Research ArticleOpen-Lake Experimental Investigation of Azimuth AngleEstimation Using a Single Acoustic Vector Sensor

Anbang Zhao,1,2,3 Lin Ma,1,2 Juan Hui ,1,2 Caigao Zeng,1,2 and Xuejie Bi1,2

1College of Underwater Acoustic Engineering, Harbin 150001, China2Science and Technology on Underwater Acoustic Laboratory, Harbin 150001, China3National Key Laboratory of Science and Technology on Underwater Acoustic Antagonizing, China State Shipbuilding CorporationSystems Engineering Research Institute, Beijing 100036, China

Correspondence should be addressed to Juan Hui; huijuan_heu@126.com

Received 22 July 2017; Revised 10 November 2017; Accepted 5 February 2018; Published 27 March 2018

Academic Editor: Jaime Lloret

Copyright © 2018 Anbang Zhao 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.

Five well-known azimuth angle estimation methods using a single acoustic vector sensor (AVS) are investigated in open-lakeexperiments. A single AVS can measure both the acoustic pressure and acoustic particle velocity at a signal point in space andoutput multichannel signals. The azimuth angle of one source can be estimated by using a single AVS in a passive sonar system.Open-lake experiments are carried out to evaluate how these different techniques perform in estimating azimuth angle of asource. The AVS that was applied in these open-lake experiments is a two-dimensional accelerometer structure sensor. Itconsists of two identical uniaxial velocity sensors in orthogonal orientations, plus a pressure sensor—all in spatial collocation.These experimental results indicate that all these methods can effectively realize the azimuth angle estimation using only oneAVS. The results presented in this paper reveal that AVS can be applied in a wider range of application in distributedunderwater acoustic systems for passive detection, localization, classification, and so on.

1. Introduction

Research on underwater acoustic systems has been receiv-ing an increasing attention in both military and civilianapplications [1–4]. Compared with acoustic pressure sen-sors (a.k.a. scalar hydrophone), acoustic vector sensors(AVS) can simultaneously measure the acoustic pressurealong with acoustic particle velocity at a signal point inspace [1, 3]. Better detection effectiveness and higher esti-mation precision can be achieved by fully making use ofthe pressure and the additional particle velocity infor-mation [5]. For several decades, AVSs have been ubiqui-tously applied in source direction of arrival (DOA)estimation and localization [6, 7]. In recent years, AVSshave been increasingly extended to multiple researchfields, such as feature extraction of underwater targetsignal [8], underwater target tracking [1], underwateracoustic communication [9, 10], acoustic focusing andshielding [3, 11], and geoacoustic inversion problem[12]. Therefore, experimental investigation of the AVS

signal processing methods is very important in practicalengineering applications.

It is well known that the AVS array processing couldgreatly enhance the performance of detection and estimation[13–16]. AVS arrays are able to estimate both elevation andazimuth without left-right ambiguity and give better resultcompared with scalar sensor. However, as demand forsmaller arrays has significantly increased, the large-scaleaperture of traditional sensor arrays restricts their practicalapplication fields. Consequently, single-transmit single-receive (SISO) distributed sonar system, such as sonobuoysand other small-scale detection equipment, is very popularin distributed detection systems for their own characteristicsof layout convenience, high stealthiness [17], and so on TheDOA estimation of the underwater source could be realizedby using only one single AVS. Thus, the single AVS passivesonar detection system and the AVS signal processingresearch attract ever-increasing attention.

A sizable literature exists on the methods for processingsignals of a single AVS [5, 6, 17–23]. Researchers put forward

HindawiJournal of SensorsVolume 2018, Article ID 4324902, 11 pageshttps://doi.org/10.1155/2018/4324902

a method for DOA estimation based on average acousticintensity processing. This method is experimentally investi-gated in [18]. Another proposed azimuth angle estimationalgorithm based on complex acoustic intensity measurementis experimentally investigated in [19]. These results showthat the method is able to effectively detect the underwatersource and estimate its azimuth angle. Furthermore,researchers also propose an improved method based oncomplex acoustic intensity weighted statistics and anothermethod aiming to detect a target that radiating line spec-tra. The method is experimentally verified in [17]. Thisapproach based on complex acoustic intensity weightedstatistics can suppress broadband coherent interference.Methods described in [17–19] are all based on acousticintensity measurement. The azimuth angle is estimatedby directly computing the acoustic intensity componentof the different coordinate axis.

