High-Resolution Source Localization Algorithm Based on the Conjugate Gradient
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Research Article High-Resolution Source Localization Algorithm Based on the Conjugate Gradient Hichem Semira,1 Hocine Belkacemi,2 and Sylvie Marcos2 1 D´ epartement 2 Laboratoire
d’´electronique, Universit´e d’Annaba, BP 12, Sidi Amar, Annaba 23000, Algeria des Signaux et Syst`emes (LSS), CNRS, 3 Rue Joliot-Curie, Plateau du Moulon, 91192 Gif-sur-Yvette Cedex, France
Received 28 September 2006; Revised 5 January 2007; Accepted 25 March 2007 Recommended by Nicola Mastronardi This paper proposes a new algorithm for the direction of arrival (DOA) estimation of P radiating sources. Unlike the classical subspace-based methods, it does not resort to the eigendecomposition of the covariance matrix of the received data. Indeed, the proposed algorithm involves the building of the signal subspace from the residual vectors of the conjugate gradient (CG) method. This approach is based on the same recently developed procedure which uses a noneigenvector basis derived from the auxiliary vectors (AV). The AV basis calculation algorithm is replaced by the residual vectors of the CG algorithm. Then, successive orthogonal gradient vectors are derived to form a basis of the signal subspace. A comprehensive performance comparison of the proposed algorithm with the well-known MUSIC and ESPRIT algorithms and the auxiliary vectors (AV)-based algorithm was conducted. It shows clearly the high performance of the proposed CG-based method in terms of the resolution capability of closely spaced uncorrelated and correlated sources with a small number of snapshots and at low signal-to-noise ratio (SNR). Copyright © 2007 Hichem Semira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Array processing deals with the problem of extracting information from signals received simultaneously by an array of sensors. In many fields such as radar, underwater acoustics and geophysics, the information of interest is the direction of arrival (DOA) of waves transmitted from radiating sources and impinging on the sensor array. Over the years, many approaches to the problem of source DOA estimation have been proposed [1]. The subspace-based methods, which resort to the decomposition of the observation space into a noise subspace and a source subspace, have proved to have high-resolution (HR) capabilities and to yield accurate estimates. Among the most famous HR methods are MUSIC [2], ESPRIT [3], MIN-NORM [4], and WSF [5]. The performance of these methods however degrades substantially in the case of closely spaced sources with a small number of snapshots and at a low SNR. These methods resort to the eigendecomposition (ED) of the covariance matrix of the received signals or a singular value decomposition (SVD) of the data matrix to build the signal or noise subspace, which is computationally intensive specially when the dimension of these matrices is large.
The conjugate
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