Normal-Mode Based MUSIC for Bearing Estimation in Shallow Water Using Acoustic Vector Sensors

To realize unbiased bearing estimates of multiple acoustic sources in a range-independent shallow water, Normal-Mode based MUSIC (NM-MUSIC) method using acoustic vector sensor (AVS) array is proposed in this paper. Comparing to NM-MUSIC method based on scalar array, the method based on AVS array solves the problem of port and starboard ambiguity, and also breaks through the limitation of half wavelength. Meanwhile, the method realizes unbiased bearing estimates, while most of the conventional Direction of Arrival (DOA) methods result in biased bearing estimates in shallow water. Simulation results show that the performance of the new method proposed is better than that of the original method. 1.Introduction DOA estimation of underwater targets is an important research content in underwater acoustics. Traditional methods are mostly based on the scalar sensors, which measure only the acoustic pressure. There is an AVS which can not only measure the acoustic pressure, but also get the three orthogonal components of particle velocity at a point. The information contained in the measurements of AVS provides a complete characterization of the acoustic field. The classic methods based on AVS array contain CBF and MUSIC algorithms. But these methods result in biased DOA estimation, because plane-wave propagation is assumed. To solve this problem, Matched field processing (MFP) techniques was proposed by Gong [1], but this method works at the expense of computational complexity because of the three-dimensional search in the bearing-range-depth space. The subspace intersection method given by Lakshmipathi provides high-resolution bearing estimation based on a more appropriate normal mode propagation model [2]. SI alleviates the problems of both bias and computational complexity compared to MFP because of a one-dimensional search of bearing without range and depth. But the robustness of SI is poor because of the QR decomposition. Nagananda [3] extend SI to an array of acoustic vector sensors. Lijie Zhang provided a Normal-Mode based MUSIC (NM-MUSIC) method using scalar sensors, which is adapted from the classical MUSIC method [4]. NM-MUSIC provides unbiased DOA estimates of sources by one dimensional searching without requiring any prior information of source locations. In this paper, we extend NM-MUSIC to an array of acoustic vector sensors, which combines the advantages of NM-MUSIC algorithm and AVS array. Simulations show that the performance of the new method proposed in this paper is better than that of the original method. 2.AVS array data model based on normal mode propagation model The AVS array data model in shallow ocean used in this paper is the same as that described in [3]. A linear AVS array of N sensors at depth m a z is taken into account, and the inter-sensor spacing is d. There are J narrowband sources of centre frequency f, which are located at depth m j z , ranges j r and bearing j  1,..., j J  . Bearing is measured with respect to the end-fire direction of the array. AVS can get three orthogonal component of particle velocity ( , , ) x y z v v v . Among them, z v has little impact on bearing estimates, so we only use the particle velocity ( , ) x y v v . International Conference on Mechatronics Engineering and Information Technology (ICMEIT 2016) © 2016. The authors Published by Atlantis Press 191 The output of the acoustic vector sensors array could be expressed as ( ) ( ) ( ) ( ) t t t   X P Φ S n (1) where n is the array noise vector and [ , , ]  Φ θ r z (2) 1 [ ,..., ] T J    θ (3) 1 [ ,..., ] T J r r  r (4) 1 [ ,..., ] T J z z  z (5) are the vector of unknown parameters, and   1 2 ( ) ( ), ( ), , ( ) T J t s t s t s t  S  (6) is the source signal vector, and   P Φ is the matrix defined as ( ) ( ) ( , )  P Φ A θ B r z (7) and   1 [ ( ),..., ( )] J    A θ A A (8)   1 1 , diag( ( , ),..., ( , )) J J r z r z  B r z b b (9) 1 2 ( ) ( ), ( ), , ( ) j j j M j          Α a a a  (10)       1 , , ,..., , j j j j M j j r z b r z b r z      b (11)       0 , m j m j ik r r m j j m a m j m j e b r z B z z k r              (12) In these formulas, M is the total number of the normal modes, and B0 is a complex quantity independent of rj, zj, j  , za. For acoustic vector sensors array, cos ( 1) cos cos( ) sin( ) ( ) [1, , , ] [1, , ] m j m j jk d j N k d m j m j T T m j k k a e e k k          (13) ( ) m z  and m k are the eigenfunction and wavenumber of the mth normal mode. Considering that the sound sources ( ) j s t are uncorrelated white Gaussian noise with variances 2 j  , and the sound sources S(t) are uncorrelated with the noise n(t), and n(t) is uncorrelated white Gaussian noise with variances 2 n  . The correlation matrix of ( ) t X is defined as H ( ) ( ) E t t      R X X (14) where the notation   E  indicates expectation operation,    is Hermit Transpose. In practical applications, we use the following formula to estimate the true correlation matrix