As mentioned earlier, a single AVS measures a Cartesiancomponent of the acoustic particle velocity vector of theincident wavefield and simultaneously outputs multichannelsignals. Hence, array signal processing methods can beapplied by regarding the AVS as an array. A two-dimensional AVS has 3× 1 array manifold, in response to aunit-power underwater acoustic wave front [1]. In [18, 19],the conventional beamforming approach to estimatingDOA based on a single AVS is evaluated by experiments. Ref-erence [6] introduces a new underwater acoustic eigenstruc-ture ESPRIT-based algorithm that yields closed-form DOAestimates using a single AVS. The minimum variance distor-tionless response (MVDR) beam patterns associated with asingle AVS distant from any reflecting boundary is character-ized in [20]. Most of the direction-finding (DF) methodsusing an AVS are based on the far-field measurement model.Missing in the literature is a near-field measurement modelfor the AVSs. In [21], a measurement model is presentedthere for an AVS located near a reflecting boundary. Takinginto account the characteristics of one single AVS, the high-resolution DOA estimation based on time-space transformand subspace decomposing theory is realized in [22]. More-over, [23] investigates how the AVS’s DF accuracy wouldbe degraded by random deviations from its nominal gainresponse and/or phase response.

Even though extensive researches on AVS processinghave been done in the past thirty years, studies focusing onthe experimental investigation are rarely presented. In orderto motivate practical engineering application demands inpassive sonar detection system, we study five well-knownazimuth angle estimation methods using a single AVSand carry out a comprehensive experimental research ofthese methods.

The five noted methods, namely, complex acoustic inten-sity measurement (CAIM) method, weighted complex acous-tic intensity measurement (WCAIM) method, conventionalbeamforming (CBF) method, minimum variance distortion-less response (MVDR) beamforming method, and multiplesignal characteristic (MUSIC) method, are investigated inthis paper. The first two methods are based on complexacoustic intensity measurement. Compared with othermethods based on acoustic intensity measurement, they do

well in the condition of either in line-spectra coherent inter-ference lying in wideband signal or in wideband coherentinterference lying in a line-spectra signal. The rest threemethods investigated are mainly applied in an array that con-sists of many sensors. The same as [18–23], these methodscan be extendedly applied by regarding the AVS as an array.CBF is the most traditional and the most classic techniqueused to estimate azimuth angle of an acoustic source. MVDRaims to let the signal of interest be received without any dis-tortion while minimizing the noise arriving from other direc-tions. MUSIC is one of the most popular algorithms capableof super-resolution performance. MUSIC method requiresknowledge of a number of sources to perform accuratesubspace decomposition of the covariance matrix.

The main contribution of this paper is the experimen-tal investigation of five azimuth angle estimation methodsupon a single vector-sensor configuration. In this paper,our attention will be restricted to the case of one singleunderwater acoustic source. The rest of this paper is orga-nized as follows: Section 2 describes the theoretical back-ground. The AVS measurement model and the fiveinvestigated methods are briefly reviewed. Section 3 con-sists of open-lake experiments, data processing results,and estimation performance discussion. Finally, conclu-sions are totally drawn in Section 4.

2. Measurement Model and Methods

2.1. AVSModel. From now on, and without loss of generality,an acoustic wave is assumed to be propagating in a quiescent,homogeneous, and isotropic fluid in this paper. In addition, itis explicitly assumed that the impinging signals are planewaves. The plane-wave acoustic pressure at a frequency ωcan be given as [18, 19]

p r, t = p0ej kT ⋅r−ωt , 1

x

y

z

O ry

rx

rz

AVS

Source

�휃

�휑

Figure 1: AVS coordinates and the propagation of planar wavefront with azimuth angle θ and elevation angle φ. (Figurereproduced from Zhao et al. [17], under the Creative CommonsAttribution License/public domain).

2 Journal of Sensors

where ω denotes the angular frequency, k symbolizes thewavenumber vector, and r represents the space vector.Figure 1 represents the AVS coordinates, when a sourcesignal impinges upon the sensors from an azimuth angle θand an elevation angle φ.

