Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems

Kumar Vishwajeet; Puneet Singla

doi:10.1109/acc.2013.6580001

Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems

Kumar Vishwajeet, Puneet Singla

Aerospace Engineering

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

6 Scopus citations

Abstract

A new method is proposed to determine the number of components that are sufficient to estimate the probability density function of a non-linear dynamic system using Gaussian sum filter. This method is based upon the combination of L₁ and L₂ norm. While L₁ norm tries to shift the solution towards one of the vertices of the simplex, thus, minimizing the number of non-zero quantities, the L₂ norm tries to reduce the error to as low as possible. Unlike previous methods, the method proposed in this paper is simple and computationally less expensive.

Original language	English (US)
Title of host publication	2013 American Control Conference, ACC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1213-1218
Number of pages	6
ISBN (Print)	9781479901777
DOIs	https://doi.org/10.1109/acc.2013.6580001
State	Published - 2013
Event	2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013

Publication series

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

Other

Other	2013 1st American Control Conference, ACC 2013
Country/Territory	United States
City	Washington, DC
Period	6/17/13 → 6/19/13

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2013.6580001

Cite this

Vishwajeet, K., & Singla, P. (2013). Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems. In 2013 American Control Conference, ACC 2013 (pp. 1213-1218). Article 6580001 (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2013.6580001

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title = "Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems",

abstract = "A new method is proposed to determine the number of components that are sufficient to estimate the probability density function of a non-linear dynamic system using Gaussian sum filter. This method is based upon the combination of L1 and L2 norm. While L1 norm tries to shift the solution towards one of the vertices of the simplex, thus, minimizing the number of non-zero quantities, the L2 norm tries to reduce the error to as low as possible. Unlike previous methods, the method proposed in this paper is simple and computationally less expensive.",

author = "Kumar Vishwajeet and Puneet Singla",

year = "2013",

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language = "English (US)",

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series = "Proceedings of the American Control Conference",

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note = "2013 1st American Control Conference, ACC 2013 ; Conference date: 17-06-2013 Through 19-06-2013",

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Vishwajeet, K & Singla, P 2013, Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems. in 2013 American Control Conference, ACC 2013., 6580001, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1213-1218, 2013 1st American Control Conference, ACC 2013, Washington, DC, United States, 6/17/13. https://doi.org/10.1109/acc.2013.6580001

Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems. / Vishwajeet, Kumar; Singla, Puneet.
2013 American Control Conference, ACC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1213-1218 6580001 (Proceedings of the American Control Conference).

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

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AU - Singla, Puneet

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N2 - A new method is proposed to determine the number of components that are sufficient to estimate the probability density function of a non-linear dynamic system using Gaussian sum filter. This method is based upon the combination of L1 and L2 norm. While L1 norm tries to shift the solution towards one of the vertices of the simplex, thus, minimizing the number of non-zero quantities, the L2 norm tries to reduce the error to as low as possible. Unlike previous methods, the method proposed in this paper is simple and computationally less expensive.

AB - A new method is proposed to determine the number of components that are sufficient to estimate the probability density function of a non-linear dynamic system using Gaussian sum filter. This method is based upon the combination of L1 and L2 norm. While L1 norm tries to shift the solution towards one of the vertices of the simplex, thus, minimizing the number of non-zero quantities, the L2 norm tries to reduce the error to as low as possible. Unlike previous methods, the method proposed in this paper is simple and computationally less expensive.

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ER -

Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems

Abstract

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Other

All Science Journal Classification (ASJC) codes

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