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

Connor Delaosa; Fraser K. Coutts; Jennifer Pestana; Stephan Weiss

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

Connor Delaosa, Fraser K. Coutts, Jennifer Pestana, Stephan Weiss

Research output: Contribution to conference › Paper › peer-review

8 Citations (Scopus)

52 Downloads (Pure)

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.

Original language	English
Pages	1-5
Number of pages	5
Publication status	Published - 8 Jul 2018
Event	10th IEEE Workshop on Sensor Array and Multichannel Signal Processing - Sheffield, United Kingdom Duration: 8 Jul 2018 → 11 Jul 2018

Conference

Conference	10th IEEE Workshop on Sensor Array and Multichannel Signal Processing
Abbreviated title	SAM 2018
Country/Territory	United Kingdom
City	Sheffield
Period	8/07/18 → 11/07/18

Keywords

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

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Delaosa-etal-SAM-2018-Impact-of-space-time-covariance-estimation-errors-on-a-parahermitian-matrix-EVDAccepted author manuscript, 408 KB

Best Student Paper Award
Delaosa, Connor (Recipient), Coutts, Fraser Kenneth (Recipient), Pestana, Jennifer (Recipient) & Weiss, Stephan (Recipient), 2018
Prize: Prize (including medals and awards)

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Cite this

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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",

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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

T2 - 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing

Y2 - 8 July 2018 through 11 July 2018

ER -

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

Abstract

Conference

Keywords

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Prizes

Best Student Paper Award

Cite this