The wavenumber vector k has the form

k =kx

ky

kz

= k

cos θ cos φsin θ cos φ

sin φ

, 2

where k is defined as

k = k2x + k2y + k2z =ω

c= 2πf

c, 3

where c denotes the speed of acoustic propagation. Any pointin a three-dimensional space can be commonly located by avector r = rx, ry, rz T , where rx, ry, and rz are the coordinatesof the point in the Cartesian coordinate system. Hence, (1)has the following form:

p r, t = p0exp j krxcos θ cos φ + krysin θ cos φ+ krzsin φ − ωt

4

And then, (4) is substituted into the equation of motion:

∂v∂t

+ 1ρ∇p = 0, 5

where ρ is the medium density, and we can express (5) as

v = −1ρ

∇p ⋅ dt,

v r, t = p r, tρc

cos θ cos φ ξ + sin θ cos φ η + sin φ ζ ,

6

where ζ, η, and ξ, respectively, symbolize the unit vectorof x-, y-, and z-axes. This paper will only concentrateon azimuth angle θ. In this case, elevation angle φ isassumed to be equal to zero. The acoustic pressure andacoustic particle velocity depend on time only in the mea-surement model. Therefore, the parameter r is omittedfrom these variables.

AVS is applied to measure the acoustic pressure com-ponent and two orthogonal components of particle veloc-ity in the x-O-y plane. Finally, the copoint output

mathematical expression of the measurement model canbe reduced as

p t = p t ,

vx t = 1ρc

p t cos θ,

vy t = 1ρc

p t sin θ

7

Equation (7) indicates that the velocity direction charac-teristics of AVS are independent of frequency. The directivityof AVS is frequency independent as well. Consequently, asingle AVS array manifold is equivalently defined in a generalform as

as θ = 1, 1ρc

cos θ , 1ρc

sin θT

, 8

where θ ∈ 0, 2π is the corresponding azimuth angle ofan acoustic source measured from the positive x-axisand T denotes the transpose. The AVS’s array mani-fold is independent of the incident wavefield’s frequencyand bandwidth.

2.2. Methods. There are a variety of methods proposed byresearchers to estimate the azimuth angle of the underwateracoustic source using a single AVS. In this paper, five popularmethods are experimentally investigated and compared.These methods’ theoretical background is briefly reviewedin the following text.

2.2.1. CAIM and WCAIM. The WCAIM method isderived from CAIM method. As shown in Figure 2 [17, 19],azimuth angle estimation by these two methods is allbased on complex acoustic intensity measurements. How-ever, they are quite different in terms of their statisticalweighted value.

Conjugatecross-spectrum

ConjugateCross-spectrum A

zim

uth

angl

ees

timat

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Bar g

raph

statis

tic

Bear

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time

resu

lt

p

vx

vy

I x (f)

I y (f)

P(ω)

Vx(ω)

Vy(ω)Dig

ital fi

lter

AVS

FFT

Figure 2: Illustration of CAIM and WCAIM. (Figure reproduced from Zhao et al. [17], under the Creative Commons Attribution License/public domain).

Bear

ing-

time

resu

lt

p

vx

vy Dig

ital fi

lter

AVS

R P̂(�휃)w(�휃)

Figure 3: Illustration of azimuth angle estimation by CBF.

3Journal of Sensors

It yields frequency spectrum P(ω) and Vi(ω) (i= x, y) byapplying fast Fourier transform (FFT) to p(t) and vi(t)(i= x, y). Hence, the acoustic pressure and velocity cross-spectrum is defined as

Spvi = P ω ⋅ V∗i ω   i = x, y , 9

where “∗” symbolizes the complex conjugate operation. Theazimuth angle of each frequency based on the acoustic pres-sure and velocity conjugate cross-spectrum is straightfor-ward to calculate

θ ω = arctanIRy

IRx

= arctanRe <P ω V∗

y ω >Re <P ω V∗

x ω > , 10

where “Re” represents the real part. Then, the probabilitydensity statistics can be estimated by counting the azimuthangle calculation results of all frequency points. The resultis the azimuth estimation curve at a certain moment.

The typical bar graph statistics are given by

n = θ ω × 180π

,

η n = η n + 1,11

where n is denoted as angle characterized by degree and “[]”represents getting integer operation. η denotes a data array,which stores the frequency of each angle in [0, 360). The ini-tial value of η is set to be zero. We note that all the statisticweighted value is one in each frequency. This is the so-called CAIM method.

CAIM is improved by particularly considering the influ-ence of the cross-spectrum energy in different frequencypoint as [17, 19]

η n = η n +W, 12

where W is the statistic weighted value of cross-spectrum.The only difference between CAIM andWCAIM is the statis-tic weighted value, that is, (10) and (11). The corresponding

maximum value on the result curve is the source azimuthangle estimated value.

