
author = "Juha Ala-Luhtala and Simo S{\"a}rkk{\"a} and Robert Piche",
note = "Available online 19 Dec,2014, preprint http://arxiv.org/abs/1407.5874 (vol 111, June2015, s. 124-136)<br/>Contribution: organisation=ase,FACT1=0.5<br/>Contribution: organisation=mat,FACT2=0.5<br/>Portfolio EDEND: 2015-01-09<br/>Publisher name: Elsevier <br /> publication_forum:67104",
year = "2015",
month = "6",
doi = "10.1016/j.sigpro.2014.12.013",
language = "English",
volume = "111",
pages = "124--136",
journal = "Signal Processing",
issn = "0165-1684",
publisher = "Elsevier",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems

AU - Ala-Luhtala, Juha

AU - Särkkä, Simo

AU - Piche, Robert

N1 - Available online 19 Dec,2014, preprint http://arxiv.org/abs/1407.5874 (vol 111, June2015, s. 124-136)<br/>Contribution: organisation=ase,FACT1=0.5<br/>Contribution: organisation=mat,FACT2=0.5<br/>Portfolio EDEND: 2015-01-09<br/>Publisher name: Elsevier <br /> publication_forum:67104

PY - 2015/6

Y1 - 2015/6

N2 - The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and sigma-point methods to approximate the intractable Gaussian expectations in the variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix.

AB - The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and sigma-point methods to approximate the intractable Gaussian expectations in the variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix.

U2 - 10.1016/j.sigpro.2014.12.013

DO - 10.1016/j.sigpro.2014.12.013

M3 - Article

VL - 111

SP - 124

EP - 136

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -