Oblique Projections for Direction-of-Arrival Estimation With Prior Knowledge

• Published in: IEEE transactions on signal processing Vol. 56; no. 4; pp. 1374 - 1387
• Main Authors: Boyer, R., Bouleux, G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Blocking; Computer Science; Conferences; Covariance; Cramer-Rao bounds; CramÉr-Rao bound; Detection, estimation, filtering, equalization, prediction; Direction of arrival estimation; Engineering Sciences; Exact sciences and technology; Information, signal and communications theory; Manifolds; Multiple signal classification; MUSIC algorithm; orthogonal and oblique projectors; Passive radar; Position (location); Position measurement; prior knowledge of DOA; Projection; Radar applications; Seismology; Sensor arrays; Signal and communications theory; Signal and Image processing; Signal to noise ratio; Signal, noise; Sonar; Steering; Studies; Telecommunications and information theory; Direction-of-arrival estimation; Parameter estimation; Signal estimation; Subspace method; MUSIC algorithm; Algorithm; orthogonal and oblique projectors; Orthogonal projection; Covariance; Source localization; A priori estimation; prior knowledge of DOA; Antenna array; Target detection; Cramér-Rao bound; Cramer Rao inequality; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.909348

Estimation of directions-of-arrival (DOA) is an important problem in various applications and a priori knowledge on the source location is sometimes available. To exploit this information, standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known DOA. In this paper, we derive and analyze the Cramer-Rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown DOA are closely spaced and the associated sources are uncorrelated (block-diagonal source covariance). To fill this need, we propose to integrate a priori known locations of several sources into the MUSIC algorithm based on oblique projection of the steering manifold. Finally, we show that the proposed approach is able to almost completely cancel the influence of the known DOA on the unknown ones for block-diagonal source covariance and for sufficient signal-to-noise ratio (SNR).