2.2.2. AVS CBF. We assume that a signal s(t) is impingingupon the AVS from the angle θ and that the source isin the far field of the AVS. The vector array output y(t)is then [6]

y t = as θ s t + n t , 13

where n(t) is a vector of additive noise representing the effectof undesired signals. The combined beamformer output isgiven by

yc t =wHy t =wHas θ s t + wHn t , 14

Signal generator

Power amplifier

AVS

Surface

Bottom

Transmittingtransducer

7 km

Data acquisition unit

Data processing

38 m43 m

20 m 25 m

Figure 4: The experimental setup for azimuth angle estimation using a single AVS.

Figure 5: Map of the experiment site.

4 Journal of Sensors

where w is a vector of weights and “H” denotes the conjugatetranspose. The spatial spectra obtained by beam scanning isdefined as

P̂ θ = yc t, θ 2 = wHRw, 15

where

R = E yyH = as θ aHs θ E s2 t + E n t nH t , 16

where E s2 t and E n t nH t are independent of t. Thus,Ris independent of t. In practical applications, R is replaced bythe sample covariance matrix R̂, where

R̂ = 1N〠N

n=1ynyHn , 17

with N denoting the number of snapshots and yn represent-ing the nth snapshot.

The position corresponding to maximum value of P̂ θis the source azimuth angle estimated result. In Figure 3,we show an illustration of azimuth angle estimation byAVS CBF.

2.2.3. AVS MVDR. Another extensively used estimationtechnique is MVDR. The beamformer mainly aims tolet the signal of interest be received without any distor-tion while minimizing the noise arriving from otherdirections. The design issue on weight vector can beformulated as

minw

 wHRw,

s t  wHas θ = 118

20

10

30

30

0

330

300270

240

210

180

150

12090 40 dB

60

VxVyP

(a)

VxVy

P

200 400 600 800 1000 1200 1400Frequency (Hz)

−100

−150

−200

−250

M (d

B)(d

B)(r

e 1 V

/�휇Pa

)

(b)

Figure 6: (a) The AVS directivity patterns (at 1000Hz). (b) The AVS sensitivity between 200Hz and 1500Hz. (Figure reproduced from Zhaoet al. [17], under the Creative Commons Attribution License/public domain).

0

5

10

15

20

25

30

35

40

45

501430 1440 1450 1460 1470

Sound speed (m/s)

Dep

th (m

)

1480 1490 1500 1510

Figure 7: The sound speed profile. (Figure reproduced from Zhaoet al. [17], under the Creative Commons Attribution License/public domain).

Table 1: Experiment geographical environment parameters.

Parameters Acoustic source ship Receiver ship

GPS coordinates32°45.683′N 32°42.272′N111°33.807′E 111°31.762′E

Water depth (m) 38 43

Deu1 (m) 20 25

1Deu: depth of equipment underwater.

5Journal of Sensors

The solution to this optimization problem is generallyreferred to as minimum variance distortionless response(MVDR) beamformer. The weighted vector of MVDR beam-former is easily derived [20]:

w = R−1as θaHs θ R−1as θ

19

Then, the spatial spectra are estimated by

P̂ θ =wHRw = 1aHs θ R−1as θ

20

In practice, the matrix R is replaced by an estimate matrixR̂. The same as the AVS CBF azimuth angle estimationmethod, the position corresponding to maximum value ofP̂ θ is the estimated source azimuth angle. The estimationprocedure can be illustrated by Figure 3 as well.

2.2.4. AVS Music. AVSMUSIC azimuth spectrum estimationis realized by multiple signal classification technique basedon exploiting the eigenstructure of the input covariancematrix. The covariance matrix can be decomposed into

R = 〠3

i=1λiΦiΦH

i , 21

where λi is the ith eigenvalues and eigenvectors of thecovariance matrix and Φi is the corresponding ith eigenvec-tors. We assume there is only one acoustic source, sortingthe eigenvalue, that satisfies

λ1 ≥ λ2 = λ3 = σ2 22

Equation (20) holds under the assumption of white noise,that is E n t nH t = σ2I.

The signal subspace is composed of the first eigenvector.The noise subspace is composed of the rest two eigenvectorsthat uncorrelated with the signal eigenvector, as

Us = Φ1 ,Un = Φ2,Φ3

23

Consequently, the corresponding spatial spectrum out-put is

P̂ θ = 1aHs θ UnUH

n as θ= 1aHs θ I −UsUH

s as θ24

3. Experiments and Results

3.1. Experimental Setup. To evaluate and compare the practi-cal application performance of the five investigated AVSazimuth angle estimation methods, we carried out serialopen-lake experiments in Danjiangkou Reservoir from Aprilto June 2016. The experimental setup is shown in Figure 4.The map of the site of these experiments is shown inFigure 5. As it shows, the reservoir is approximately 20 kmlong and 10 km wide. The bottom is muddy and sandy.

