Journal of Sensors

Volume 2018, Article ID 8526092, 10 pages

https://doi.org/10.1155/2018/8526092

## Steering Acoustic Intensity Estimator Using a Single Acoustic Vector Hydrophone

^{1}Acoustic Science and Technology Underwater Laboratory, Harbin Engineering University, Harbin 150001, China^{2}Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China^{3}College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China^{4}Science and Technology on Sonar Laboratory, Hangzhou Applied Acoustics Research Institute, Hangzhou 310023, Zhejiang, China

Correspondence should be addressed to Wang Sheng Lin; moc.361@krowgnehsgnawnil

Received 17 April 2018; Revised 30 July 2018; Accepted 19 September 2018; Published 25 November 2018

Academic Editor: Armando Ricciardi

Copyright © 2018 Guang Pu Zhang 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.

#### Abstract

Azimuth angle estimation using a single vector hydrophone is a well-known problem in underwater acoustics. In the presence of multiple sources, a conventional complex acoustic intensity estimator (CAIE) cannot distinguish the azimuth angle of each source. In this paper, we propose a steering acoustic intensity estimator (SAIE) for azimuth angle estimation in the presence of interference. The azimuth angle of the interference is known in advance from the global positioning system (GPS) and compass data. By constructing the steering acoustic energy fluxes in the and channels of the acoustic vector hydrophone, the azimuth angle of interest can be obtained when the steering azimuth angle is directed toward the interference. Simulation results show that the SAIE outperforms the CAIE and is insensitive to the signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR). A sea trial is presented that verifies the validity of the proposed method.

#### 1. Introduction

Acoustic vector hydrophones (AVHs) employ a colocated sensor structure consisting of two or three orthogonally oriented velocity sensors and a pressure sensor [1–3]. The manifold structure suggests that AVHs have the following advantages over traditional pressure sensors: (1) they measure acoustic pressure as well as particle velocity at the sensor position and thus produce extra information for localization, and (2) the manifold is independent of the frequency of the source signal, which makes AVHs suitable for wideband source signals [4]. Because of these advantages, both the theoretical aspects and applications of AVHs have been widely studied over the last few decades.

An array of AVHs is introduced for multiple-source localization problems in [5]. A maximum-likelihood algorithm was developed in [6]. Conventional beamforming (Bartlett beamforming) and Capon beamforming (minimum-variance distortionless response beamforming) for two-dimensional direction of arrival (DOA) estimation using an array of AVHs were investigated in [7]. Subspace-based approaches such as MUSIC [8] and ESPRIT [9] have been applied to the localization problem. In [10], the authors proposed a method for underwater acoustic direction-finding using arbitrarily spaced AVHs.

Although the AVH array processing can provide better detection and estimation performance, these methods are computationally expensive and require consistency of each component of the pressure and particle velocity. Therefore, in some engineering applications, single-transmit single-receive (SISO) sonar systems, such as sonobuoys and other small-scale detection equipment, are widely used [11]. DOA estimation using a single vector sensor is investigated in [12–14]. In [12], the authors introduce an ESPRIT-based algorithm for azimuth and elevation estimation using a single vector hydrophone. A comparison of different techniques in estimating the azimuth angle of a source is investigated in [13]. Given a single source with continuous spectrum against a background of isotropic and band-limited white Gaussian noise, azimuth angle estimation can be performed using a complex acoustic intensity estimator (CAIE, also known as an acoustic energy flux estimator), which is a maximum-likelihood detector, and an azimuth angle estimator that employs a single vector hydrophone, as discussed in [14]. The use of a complex acoustic intensity estimator is further discussed in [15–17]. In the presence of interference or multiple sources, the acoustic energy flux is a mixture of the signals from all the sources. Hence, a CAIE becomes ineffective unless the acoustic energy flux of each source can be separated out [17]. If the acoustic energy flux is separable in the frequency domain, a CAIE is applicable for azimuth angle estimation of multiple sources. However, it essentially relies on the difference in the frequency domain. It is unable to distinguish the azimuth angles of multiple sources when the acoustic energy fluxes overlap in the frequency domain.

In this paper, we propose an efficient azimuth angle estimation method for a source of interest in the presence of interference. The azimuth angle of interference is assumed to be known from the global positioning system (GPS) and compass data. Taking advantage of acoustic energy flux characteristics in the spatial domain, we construct two variables of acoustic energy flux in the and channels of the AVH, defined as the steering acoustic energy flux. Thus, the azimuth angle of interest can be obtained when the steering azimuth angle is directed toward the interference. Simulations verify that this method can estimate the azimuth angle of interest accurately against the background of interference. Moreover, it is computationally inexpensive, requiring only simple multiplication and division operations plus fast Fourier transformation (FFT). In contrast to traditional approaches, matrix inversion is not required and the FFT is based on a fast algorithm.

