Digital Signal Processing 19 (2009) 452–462 www.elsevier.com/locate/dsp Underwater acoustic azimuth and elevation angle estimation using spatial invariance of two identically oriented vector hydrophones at unknown locations in impulsive noise Jin He ∗ , Zhong Liu Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, PR China Available online 9 November 2007 Abstract This paper proposes a new underwater acoustic 2-D direction finding algorithm using two identically oriented vector hy- drophones at unknown locations in non-Gaussian impulsive noise. The two applied vector hydrophones are four-component, orienting identically in space with arbitrarily and possibly unknown displacement. Each vector hydrophone has three spatially co-located but orthogonally oriented velocity hydrophones plus another pressure hydrophone. The proposed algorithm employs the spatial invariance between the two vector hydrophones, but requires no a priori information of vector hydrophones’ spatial factors and impinging sources’ temporal forms. We apply ESPRIT to estimate vector hydrophones manifold and then to pair the x -axis direction cosines with y -axis direction cosines automatically and yield azimuth and elevation angle estimates. We also consider the additive noise be non-Gaussian impulsive, which is often encountered in underwater acoustics applications. Two typical impulsive noise model, Gaussian-mixture noise and symmetric α-stable (SαS ) noise models are adopted. Instead of using conventional second order correlation of array output data, we define the vector hydrophone array sign covariance matrix (VSCM) for Gaussian-mixture noise and vector hydrophone array fractional lower order moment (VFLOM) matrix for SαS noise with 1 <α  2. These defined matrices may readily substitute customary vector hydrophone array covariance matrix for 2-D direction finding in impulsive noise.  2007 Elsevier Inc. All rights reserved. Keywords: Array signal processing; Direction-of-arrival estimation; Vector hydrophone; ESPRIT; Impulsive noise; Gaussian-mixture noise; Symmetric α-stable noise; Sign covariance matrix; Fractional lower order moment 1. Introduction Underwater acoustic vector hydrophone has been received a significant amount of interest both in theory and in engineering in the past decades [1,2]. A vector hydrophone can compose of two or three identical orthogonally oriented velocity hydrophones 1 (with each measuring one Cartesian component of the impinging underwater velocity vector of sonar field) and one optional pressure hydrophone (which measures the underwater acoustic pressure of the sonar field). A large number of types of velocity hydrophones have been constructed for applications using various techniques including mechanics, optics and many derivative based techniques. (See [3] and references therein.) * Corresponding author. Fax: +86 25 84315550. E-mail address: andrie1111@hotmail.com (J. He). 1 The velocity hydrophones can also be diversely oriented. 1051-2004/$ – see front matter  2007 Elsevier Inc. All rights reserved. doi:10.1016/j.dsp.2007.10.012