Journal ArticleDOI
Sensor array processing based on subspace fitting
Mats Viberg,Bjorn Ottersten +1 more
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TLDR
It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method.Abstract:
Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. >read more
Citations
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Journal ArticleDOI
Two decades of array signal processing research: the parametric approach
Hamid Krim,Mats Viberg +1 more
TL;DR: The article consists of background material and of the basic problem formulation, and introduces spectral-based algorithmic solutions to the signal parameter estimation problem and contrast these suboptimal solutions to parametric methods.
Book
Spectral analysis of signals
Petre Stoica,Randolph L. Moses +1 more
TL;DR: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra.
Journal ArticleDOI
Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations
TL;DR: This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them.
Journal ArticleDOI
Multiple dipole modeling and localization from spatio-temporal MEG data
TL;DR: The authors present general descriptive models for spatiotemporal MEG (magnetoencephalogram) data and show the separability of the linear moment parameters and nonlinear location parameters in the MEG problem and present a subspace methodology and computational approach to solving the conventional least-squares problem.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
Detection of signals by information theoretic criteria
Mati Wax,Thomas Kailath +1 more
TL;DR: Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.
Journal ArticleDOI
MUSIC, maximum likelihood, and Cramer-Rao bound
Petre Stoica,Nehorai Arye +1 more
TL;DR: The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established.
Journal ArticleDOI
An Analysis of the Total Least Squares Problem
Gene H. Golub,Charles Van Loan +1 more
TL;DR: In this article, a singular value decomposition analysis of the TLS problem is presented, which provides a measure of the underlying problem's sensitivity and its relationship to ordinary least squares regression.
Journal ArticleDOI
Maximum likelihood localization of multiple sources by alternating projection
I. Ziskind,Mati Wax +1 more
TL;DR: An algorithm, referred to as APM, for computing the maximum-likelihood estimator of the locations of simple sources in passive sensor arrays is presented and the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios.
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