^{1}

^{2}

^{3}

^{1}

^{2}

^{1}

^{2}

^{1}

^{2}

^{1}

^{2}

^{1}

^{2}

^{3}

Five well-known azimuth angle estimation methods using a single acoustic vector sensor (AVS) are investigated in open-lake experiments. A single AVS can measure both the acoustic pressure and acoustic particle velocity at a signal point in space and output 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 a source. The AVS that was applied in these open-lake experiments is a two-dimensional accelerometer structure sensor. It consists 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 one AVS. The results presented in this paper reveal that AVS can be applied in a wider range of application in distributed underwater acoustic systems for passive detection, localization, classification, and so on.

Research on underwater acoustic systems has been receiving an increasing attention in both military and civilian applications [

It is well known that the AVS array processing could greatly enhance the performance of detection and estimation [

A sizable literature exists on the methods for processing signals of a single AVS [

As mentioned earlier, a single AVS measures a Cartesian component of the acoustic particle velocity vector of the incident wavefield and simultaneously outputs multichannel signals. Hence, array signal processing methods can be applied by regarding the AVS as an array. A two-dimensional AVS has 3 × 1 array manifold, in response to a unit-power underwater acoustic wave front [

Even though extensive researches on AVS processing have been done in the past thirty years, studies focusing on the experimental investigation are rarely presented. In order to motivate practical engineering application demands in passive sonar detection system, we study five well-known azimuth angle estimation methods using a single AVS and carry out a comprehensive experimental research of these methods.

The five noted methods, namely, complex acoustic intensity measurement (CAIM) method, weighted complex acoustic intensity measurement (WCAIM) method, conventional beamforming (CBF) method, minimum variance distortionless response (MVDR) beamforming method, and multiple signal characteristic (MUSIC) method, are investigated in this paper. The first two methods are based on complex acoustic intensity measurement. Compared with other methods based on acoustic intensity measurement, they do well in the condition of either in line-spectra coherent interference lying in wideband signal or in wideband coherent interference lying in a line-spectra signal. The rest three methods investigated are mainly applied in an array that consists of many sensors. The same as [

The main contribution of this paper is the experimental investigation of five azimuth angle estimation methods upon a single vector-sensor configuration. In this paper, our attention will be restricted to the case of one single underwater acoustic source. The rest of this paper is organized as follows: Section

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, it is explicitly assumed that the impinging signals are plane waves. The plane-wave acoustic pressure at a frequency

AVS coordinates and the propagation of planar wave front with azimuth angle

The wavenumber vector _{x}_{y}_{z}

And then, (

AVS is applied to measure the acoustic pressure component and two orthogonal components of particle velocity in the

Equation (

There are a variety of methods proposed by researchers to estimate the azimuth angle of the underwater acoustic source using a single AVS. In this paper, five popular methods are experimentally investigated and compared. These methods’ theoretical background is briefly reviewed in the following text.

The WCAIM method is derived from CAIM method. As shown in Figure

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

It yields frequency spectrum _{i}_{i}

The typical bar graph statistics are given by

CAIM is improved by particularly considering the influence of the cross-spectrum energy in different frequency point as [17, 19]

We assume that a signal _{n}

The position corresponding to maximum value of

Illustration of azimuth angle estimation by CBF.

Another extensively used estimation technique is MVDR. The beamformer mainly aims to let the signal of interest be received without any distortion while minimizing the noise arriving from other directions. The design issue on weight vector can be formulated as

The solution to this optimization problem is generally referred to as minimum variance distortionless response (MVDR) beamformer. The weighted vector of MVDR beamformer is easily derived [

Then, the spatial spectra are estimated by

In practice, the matrix

AVS MUSIC azimuth spectrum estimation is realized by multiple signal classification technique based on exploiting the eigenstructure of the input covariance matrix. The covariance matrix can be decomposed into

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

Consequently, the corresponding spatial spectrum output is

To evaluate and compare the practical application performance of the five investigated AVS azimuth angle estimation methods, we carried out serial open-lake experiments in Danjiangkou Reservoir from April to June 2016. The experimental setup is shown in Figure

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

Map of the experiment site.