The two different ships are clearly identified as follows:

(a) Acoustic source ship, equipped with high-powertransmitting acoustic source

(b) Receiver ship, equipped with AVSs and other relatedelectronic devices

3.1.1. The AVS Introduction. A two-dimensional accelerome-ter structure AVS was applied in these open-lake experi-ments. It consists of two orthogonally oriented velocityhydrophones plus a pressure hydrophone, all colocated inspace. Its directivity patterns (at 1000Hz) measured in thelaboratory are shown in Figure 6(a).

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Vy channel

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uenc

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z)

100020003000

(b)

Figure 8: (a) The AVS output in time domain. (b) The corresponding spectrograms.

6 Journal of Sensors

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Figure 9: The real measurement data processing results: (a) CAIM; (b) WCAIM; (c) CBF; (d) MVDR; (e) MUSIC.

7Journal of Sensors

Consistent with theoretical measurement model, the sen-sitivity pattern of pressure is omnidirectional and that ofvelocity is dipole directional. A lateral rejection ratio of38 dB or more against the other orthogonal axis is offeredby the acceleration sensitivity on each axis. Meanwhile, aswe can see in Figure 6(b), the maximum receiving sensitivityof the AVS between 200Hz and 1500Hz is −188.8 dB re1μPa at 1m. In these experiments, the data from the AVSwas acquired by the designated data acquisition unit.

3.1.2. Experiment Environment Parameters. Before the startof these lake experiments, the sound speed profile was mea-sured by the CTD on the receiver ship. The sound speed pro-file of the site of these experiments is shown in Figure 7.

As shown in Figure 7, there is a serious negative soundspeed gradient layer near the surface. The acoustic wavepropagation is refracted downward in this layer. Withincreasing water depth, there exists an equal velocity profilelayer below the depth of 35m. In accordance with

underwater acoustic theory, this layer is relatively conduciveto acoustic signal transmission. However, the AVS was downto about 25m under the water surface since the bottom of theexperiment site is an undulating area.

During the experiments, these two ships applied in thelake experiments were, respectively, anchored at a specificspot. The GPS coordinates of the two spots and the actualfield-measured environment parameters are provided indetail in Table 1.

The actual distance and azimuth angle could be calcu-lated according to the information of the GPS coordinates.The actual distance between the receiver ship and the acous-tic source ship is 7.068 km, and the actual azimuth anglebetween the connecting line and the geographic North Poleis 26.9°.

3.2. Results and Discussion. In these open-lake experiments,the acoustic source signal is a 650Hz–850Hz symmetricallinear frequency-modulated (SLFM) signal. The duration of

Table 2: Analysis of the azimuth angle estimated results (true azimuth angle is 26.9°).

S. number CAIM(°) WCAIM(°) CBF(°) MVDR(°) MUSIC(°)

1 26.1 26.1 26.1 26.1 26.1

2 24.1 25.1 26.1 26.1 26.1

3 26.6 25.6 25.6 25.6 25.6

4 26.8 25.8 25.8 25.8 25.8

5 26.6 26.6 26.6 26.6 26.6

6 27.4 26.4 26.4 26.4 26.4

7 28.7 25.7 25.7 25.7 25.7

Mean 26.6 25.9 26.0 26.0 26.0

RMSE1 1.32 1.11 0.93 0.93 0.931RMSE: root mean square error.

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Figure 10: (a) The AVS output in time domain. (b) The corresponding spectrograms.

8 Journal of Sensors

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Figure 11: The real measurement data processing results: (a) CAIM; (b) WCAIM; (c) CBF; (d) MVDR; (e) MUSIC.

9Journal of Sensors

the SLFM signal transmitted in these experiments is 2 sec-onds. The measured actual sound source level (SL) of thetransmitted signal is 194.6 dB (1 re μPa at 1m).

The multichannel output data in time domain from theAVS are shown in Figure 8(a). The variation in normalizedamplitude of the different channel signals is clearly visible.Spectral domain analysis is further conducted and the corre-sponding spectrograms are shown in Figure 8(b). The colorbar indicates the energy scale in this figure.

