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Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs

Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs
Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs
Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for implementing grid-based Bayesian estimation which largely sidesteps the severe computational expense that has prevented the widespread use of such methods. The method represents the evolution of the probability density function (PDF) in phase space, px(x?,t),discretized on a fixed Cartesian grid over all of phase space, and consists of two main steps: (i) between measurement times, px(x?,t) is evolved via numerical discretization of the Kolmogorov forward equation, using a Godunov method with second-order corner transport upwind correction and a total variation diminishing flux limiter; (ii) at measurement times, px(x?,t) is updated via Bayes’ theorem. Computational economy is achieved by exploiting the localized nature of px(x?,t). An ordered list of cells with non-negligible probability, as well as their immediate neighbors, is created and updated, and the PDF evolution is tracked only on these active cells.
nonlinear/non-gaussian observer design, grid-based bayesian estimation
0005-1098
1286-1290
Bewley, T.R.
cd9487d6-d278-4d05-a34f-5581b81e7542
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Bewley, T.R.
cd9487d6-d278-4d05-a34f-5581b81e7542
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718

Bewley, T.R. and Sharma, A.S. (2012) Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs. Automatica, 48 (7), 1286-1290. (doi:10.1016/j.automatica.2012.02.039).

Record type: Article

Abstract

Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for implementing grid-based Bayesian estimation which largely sidesteps the severe computational expense that has prevented the widespread use of such methods. The method represents the evolution of the probability density function (PDF) in phase space, px(x?,t),discretized on a fixed Cartesian grid over all of phase space, and consists of two main steps: (i) between measurement times, px(x?,t) is evolved via numerical discretization of the Kolmogorov forward equation, using a Godunov method with second-order corner transport upwind correction and a total variation diminishing flux limiter; (ii) at measurement times, px(x?,t) is updated via Bayes’ theorem. Computational economy is achieved by exploiting the localized nature of px(x?,t). An ordered list of cells with non-negligible probability, as well as their immediate neighbors, is created and updated, and the PDF evolution is tracked only on these active cells.

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e-pub ahead of print date: 3 May 2012
Published date: July 2012
Keywords: nonlinear/non-gaussian observer design, grid-based bayesian estimation
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 350131
URI: https://eprints.soton.ac.uk/id/eprint/350131
ISSN: 0005-1098
PURE UUID: e3f943be-fc42-4f1b-9927-554a74fefb92
ORCID for A.S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 25 Mar 2013 10:11
Last modified: 20 Jul 2019 00:39

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Contributors

Author: T.R. Bewley
Author: A.S. Sharma ORCID iD

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