An Iteratively Reweighted Instrumental-Variable Estimator for Robust 3-D AOA Localization in Impulsive Noise

This paper considers the problem of robust three-dimensional (3-D) angle-of-arrival (AOA) source localization in the presence of impulsive <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-stable noise based on the <inline-formula>&...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 18; pp. 4795 - 4808
Main Authors: Nguyen, Ngoc Hung, Dogancay, Kutluyil, Kuruoglu, Ercan Engin
Format: Journal Article
Language:English
Published: New York IEEE 15.09.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Angle of arrival
Azimuth
Computer simulation
Correlation analysis
Covariance
Cramer-Rao bounds
Dispersion
Elevation angle
Estimation
Formulas (mathematics)
instrumental variables
Instruments
iteratively reweighted least-squares
least <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> l_p</tex-math> </inline-formula>-norm
Least squares
Localization
Lower bounds
Matrix algebra
Matrix methods
Minimization
Noise
Noise measurement
Optimization
pseudolinear estimation
robust estimation
source localization
Three-dimensional displays
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:This paper considers the problem of robust three-dimensional (3-D) angle-of-arrival (AOA) source localization in the presence of impulsive <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-stable noise based on the <inline-formula><tex-math notation="LaTeX">l_p</tex-math></inline-formula>-norm minimization criterion. The iteratively reweighted least-squares algorithm (IRLS) is a well-known technique for solving <inline-formula><tex-math notation="LaTeX">l_p</tex-math></inline-formula>-norm minimization with the desirable global convergence property. Adopting the IRLS for 3-D AOA localization requires nonlinear-to-pseudolinear transformation of azimuth and elevation angle measurement equations, thus resulting in a new variant of the IRLS, called the iteratively reweighted pseudolinear least-squares estimator (IRPLE). Unfortunately, there exists correlation between the measurement matrix and noise vector in the pseudolinear measurement equations, which consequently makes the IRPLE biased. To counter the bias problem of the IRPLE, a new iteratively reweighted instrumental-variable estimator (IRIVE) is proposed based on the exploitation of instrumental variables. The IRIVE is analytically shown to achieve the theoretical covariance of the general least <inline-formula><tex-math notation="LaTeX">l_p</tex-math></inline-formula>-norm estimation. Extensive simulation studies are presented to demonstrate the performance advantages of the IRIVE over the IRPLE as well as other existing least-squares and least <inline-formula><tex-math notation="LaTeX">l_p</tex-math></inline-formula>-norm estimators. The IRIVE is observed to produce nearly unbiased estimates with mean squared error performance very close to the Cramér-Rao lower bound.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2931210