Then, the five methods introduced above are applied toestimate the source azimuth angle. The processing results ofthe lake experiment data are shown in Figure 9. The resultsare presented in two formats: (1) spatial spectrum and (2)bearing-time-record (BTR) plot. Both formats are very com-monly used in passive sonar detection processing. The spatialspectrum presents spatial power over azimuth bearing only,while the BTR plot represents spectral power over both azi-muth and time. The top row in each figure shows the direc-tional spectra. BTR results are simultaneously shown in thebottom row.

For a more comprehensive comparison, the estimatedresults of seven times lake experiment data processed bythese five investigated methods are listed in Table 2.

Comparing the results of the five methods in detail, wenote that all the five methods investigated in this paper caneffectively realize the azimuth angle estimation by using asingle AVS. However, they are very different in terms of spa-tial resolution. CAIM, WCAIM, MVDR, and MUSICmethods perform much better than CBF method. The peaksof CAIM,WCAIM,MVDR, andMUSIC spatial spectrum aremuch sharper than that of CBF. As clearly shown inFigure 9(c), CBF suffers from low resolution and poor accu-racy. The performance of WCAIM is very similar to that ofMUSIC, or even slightly better. However, the computationalcomplexity of WCAIM is much lower than that of theMUSIC. For WCAIM method, the azimuth angle is esti-mated by directly computing the acoustic intensity compo-nent of the different coordinate axis. But for the MUSICmethod, the azimuth angle is estimated by computingthe power spectra point by point in space range. The defi-ciency of MVDR is a weak “fake peak” emerging in themirror image position.

Moreover, it is worth to point out that the impulseresponse is generated by multiple arrivals in such shallowwater environment. The bias in these experimental resultspresented in Table 2 is due to the effect of multipathpropagation.

In another representative experiment, a high-speed boatradiating mechanical noise is applied to make a further inves-tigation of these five methods. The high-speed boat does cir-cular motion around the receiver ship. Figure 10(a) shows theAVS multichannel output data in time domain. And the cor-responding spectrograms are shown in Figure 10(b).

The frequency range of real measurement data process-ing is from 100Hz to 2500Hz. The movement trajectory esti-mated results of the high-speed boat are shown in Figure 11.

These experimental results show that the movement tra-jectory of the high-speed boat is estimated accurately. Thespectral resolution of the CBF method is much lower than

that of the other four methods. It can be seen that the resultsestimated by the other four methods provide satisfactoryinformation about the target bearing. As we expect, the sameas the results shown in Figure 9, WCAIM and MUSIC bothhave the equally highest resolution; a weak “fake peak” existsin the mirror image position in the result estimated byMVDR. The MUSIC method requires prior knowledge of anumber of sources to perform accurate subspace decomposi-tion of the covariance matrix. The other methods do notrequire any prior information about the source. Hence,WCAIM method could achieve widespread use in practice,mainly because of its computation simplicity and its relativesuperior performance.

These experimental investigation results provide a valu-able insight into the design and implementation of practicalpassive sonar detection systems. However, there are remain-ing research issues related to the azimuth estimation prob-lem. For instance, it remains to be determined whetherthese methods can achieve good performance or not in amultitarget environment.

4. Conclusions

The AVSs are practical and versatile acoustic measurementsensors, with applications in underwater acoustic detection.We provided an experimental investigation of five popularazimuth angle estimation methods, CAIM, WCAIM, CBF,MVDR, and MUSIC, upon a single AVS configuration.According to the open-lake experiments and real measure-ment data processing results, the effectiveness of thesemethods is verified, and performances of these methods arecompared in detail. All the five methods investigated in thispaper can effectively realize the azimuth angle estimationby using only one single AVS. CAIM, WCAIM, MVDR,and MUSIC methods provide much superior performancein spatial resolution than CBF method. CBF suffers from rel-atively low resolution and poor accuracy. The performance ofWCAIM is very similar to that of MUSIC, or even slightlybetter. Moreover, the computational complexity of WCAIMis much lower than that of the MUSIC. ForWCAIMmethod,no prior information is required to estimate the azimuthangle. Therefore, among these methods, WCAIM methodcould achieve widespread use in practical engineering. Theresults presented in this paper reveal that AVS can be appliedin a wider range of application in distributed underwateracoustic detection systems.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgments

This paper was funded by the China Scholarship Council(CSC), National Science Foundation of China (Grant no.61371171 and 11374072), and Foundation of National KeyLaboratory of Science and Technology on UnderwaterAcoustic Antagonizing.

10 Journal of Sensors

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