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

Kumar Vishwajeet, Puneet Singla, Manoranjan Majji

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationAstrodynamics 2015
EditorsJames D. Turner, Geoff G. Wawrzyniak, William Todd Cerven, Manoranjan Majji
PublisherUnivelt Inc.
Pages2219-2241
Number of pages23
ISBN (Print)9780877036296
StatePublished - Jan 1 2016
EventAAS/AIAA Astrodynamics Specialist Conference, ASC 2015 - Vail, United States
Duration: Aug 9 2015Aug 13 2015

Publication series

NameAdvances in the Astronautical Sciences
Volume156
ISSN (Print)0065-3438

Other

OtherAAS/AIAA Astrodynamics Specialist Conference, ASC 2015
CountryUnited States
CityVail
Period8/9/158/13/15

Fingerprint

eigenvalue
noise measurement
eigenvalues
matrix
matrices
Probability density function
probability density functions
norms
probability density function
matrix theory
random noise
effect
analytical method
distribution

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Vishwajeet, K., Singla, P., & Majji, M. (2016). Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm. In J. D. Turner, G. G. Wawrzyniak, W. T. Cerven, & M. Majji (Eds.), Astrodynamics 2015 (pp. 2219-2241). (Advances in the Astronautical Sciences; Vol. 156). Univelt Inc..
Vishwajeet, Kumar ; Singla, Puneet ; Majji, Manoranjan. / Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm. Astrodynamics 2015. editor / James D. Turner ; Geoff G. Wawrzyniak ; William Todd Cerven ; Manoranjan Majji. Univelt Inc., 2016. pp. 2219-2241 (Advances in the Astronautical Sciences).
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Vishwajeet, K, Singla, P & Majji, M 2016, Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm. in JD Turner, GG Wawrzyniak, WT Cerven & M Majji (eds), 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.

Astrodynamics 2015. ed. / James D. Turner; Geoff G. Wawrzyniak; William Todd Cerven; Manoranjan Majji. Univelt Inc., 2016. p. 2219-2241 (Advances in the Astronautical Sciences; Vol. 156).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Vishwajeet K, Singla P, Majji M. Random matrix based approach to quantify the effect of measurement noise on model identified by the eigenvalue realization algorithm. In Turner JD, Wawrzyniak GG, Cerven WT, Majji M, editors, Astrodynamics 2015. Univelt Inc. 2016. p. 2219-2241. (Advances in the Astronautical Sciences).