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This paper presents an approach for the estimation of two-directional (2D)direction-of-arrival (DOA) using Acoustic Vector Sensor array based on greedy block coordinate descent(GBCD) algorithm, which can achieve faster convergence rate and better estimation accuracy. Moreover, a weighted form of block selection rule is proposed with the MUSIC prior. The identifiability of the presented approach is studied using computer simulations. It is demonstrated that the 2D DOAs of AVS can be realized using the approach, which has a superior resolution. Introduction Two-dimensional (2D) direction of arrival (DOA) estimation with array sensors is essential for source localization in audio surveillance, auditory scene analysis, hearing aids etc. The most well-known classical DOA estimation methods include Capon’s method [1], MUSIC [2], ESPRIT [3], etc. The four-element Acoustic Vector Sensor (AVS) first presented in [4] for DOA estimation is an acoustic sensor that is capable of measuring acoustic pressure gradient as well as pressure as in a standard microphone. This combination makes it possible for the sensor to measure the complete sound field. Recently, along with the development of AVS technique, the Direction of Arrival (DOA) estimation based on AVS has been researched widely and deeply [5-8]. By introducing Compressed Sensing (CS) [9] into DOA estimation field, we can obtain better performance than traditional angle estimation methods using the prior sparse information of target scene. In 2011, Fu applied CS to the DOA estimation of AVS [10], the echo signal received by an uniform linear array (ULA) is used for recovering target angle through OMP algorithm. But limited by the inherent error probability, OMP is not stable under noisy environment. Liang proposed an acoustic vector sensor array space time filtering approach for azimuth estimation with 1 l -norm optimization [11] and obtains superior resolution and accuracy to the conventional methods. However, the huge computational complexity of 1 l -norm optimization restricts potential application. Aiming at these problems, 2D DOA estimation for AVS based on GBCD algorithm is studied in this paper. In section 2, the acoustic vector sensor array signal model is introduced. Simulations are given in section 3 and summary in section 4. Signal Model Acoustic Vector Sensor Array Signal Model. An acoustic vector sensor consists of an acoustic pressure channel and three orthogonally oriented acoustic velocity channels, respectively receive International Conference on Automation, Mechanical Control and Computational Engineering (AMCCE 2015) © 2015. The authors Published by Atlantis Press 1583 the acoustic pressure P and three components ) , , ( z y x v v v of the acoustic particle velocity on coordinate axes x, y, x. We assume there is a linear array with N vector sensors. The output of each AVS is a 4-dimensional vector which contains all the 4 components. We assume K far-field sources are in the surveillance region, impinging on this linear array from directions, where k φ and k θ represent the azimuth and the elevation angles of the kth signal respectively. We assume 2 2 π θ π ≤ ≤ − and π φ π ≤ ≤ − . The measurement received at the array at time t can be modeled as [12] ) ( ) ( ) ( t e t Ax t y + = (1) where ) (t y and ) (t e are 1 4 × N complex vectors, respectively, and ) (t x is the 1 × K source vector. The K N × 4 array manifold A can be expressed as ] [ ,, 1 k a a A = (2) Where k k k p d a ⊗ = , with T k N j k j k e e d ] ,..., , 1 [ sin ) 1 ( sin 2 θ π θ π − = T k k k k k k p ] sin , sin sin , sin cos , 1 [ θ θ φ θ φ = Here, k a is the 1 4 × N steering vector of the array associated with a signal coming from the direction ) , ( k k θ φ . k d denotes the phase delay of the kth signal at the N sensors with respect to the origin, k p is the steering vector of a single vector sensor located at the origin. Joint Sparse Signal Model of Acoustic Vector Sensor Array. Supposing we process L snapshots at a time, the echo vector, source vector and noise vector received at the lth snapshot can be represented by ) (l y , ) (l s and ) (l e respectively, which independent from each other between different snapshots L l ,..., 1 = ,we can get E S y y Y L + Φ = = ] ... [ : ) ( ) 1 ( (3) PM N pM p M p p R p d p d p d p d × ∈ ⊗ ⊗ ⊗ ⊗ = Φ 4 1 1 1 11 1 ] ,..., ,..., ,..., [ where ] .... [ ) ( ) 1 ( L s s S = is the source matrix, ] ... [ ) ( ) 1 ( L e e E = is the noise matrix. Compared with the 1-D overcomplete dictionary, 2-D overcomplete dictionary is designed by expanding the overcomplete basis in 1-D way. Basing on the spatial sparsity, in each snapshot, ) (l s has only few nonzero elements, and the targets haven’t moved cross resolution units during L snapshots, that means for any ) (i s and ) ( j s ) ( j i ≠ , the nonzero elements are at the same position, so there are only few rows in S which are nonzero, and (3) is called the joint row sparse signal model of acoustic vector sensor array. Singular Value Decomposition. In order to reduce the dimension of (3), we apply Singular Value Decomposition to the echo matrix H N s H V U U V U Y Λ = Λ = ] [ (4) where s U is the signal subspace matrix and N U is the noise subspace matrix. s U consists of the eigenvectors correspond to the former K large eigenvalues and N U consists of the eigenvectors correspond to the rest L-K small eigenvalues. Let H H K L K K K k D ] 0 [ ) ( 1 − × − × Λ = , where K K× Λ represents the diagonal matrix constructed by the former K large eigenvalues, thus the signal subspace matrix can be represented as k s YVD U = . Let s s U Y = , k s SVD S = , k s EVD E = , substituted into (3), there is the dimensional reduction representation s s s E S Y + Φ = (5) Through comparing (5) with (3), we know that the dimension of echo signal is reduced from L P× 3 to K P× 3 . In practice, L K << , so the calculation of (5) is much faster. This fact motivates

2-D DOA Estimation for Acoustic Vector Sensor Array Based on Greedy Block Coordinate Descent Algorithm