Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models

Gabriel Terejanu, Puneet Singla, Tarunraj Singh, Peter D. Scott

Research output: Contribution to journalArticle

118 Citations (Scopus)

Abstract

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different components of a Gaussian-mixture model for uncertainty propagation through nonlinear system. The first method updates the weights such that they minimize the integral square difference between the true forecast probability density function and its Gaussian-sum approximation. The second method uses the Fokker-Planck-Kolmogorov equation error as feedback to adapt for the amplitude of different Gaussian components while solving a quadratic programming problem. The proposed methods are applied to a variety of problems in the open literature and are argued to be an excellent candidate for higher-dimensional uncertainty-propagation problems.

Original languageEnglish (US)
Pages (from-to)1623-1633
Number of pages11
JournalJournal of Guidance, Control, and Dynamics
Volume31
Issue number6
DOIs
StatePublished - Nov 1 2008

Fingerprint

Uncertainty Propagation
Nonlinear Dynamic System
Gaussian Mixture Model
Probability density function
Dynamical systems
probability density function
propagation
Nonlinear systems
Nonlinear Systems
Update
probability density functions
nonlinear systems
Fokker Planck equation
Transition Density
Kolmogorov Equation
Gaussian Function
Quadratic programming
Fokker-Planck Equation
quadratic programming
Quadratic Programming

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Terejanu, Gabriel ; Singla, Puneet ; Singh, Tarunraj ; Scott, Peter D. / Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models. In: Journal of Guidance, Control, and Dynamics. 2008 ; Vol. 31, No. 6. pp. 1623-1633.
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Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models. / Terejanu, Gabriel; Singla, Puneet; Singh, Tarunraj; Scott, Peter D.

In: Journal of Guidance, Control, and Dynamics, Vol. 31, No. 6, 01.11.2008, p. 1623-1633.

Research output: Contribution to journalArticle

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