The remainder of this paper is organized as follows. In Section 2, the AVH signal model and steering acoustic intensity estimator are introduced. Simulations are presented in Section 3. Section 4 presents the estimation results and an analysis of a sea trial in the South China Sea. Finally, conclusions are drawn in Section 5.

#### 2. Steering Acoustic Intensity Estimator

Estimation using an AVH is based on analysis of three velocity components located at the origin of a three-dimensional space, with coordinates , , and . Let denote the particle velocity of an acoustic wave at position in three-dimensional space, and let be the acoustic pressure. The relation between the acoustic pressure and the particle velocity is obtained from Euler’s equation [18] and is given by where and are the ambient pressure and the speed of sound in the medium. is the unit vector pointing from the origin toward the source position, given by where and denote the azimuth angle and the elevation angle, respectively. We consider two statistically independent broadband plane waves, traveling in an isotropic, quiescent, homogeneous fluid medium and impinging on a single AVH. Only the azimuth angle is considered in this paper, and the elevation angle is neglected. The unit vector then becomes

Hence, the two plane waves are parameterized by their respective azimuth angles and . Source 1 is considered as the interference, and its azimuth angle is known in advance from GPS and compass data. Then, is the azimuth angle of interest. The received-signal model can be written as for sources . Here, and represent the corresponding pressure and velocity noise terms, respectively. We assume (i) that the noise terms in (4) are independent and identically distributed (i.i.d.), zero-mean complex circular Gaussian processes and are independent of the different channels and (ii) that the source signal and the noise are independent. The location of the AVH, , which is known and fixed at all time steps, can be omitted from these variables. Thus, the mathematical expressions for the different channels can be written as for sources . Equation (4) can be simplified as where and , and superscript denotes the matrix transpose. On applying an FFT to , the received signal at frequency can be written as

The covariance matrix of the received signal can be expressed as where superscript denotes the conjugate transpose. denotes the acoustic intensity of source , and denotes the noise intensity, given by

Substituting (10) and (12) into (8), the individual elements of the covariance matrix can be given as

We construct two variables and based on the covariance matrix of the received signal and defined as the steering acoustic energy fluxes of the and channels, respectively, given by where denotes the steering azimuth angle. The purpose of defining these two expressions is to derive an analytic solution that contains the relationship between and . These definitions are obtained through reverse derivation. The azimuth angle of interference can be estimated from the GPS and compass data, denoted as . The steering azimuth angle is directed toward the estimated azimuth angle, given as . Moreover, the steering azimuth angle is assumed in the neighborhood of the interference . Substituting the elements of covariance matrix from (13), (14), (15), (16), (17), and (18) into (19) and (20), we have

Straightforward derivations are given in the appendix. Thus, we obtain an estimate of in the form of its tangent, given by

Intuitively, we can estimate by an arctangent estimator based on the steering acoustic energy fluxes and called the steering acoustic intensity estimator (SAIE), which is given by where and . As we can see, the form of the SAIE is similar to that of a conventional acoustic intensity estimator [17]. As we can see, multiple estimates of the azimuth angle can be obtained using (24), not all of which are correct. False values can be eliminated by inserting into (8).

Related to (19) and (20), we need to estimate the azimuth angle of interference, , and the noise intensities related to the and channels, and . Assuming that the noise terms are stationary and that interference exists at all time steps, we can obtain estimates of the noise intensity before the source of interest appears, which are given by where denotes the complex conjugate. It is worth mentioning that there are errors when estimating the parameters , , and . Considering the estimation errors of these parameters, the performance of SAIE will be presented in the next section.

In the case where two sources are present, SAIE can give an estimate of with high precision. From (21) and (22), and are the singular points of , and are the singular points of . The area in the neighborhood of and is defined as the singular area. When the source of interest is located in the singular area, noise fluctuations can have a strong influence on the acoustic energy flux, causing the performance of SAIE to deteriorate rapidly.

#### 3. Simulations

In this section, several experiments are presented to investigate the performance of the SAIE method in the presence of interference with different powers and azimuth angles of acoustic sources.

Source 1 is the interference and source 2 is the source of interest. These two sources are generated with broadband continuous spectra. The integration time is 1 second. The performance is evaluated over 500 Monte Carlo runs. The unit of estimation in all figures presented here is the degree (°).

##### 3.1. Performance for Different SNR and SIR

The interference is located at ° and the source of interest at °. Figure 1 presents the performance of estimation of the azimuth angle of source 2, , with Figure 1(a) corresponding to the mean signed deviation (MSD), defined as where is the th estimate of the azimuth angle of interest and is the times of Monte Carlo runs.