Generalized Least Squares for ESPRIT-Type Direction of Arrival Estimation

• Published in: IEEE signal processing letters 2017-11, Vol.24 (11), p.1681-1685
• Main Authors: Steinwandt, Jens, Roemer, Florian, Haardt, Martin
• Format: Article
• Language: English
• Subjects: Covariance matrices; Direction of arrival (DOA) estimation; Direction-of-arrival estimation; ESPRIT; Estimation error; generalized least squares (GLS); Linear systems; shift invariance equation (SIE); Signal processing algorithms
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2017.2751303

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 letter, 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).