Impact of space-time covariance estimation errors on a parahermitian matrix EVD

Research output: Contribution to conferencePaper

1 Citation (Scopus)

Abstract

This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations.

Conference

Conference10th IEEE Workshop on Sensor Array and Multichannel Signal Processing
Abbreviated titleSAM 2018
CountryUnited Kingdom
CitySheffield
Period8/07/1811/07/18

Fingerprint

Covariance Estimation
Estimation Error
Covariance matrix
Eigenvalues and eigenfunctions
Error analysis
Space-time
Eigenvalue
Perturbation
Eigenvector
Subspace
Eigenvalue Decomposition
Matrix Decomposition
Decomposition
Norm
Simulation

Keywords

  • broadband array processing
  • space-time convariance estimation
  • parahermitian matrix
  • eigenvalue decomposition

Cite this

Delaosa, C., Coutts, F. K., Pestana, J., & Weiss, S. (2018). Impact of space-time covariance estimation errors on a parahermitian matrix EVD. 1-5. Paper presented at 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, Sheffield, United Kingdom.
Delaosa, Connor ; Coutts, Fraser K. ; Pestana, Jennifer ; Weiss, Stephan. / Impact of space-time covariance estimation errors on a parahermitian matrix EVD. Paper presented at 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, Sheffield, United Kingdom.5 p.
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title = "Impact of space-time covariance estimation errors on a parahermitian matrix EVD",
abstract = "This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations.",
keywords = "broadband array processing, space-time convariance estimation, parahermitian matrix, eigenvalue decomposition",
author = "Connor Delaosa and Coutts, {Fraser K.} and Jennifer Pestana and Stephan Weiss",
note = "{\circledC} 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works; 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, SAM 2018 ; Conference date: 08-07-2018 Through 11-07-2018",
year = "2018",
month = "7",
day = "8",
language = "English",
pages = "1--5",

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Delaosa, C, Coutts, FK, Pestana, J & Weiss, S 2018, 'Impact of space-time covariance estimation errors on a parahermitian matrix EVD' Paper presented at 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, Sheffield, United Kingdom, 8/07/18 - 11/07/18, pp. 1-5.

Impact of space-time covariance estimation errors on a parahermitian matrix EVD. / Delaosa, Connor; Coutts, Fraser K.; Pestana, Jennifer; Weiss, Stephan.

2018. 1-5 Paper presented at 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, Sheffield, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Impact of space-time covariance estimation errors on a parahermitian matrix EVD

AU - Delaosa, Connor

AU - Coutts, Fraser K.

AU - Pestana, Jennifer

AU - Weiss, Stephan

N1 - © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

PY - 2018/7/8

Y1 - 2018/7/8

N2 - This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations.

AB - This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on the norm of the estimation error in the space-time covariance matrix, while the perturbation of eigenvector subspaces can additionally be influenced by the spectral distance of the eigenvalues. We confirm these theoretical results by simulations.

KW - broadband array processing

KW - space-time convariance estimation

KW - parahermitian matrix

KW - eigenvalue decomposition

M3 - Paper

SP - 1

EP - 5

ER -

Delaosa C, Coutts FK, Pestana J, Weiss S. Impact of space-time covariance estimation errors on a parahermitian matrix EVD. 2018. Paper presented at 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, Sheffield, United Kingdom.