Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem wi...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 68; pp. 5322 - 5333
Main Authors: Weiss, Amir, Yeredor, Arie
Format: Journal Article
Language:English
Published: New York IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Asymptotic properties
Calibration
Computer simulation
Covariance matrices
Covariance matrix
Cramér-Rao lower bound
direction-of-arrival
Estimates
gain estimation
Iterative methods
Linear arrays
Lower bounds
Mathematical models
maximum likelihood
Maximum likelihood estimates
Maximum likelihood estimation
Narrowband
Offsets
Optimization
OWL
Parameters
phase estimation
self calibration
Sensor array processing
Sensor arrays
Transmission line matrix methods
weighted least squares
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cramér-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.3014610