Abstract
The problem of estimating a covariance matrix plays crucial in
signal processing and other related fields. This paper proposes a novel
bilinear shrinkage estimation by simultaneously regularizing the sample
mean and the SCM via the linear shrinkage technique. Through a one-one
mapping of the weight parameters, the bilinear shrinkage estimation can
be expressed as a generalization version of the well-known linear
shrinkage estimation. Available covariance matrix estimators are
developed by parametric and nonparametric methods for different target
matrices. In our numerical simulations, the bilinear shrinkage
estimators can reach lower Frobenius losses compared with the existing
linear shrinkage estimators. Moreover, the proposed covariance matrix
estimators can work well in application to large array signal
processing.
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