Polynomial chaos based method for state and parameter estimation

Reza Madankan; Puneet Singla; Tarunraj Singh; Peter Scott

doi:10.1109/acc.2012.6315359

Polynomial chaos based method for state and parameter estimation

Reza Madankan, Puneet Singla, Tarunraj Singh, Peter Scott

Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

This paper presents a method for state and parameter estimation based on generalized polynomial chaos theory and Bayes' theorem. Generalized polynomial chaos theory (gPC) is used to propagate the joint probability density functions (pdfs) for parameter and state through forward dynamic model while the Bayes' rule is used to fuse the prior pdfs obtained through the gPC process with sensor observations to characterize non-Gaussian posterior density functions for state and parameters. Furthermore, a minimum variance based estimator is also derived which makes use of the gPC process to compute the mean and variance of actual non-Gaussian pdf. Numerical experiments involving two benchmark problems are considered to illustrate the effectiveness of the proposed ideas.

Original language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6358-6363
Number of pages	6
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315359
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2012.6315359

Cite this

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title = "Polynomial chaos based method for state and parameter estimation",

abstract = "This paper presents a method for state and parameter estimation based on generalized polynomial chaos theory and Bayes' theorem. Generalized polynomial chaos theory (gPC) is used to propagate the joint probability density functions (pdfs) for parameter and state through forward dynamic model while the Bayes' rule is used to fuse the prior pdfs obtained through the gPC process with sensor observations to characterize non-Gaussian posterior density functions for state and parameters. Furthermore, a minimum variance based estimator is also derived which makes use of the gPC process to compute the mean and variance of actual non-Gaussian pdf. Numerical experiments involving two benchmark problems are considered to illustrate the effectiveness of the proposed ideas.",

author = "Reza Madankan and Puneet Singla and Tarunraj Singh and Peter Scott",

year = "2012",

doi = "10.1109/acc.2012.6315359",

language = "English (US)",

isbn = "9781457710957",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "6358--6363",

booktitle = "2012 American Control Conference, ACC 2012",

address = "United States",

}

Madankan, R, Singla, P, Singh, T & Scott, P 2012, Polynomial chaos based method for state and parameter estimation. in 2012 American Control Conference, ACC 2012., 6315359, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 6358-6363, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6315359

Polynomial chaos based method for state and parameter estimation. / Madankan, Reza; Singla, Puneet; Singh, Tarunraj et al.
2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 6358-6363 6315359 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Polynomial chaos based method for state and parameter estimation

AU - Madankan, Reza

AU - Singla, Puneet

AU - Singh, Tarunraj

AU - Scott, Peter

PY - 2012

Y1 - 2012

N2 - This paper presents a method for state and parameter estimation based on generalized polynomial chaos theory and Bayes' theorem. Generalized polynomial chaos theory (gPC) is used to propagate the joint probability density functions (pdfs) for parameter and state through forward dynamic model while the Bayes' rule is used to fuse the prior pdfs obtained through the gPC process with sensor observations to characterize non-Gaussian posterior density functions for state and parameters. Furthermore, a minimum variance based estimator is also derived which makes use of the gPC process to compute the mean and variance of actual non-Gaussian pdf. Numerical experiments involving two benchmark problems are considered to illustrate the effectiveness of the proposed ideas.

AB - This paper presents a method for state and parameter estimation based on generalized polynomial chaos theory and Bayes' theorem. Generalized polynomial chaos theory (gPC) is used to propagate the joint probability density functions (pdfs) for parameter and state through forward dynamic model while the Bayes' rule is used to fuse the prior pdfs obtained through the gPC process with sensor observations to characterize non-Gaussian posterior density functions for state and parameters. Furthermore, a minimum variance based estimator is also derived which makes use of the gPC process to compute the mean and variance of actual non-Gaussian pdf. Numerical experiments involving two benchmark problems are considered to illustrate the effectiveness of the proposed ideas.

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M3 - Conference contribution

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SN - 9781457710957

T3 - Proceedings of the American Control Conference

SP - 6358

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BT - 2012 American Control Conference, ACC 2012

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -

Polynomial chaos based method for state and parameter estimation

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