NDLI: Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signals Case

Content Provider	IEEE Xplore Digital Library
Author	Vallet, P. Loubaton, P. Mestre, X.
Copyright Year	1963
Abstract	We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimension M and the number of snapshots N converge to +∞ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values of M and N . The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.
Sponsorship	IEEE Information Theory Society
Starting Page	1043
Ending Page	1068
Page Count	26
File Size	10221472
File Format	PDF
ISSN	00189448
Volume Number	58
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Eigenvalues and eigenfunctions Correlation Noise Mathematical model Covariance matrix Estimation Vectors subspace estimation MUSIC random matrix theory
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Improved subspace estimation for multivariate observations of high dimension: the deterministic signals case

Improved Estimation of Eigenvalues and Eigenvectors of Covariance Matrices Using Their Sample Estimates

Robust Estimates of Covariance Matrices in the Large Dimensional Regime

Fluctuations of an Improved Population Eigenvalue Estimator in Sample Covariance Matrix Models

Determining the Intrinsic Dimension of a Hyperspectral Image Using Random Matrix Theory

Fluctuations of Spiked Random Matrix Models and Failure Diagnosis in Sensor Networks

Minimax Rank Estimation for Subspace Tracking

Source Enumeration Via MDL Criterion Based on Linear Shrinkage Estimation of Noise Subspace Covariance Matrix

Asymptotic Eigenvalue Density of Noise Covariance Matrices

Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signals Case

Similar Documents

Improved subspace estimation for multivariate observations of high dimension: the deterministic signals case

Improved Estimation of Eigenvalues and Eigenvectors of Covariance Matrices Using Their Sample Estimates

Robust Estimates of Covariance Matrices in the Large Dimensional Regime

Fluctuations of an Improved Population Eigenvalue Estimator in Sample Covariance Matrix Models

Determining the Intrinsic Dimension of a Hyperspectral Image Using Random Matrix Theory

Fluctuations of Spiked Random Matrix Models and Failure Diagnosis in Sensor Networks

Minimax Rank Estimation for Subspace Tracking

Source Enumeration Via MDL Criterion Based on Linear Shrinkage Estimation of Noise Subspace Covariance Matrix

Asymptotic Eigenvalue Density of Noise Covariance Matrices

Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signals Case