The two different ships are clearly identified as follows:

Acoustic source ship, equipped with high-power transmitting acoustic source

Receiver ship, equipped with AVSs and other related electronic devices

A two-dimensional accelerometer structure AVS was applied in these open-lake experiments. It consists of two orthogonally oriented velocity hydrophones plus a pressure hydrophone, all colocated in space. Its directivity patterns (at 1000 Hz) measured in the laboratory are shown in Figure

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

Consistent with theoretical measurement model, the sensitivity pattern of pressure is omnidirectional and that of velocity is dipole directional. A lateral rejection ratio of 38 dB or more against the other orthogonal axis is offered by the acceleration sensitivity on each axis. Meanwhile, as we can see in Figure

Before the start of these lake experiments, the sound speed profile was measured by the CTD on the receiver ship. The sound speed profile of the site of these experiments is shown in Figure

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

As shown in Figure

During the experiments, these two ships applied in the lake experiments were, respectively, anchored at a specific spot. The GPS coordinates of the two spots and the actual field-measured environment parameters are provided in detail in Table

Experiment geographical environment parameters.

Parameters | Acoustic source ship | Receiver ship |
---|---|---|

GPS coordinates | 32°45.683 |
32°42.272 |

111°33.807 |
111°31.762 | |

Water depth (m) | 38 | 43 |

_{eu} |
20 | 25 |

_{eu}: depth of equipment underwater.

The actual distance and azimuth angle could be calculated according to the information of the GPS coordinates. The actual distance between the receiver ship and the acoustic source ship is 7.068 km, and the actual azimuth angle between the connecting line and the geographic North Pole is 26.9°.

In these open-lake experiments, the acoustic source signal is a 650 Hz–850 Hz symmetrical linear frequency-modulated (SLFM) signal. The duration of the SLFM signal transmitted in these experiments is 2 seconds. The measured actual sound source level (SL) of the transmitted signal is 194.6 dB (1 re

The multichannel output data in time domain from the AVS are shown in Figure

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

Then, the five methods introduced above are applied to estimate the source azimuth angle. The processing results of the lake experiment data are shown in Figure

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

For a more comprehensive comparison, the estimated results of seven times lake experiment data processed by these five investigated methods are listed in Table

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 |

RMSE |
1.32 | 1.11 | 0.93 | 0.93 | 0.93 |

Comparing the results of the five methods in detail, we note that all the five methods investigated in this paper can effectively realize the azimuth angle estimation by using a single AVS. However, they are very different in terms of spatial resolution. CAIM, WCAIM, MVDR, and MUSIC methods perform much better than CBF method. The peaks of CAIM, WCAIM, MVDR, and MUSIC spatial spectrum are much sharper than that of CBF. As clearly shown in Figure

Moreover, it is worth to point out that the impulse response is generated by multiple arrivals in such shallow water environment. The bias in these experimental results presented in Table

In another representative experiment, a high-speed boat radiating mechanical noise is applied to make a further investigation of these five methods. The high-speed boat does circular motion around the receiver ship. Figure

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

The frequency range of real measurement data processing is from 100 Hz to 2500 Hz. The movement trajectory estimated results of the high-speed boat are shown in Figure

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

These experimental results show that the movement trajectory of the high-speed boat is estimated accurately. The spectral resolution of the CBF method is much lower than that of the other four methods. It can be seen that the results estimated by the other four methods provide satisfactory information about the target bearing. As we expect, the same as the results shown in Figure

These experimental investigation results provide a valuable insight into the design and implementation of practical passive sonar detection systems. However, there are remaining research issues related to the azimuth estimation problem. For instance, it remains to be determined whether these methods can achieve good performance or not in a multitarget environment.

The AVSs are practical and versatile acoustic measurement sensors, with applications in underwater acoustic detection. We provided an experimental investigation of five popular azimuth angle estimation methods, CAIM, WCAIM, CBF, MVDR, and MUSIC, upon a single AVS configuration. According to the open-lake experiments and real measurement data processing results, the effectiveness of these methods is verified, and performances of these methods are compared in detail. All the five methods investigated in this paper can effectively realize the azimuth angle estimation by using only one single AVS. CAIM, WCAIM, MVDR, and MUSIC methods provide much superior performance in spatial resolution than CBF method. CBF suffers from relatively low resolution and poor accuracy. The performance of WCAIM is very similar to that of MUSIC, or even slightly better. Moreover, the computational complexity of WCAIM is much lower than that of the MUSIC. For WCAIM method, no prior information is required to estimate the azimuth angle. Therefore, among these methods, WCAIM method could achieve widespread use in practical engineering. The results presented in this paper reveal that AVS can be applied in a wider range of application in distributed underwater acoustic detection systems.

The authors declare no conflicts of interest.

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