Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Gain calibration methods for radio telescope arrays
IEEE Transactions on Signal Processing
Estimation of sensor gain and phase
IEEE Transactions on Signal Processing
“Almost blind” steering vector estimation usingsecond-order moments
IEEE Transactions on Signal Processing
Covariance Matrix Estimation With Heterogeneous Samples
IEEE Transactions on Signal Processing
A subspace method for estimating sensor gains and phases
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A Bayesian approach to auto-calibration for parametric array signalprocessing
IEEE Transactions on Signal Processing
Self-Calibration for the LOFAR Radio Astronomical Array
IEEE Transactions on Signal Processing
Spatial signature estimation for uniform linear arrays with unknownreceiver gains and phases
IEEE Transactions on Signal Processing
A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments
IEEE Transactions on Signal Processing
Steering vector estimation in uncalibrated arrays
IEEE Transactions on Signal Processing
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We consider the problem of estimating the gains and phases of the RF channels of a M-element transmitting array, based on a calibration procedure where M orthogonal signals are sent through M orthogonal beams and received on a single antenna. The received data vector obeys a linear model of the type y=AFg+n where A is an unknown complex scalar accounting for propagation loss and g is the vector of unknown complex gains. In order to improve the performance of the least-squares (LS) estimator at low signal to noise ratio (SNR), we propose to exploit knowledge of the nominal value of g, viz g@?. Towards this end, two approaches are presented. First, a Bayesian approach is advocated where A and g are considered as random variables, with a non-informative prior distribution for A and a Gaussian prior distribution for g. The posterior distributions of the unknown random variables are derived and a Gibbs sampling strategy is presented that enables one to generate samples distributed according to these posterior distributions, leading to the minimum mean-square error (MMSE) estimator. A second approach consists in solving a constrained least-squares problem in which h=Ag is constrained to be close to a scaled version of g@?. This second approach yields a closed-form solution, which amounts to a linear combination of g@? and the LS estimator. Numerical simulations show that the two new estimators significantly outperform the conventional LS estimator, especially at low SNR.