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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The MEMS vector hydrophone is a novel acoustic sensor with a “four-beam-cilia” structure. Based on the MEMS vector hydrophone with this structure, the paper studies the method of estimated direction of arrival (DOA). According to various research papers, many algorithms can be applied to vector hydrophones. The beam-forming approach and bar graph approach are described in detail. Laboratory tests by means of the a standing-wave tube are performed to validate the theoretical results. Both the theoretical analysis and the results of tests prove that the proposed MEMS vector hydrophone possesses the desired directional function.

Vector hydrophones can obtain both the acoustic pressure and acoustic particle velocity simultaneously, and therefore can gather more information about a point in the sound field than an ordinary acoustic pressure hydrophones. Thus, they have a unique advantage and wide applicability [

As early as in the 1940s, the United States developed a sound pressure gradient vector hydrophone, and in 1970s, the vector hydrophone was successfully applied in the DIFAR sonobuoy system. In the development of vector hydrophones, the United States and Russia have taken the lead in the World, and vector hydrophones with stable performance have not only gone into the engineering phase [

The MEMS vector hydrophone is designed based on the piezoresistive effect of silicon, The beam microstructure is manufactured by means of a silicon-on-insulator (SOI) wafer with MEMS technology. Compared with traditional piezoelectric hydrophones, the MEMS vector hydrophone has the characteristic of a being a single sensor with directional functions. In theory, two sensors can locate the target.

In this paper, we will discuss a novel hydrophone which is developed from a typical accelerometer structure. The SEM image (top view) of the microstructure is shown in

As we can see in this Figure, it is a typical mass-beam accelerometer structure, which is based on the piezoresistive effect. In order to improve the sensitivity, a cylinder (diameter: 200 μm, length: 7,000 μm) was glued in the center of the mass [

According to the auditory principle of a fish’s lateral line, we use a rigid cylinder as a stereocilia which can improve the sensitivity. When the sound signal is sensed by the cylinder, the piezoresistors located at the beam transform the sound signal into strain and finally into a differential output voltage signal via the Wheatstone bridge circuit. So the sound signal can be detected.

The sound field is the vector field, and a plane wave is a longitudinal wave, so the vector hydrophone measures the direction of sound vibration (vibration velocity v̄) and sound intensity flow Pv̄ (where P is acoustic pressure) is the direction of sound propagation, which is the goal orientation, so the measurement Pv̄ can estimate the DOA.

From the acoustic theory, we can see the plane wave acoustic pressure can be expressed as [

Where

Wave vector’s projection in the coordinate system.

In homogeneous medium, the sound field equation of motion is:

Substituting this into Expression 1,we get:
_{0} is the medium density,

From (3) we can get the three components of the particle velocity:

So, as long as we measured the two components ν_{x}, ν_{y} of particle velocity in the horizontal plane, we can get the azimuth

According to the different types of noise background and signals, there are several approaches to estimate azimuth angle based on a single vector hydrophone [

The term beam-forming refers to the various output signals whereby a vector hydrophone can determine space directivity after processing (weighted, delay, summation etc.), It can focus the receive direction of hydrophone on a direction, which is equivalent to a beam, rotating the beam to find the maximum peak, that is the target azimuth. The algorithm can be seen as a space filter that can separate the signal from interference, according to the azimuth difference between signal and interference.

There are many weighted modes, this paper only analyzes two of them. If only in the plane, according to (4) we can obtain the following equation:

The first weighted method: _{x}_{y}

Substituting (7) into it and assuming

The second weighted method, adds the acoustic pressure

The directivity patterns of two weighted functions (8) and (9) are as follows, respectively:

The

The principle chart of the beam-forming approach is shown in _{x}(t) and ν_{y}(t) output of hydrophone by 1, cos

The average power of _{0}, so _{0} is the azimuth angle of the sound signal. Virtually, this is a process of beam-forming [

From _{x} and ν_{y}, a single vector hydrophone can estimate the direction of the sound source. Although this method is simple, the error would be great, this is mainly because the three velocity components ν_{x}, ν_{y}and ν_{z,} measured by the vector hydrophone not only contain a valid signal, but also noise. Noise has a great impact on the estimated results, and this impact is more serious with lower SNR (signal-to-noise ratio).

We assume the signals received from vector hydrophone are as follows:

In the equation,

_{s}

ν_{s}(

_{n}

ν_{n}

Target signal and interference noise is independent of each other, and they are ergodic. Calculating average sound intensity by above formula, we get:

For _{n}_{n}_{s}

Bar graph estimation is a statistical approach based on cross-spectrum estimation. First we calculate the angle corresponding to each frequency, and then count the probability density of each estimated value, to get the estimated curve of a certain moment, the curve maximum position corresponds to the estimated value of which is the target position. _{x}_{y}_{x}(t) and ν_{y}(t), we can get the expression of calculated azimuth:

Bar graph statistics mainly estimates the azimuth of every frequency, if 1° is the statistical unit, we get:

In

The DOA estimation experiment has been completed by means of the a test vector hydrophone instrument in the laboratory,

Using a signal generator to generate a single-frequency sine wave S_{1}(t), DOA is 45°. The Data Acquisition Card collects a three-way signal at the same time P, V_{x}, V_{y}, data sampling rate is set to 10 KHz. The two methods are applied to DOA estimates. The results in

As sound source a broadband signal (white noise) S_{2}(t) is used, DOA is 0°. The results of the two methods are shown in

The results of the two methods (DOA=0°)

As sound source we enter a single-frequency signal with attached white noise S_{1}(t) + S_{2}(t), DOA is 90°. The results of the two methods are shown in

The results of the two methods (DOA = 90°).

In this paper, by testing and analyzing the directional functions of a MEMS vector hydrophone in an ideal room environment, we obtained better results. From the test results, the MEMS hydrophone can not only direct but also have high orientation accuracy. For a continuous wave, two methods are feasible, but because of the requirements of frequency resolution, the bar graph approach is not suitable for pulse waves. There are two main reasons of error: first, because of the inaccuracy of the measured angle and the other is the rounding error of the bar graph. It remains to be determined whether the MEMS vector hydrophone can achieve good goal orientation or not in the actual marine environment.

This work has been financially supported by the National Natural Science Foundation of China (Grant No. 50405025, 50535030, 50775209).

SEM images of the microstructure.

Schematic view of the bionic structure of the MEMS hydrophone.

Frequency response of the structure.

Directivity patterns of function (8) (

Directivity patterns of function (9) (

Principle chart of the beam-forming approach.

Principle chart of the bar graph approach.

The photo of the MEMS vector hydrophone.

Principle chart of the calibration instrument.

The results of the two methods (DOA = 45°).