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Generalized least squares for ESPRIT-type direction of arrival estimation

: Steinwandt, Jens; Römer, Florian; Haardt, Martin


IEEE Signal Processing Letters 24 (2017), Nr.11, S.1681-1685
ISSN: 1070-9908
ISSN: 1558-2361
Fraunhofer IIS ()
Richtungsschätzung (DoA)

The key task in ESPRIT-based parameter estimation is finding the solution to the shift invariance equation (SIE), which is often an overdetermined, linear system of equations. Additional structure is imposed if the two selection matrices, applied to an estimate of the signal subspace, overlap such that the subspace estimation errors on both sides of the SIE are highly correlated. In this paper, we propose a novel SIE solution for Standard ESPRIT and Unitary ESPRIT based on generalized least squares (GLS), assuming a uniform linear array (ULA) and maximum subarray overlap. GLS directly incorporates the statistics of the subspace estimation error via its covariance matrix, which is found analytically by a first-order perturbation expansion. As the subspace error covariance matrix is not invertible, we introduce a regularization with a clever choice of the regularization parameter. The resulting GLS-based Standard ESPRIT and Unitary ESPRIT algorithms achieve a superior performance over existing ESPRIT-type methods and almost attain the Cramér-Rao bound (CRB).