### 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 language | English (US) |
---|---|

Pages (from-to) | 1623-1633 |

Number of pages | 11 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 31 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2008 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Guidance, Control, and Dynamics*,

*31*(6), 1623-1633. https://doi.org/10.2514/1.36247

}

*Journal of Guidance, Control, and Dynamics*, vol. 31, no. 6, pp. 1623-1633. https://doi.org/10.2514/1.36247

**Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models.** / Terejanu, Gabriel; Singla, Puneet; Singh, Tarunraj; Scott, Peter D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models

AU - Terejanu, Gabriel

AU - Singla, Puneet

AU - Singh, Tarunraj

AU - Scott, Peter D.

PY - 2008/11/1

Y1 - 2008/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=57249090646&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57249090646&partnerID=8YFLogxK

U2 - 10.2514/1.36247

DO - 10.2514/1.36247

M3 - Article

AN - SCOPUS:57249090646

VL - 31

SP - 1623

EP - 1633

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 6

ER -