### Abstract

This paper focuses on the development of analytical methods for uncertainty quantification of system matrices obtained by the Eigenvalue Realization Algorithm (ERA) to quantify the effect of noise in the observation data. Starting from first principles, analytical expressions are presented for the probability density function for norm of system matrix by application of standard results in random matrix theory. Assuming the observations to be corrupted by zero mean Gaussian noise, the distribution for the Hankel matrix is represented by the nonsymmetric Wishart distribution. From the Wishart distribution, the joint density function of the singular value of the Hankel matrix are constructed. These expressions enable us to construct the probability density functions for the norm of identified system matrices. Numerical examples illustrate the applications of ideas presented in the paper.

Original language | English (US) |
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Title of host publication | Astrodynamics 2015 |

Editors | James D. Turner, Geoff G. Wawrzyniak, William Todd Cerven, Manoranjan Majji |

Publisher | Univelt Inc. |

Pages | 2219-2241 |

Number of pages | 23 |

ISBN (Print) | 9780877036296 |

State | Published - Jan 1 2016 |

Event | AAS/AIAA Astrodynamics Specialist Conference, ASC 2015 - Vail, United States Duration: Aug 9 2015 → Aug 13 2015 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 156 |

ISSN (Print) | 0065-3438 |

### Other

Other | AAS/AIAA Astrodynamics Specialist Conference, ASC 2015 |
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Country | United States |

City | Vail |

Period | 8/9/15 → 8/13/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Astrodynamics 2015*(pp. 2219-2241). (Advances in the Astronautical Sciences; Vol. 156). Univelt Inc..

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*Astrodynamics 2015.*Advances in the Astronautical Sciences, vol. 156, Univelt Inc., pp. 2219-2241, AAS/AIAA Astrodynamics Specialist Conference, ASC 2015, Vail, United States, 8/9/15.

**Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm.** / Vishwajeet, Kumar; Singla, Puneet; Majji, Manoranjan.

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

TY - GEN

T1 - Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm

AU - Vishwajeet, Kumar

AU - Singla, Puneet

AU - Majji, Manoranjan

PY - 2016/1/1

Y1 - 2016/1/1

N2 - This paper focuses on the development of analytical methods for uncertainty quantification of system matrices obtained by the Eigenvalue Realization Algorithm (ERA) to quantify the effect of noise in the observation data. Starting from first principles, analytical expressions are presented for the probability density function for norm of system matrix by application of standard results in random matrix theory. Assuming the observations to be corrupted by zero mean Gaussian noise, the distribution for the Hankel matrix is represented by the nonsymmetric Wishart distribution. From the Wishart distribution, the joint density function of the singular value of the Hankel matrix are constructed. These expressions enable us to construct the probability density functions for the norm of identified system matrices. Numerical examples illustrate the applications of ideas presented in the paper.

AB - This paper focuses on the development of analytical methods for uncertainty quantification of system matrices obtained by the Eigenvalue Realization Algorithm (ERA) to quantify the effect of noise in the observation data. Starting from first principles, analytical expressions are presented for the probability density function for norm of system matrix by application of standard results in random matrix theory. Assuming the observations to be corrupted by zero mean Gaussian noise, the distribution for the Hankel matrix is represented by the nonsymmetric Wishart distribution. From the Wishart distribution, the joint density function of the singular value of the Hankel matrix are constructed. These expressions enable us to construct the probability density functions for the norm of identified system matrices. Numerical examples illustrate the applications of ideas presented in the paper.

UR - http://www.scopus.com/inward/record.url?scp=85007369559&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007369559&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780877036296

T3 - Advances in the Astronautical Sciences

SP - 2219

EP - 2241

BT - Astrodynamics 2015

A2 - Turner, James D.

A2 - Wawrzyniak, Geoff G.

A2 - Cerven, William Todd

A2 - Majji, Manoranjan

PB - Univelt Inc.

ER -