CN114280618A - A three-dimensional beamforming method of small-size volume array based on acoustic vector hydrophone - Google Patents

Abstract

The invention discloses a small-size volume array three-dimensional beam forming method based on an acoustic vector hydrophone. The invention relates to the technical field of beam forming of small-size acoustic vector arrays, which constructs a small-size acoustic vector volume array with a vector hydrophone as a primitive and a received signal model; obtaining the spatial gradients of each order of sound pressure in different directions by using a difference method; extracting multipole modes in each order of spatial gradient; synthesizing a spherical function by utilizing a multipole mode, and extracting spherical harmonics of each order of a three-dimensional sound field; the desired three-dimensional beam is synthesized using a spherical function. The invention can obtain any desired three-dimensional wave beam by weighting the small-size acoustic vector volume array by using the weighting vector, realizes the formation of the three-dimensional wave beam, not only solves the contradiction between the very-low frequency band high three-dimensional space gain and the array aperture, but also can meet the requirement of three-dimensional space detection.

Description

A three-dimensional beamforming method of small-sized volume array based on acoustic vector hydrophone

technical field

The invention relates to the technical field of beam forming of acoustic vector arrays, and is a three-dimensional beam forming method of small-sized volume arrays based on acoustic vector hydrophones.

Background technique

In the low frequency and very low frequency working section, the Rayleigh limit of traditional sonar design seriously restricts the detection performance of underwater sonar array. The breakthrough in the research of small-scale arrays with array spacing far less than half wavelength provides a solution to this problem. In recent years, the super-directional beamforming method based on small-sized sonar array has become a research hotspot. A large number of design analysis and computer simulation show the advantages of this type of array. However, the current small-scale arrays, whether based on acoustic pressure hydrophones or vector hydrophones, are mainly based on linear arrays and planar arrays. Due to the limitations of their beamforming algorithms, they are only suitable for small Grazing angle target detection and target horizontal azimuth estimation.

With the development of underwater detection to the deep sea, the sound field information contained in the vertical direction is rich, so it is necessary to make full use of the three-dimensional information of the sound field. But so far, there is still a lack of small-sized arrays and their beamforming algorithms that work in very low frequency bands and are suitable for 3D space detection in the field of underwater acoustics. The problem.

SUMMARY OF THE INVENTION

Aiming at the problem that most small-sized array beams cannot be guided in three-dimensional space at present, the present invention invents a small-sized vector volume array beamforming algorithm based on vector hydrophones, especially the ratio of the distance between adjacent array elements of the array to the signal wavelength is d A vector volume matrix in the range of /λ≤1/6. The present invention provides a three-dimensional beamforming method based on a small-sized acoustic vector volume array, and the present invention provides the following technical solutions:

A three-dimensional beamforming method for a small-sized volume array based on an acoustic vector hydrophone, comprising the following steps:

Step 1: Construct a small-sized acoustic vector volume array with the vector hydrophone as the primitive, and construct the received signal model;

Step 2: Use the difference method to obtain the spatial gradient of each order of sound pressure to different directions;

Step 3: Extract the multipole modes in each order of spatial gradients;

Step 4: Use the multipole mode to synthesize the spherical function to extract the spherical harmonics of each order of the three-dimensional sound field;

Step 5: Synthesize the desired 3D beam using the spherical function.

Preferably, the step 1 is specifically:

Construct a small-sized volume array based on vector hydrophones, and establish a received signal model:

运算表示克罗内克积，

左侧向量中的元素分别代表阵元声压、x、y和z振速通道指向性，上标T表示转置；a(θ,φ)是阵列声压通道的导向矢量，

其中L_h＝[x_h,y_h,z_h]是第h号阵元(h＝1,2,...M)空间位置，g＝[sinθcosφ,sinθsinφ,cosθ]^T，是信号对每个坐标轴的方向余弦向量。Among them, θ and φ represent the pitch angle and azimuth angle, respectively;

The operation represents the Kronecker product,

The elements in the vector on the left represent the directivity of the array element sound pressure, x, y and z vibration velocity channels respectively, and the superscript T represents the transposition; a(θ, φ) is the steering vector of the array sound pressure channel,

where L _h =[x _h ,y _h ,z _h ] is the spatial position of the h-th array element (h=1,2,...M), g=[sinθcosφ,sinθsinφ,cosθ] ^T , is the signal pair for each The direction cosine vector of each axis.

Preferably, the step 2 is specifically:

The differential approximation operation is performed on the array vibration velocity channel to obtain the vibration velocity gradient of the sound field:

是用μ方向振速通道差分近似得到

时，各接收通道系数构成的列向量，α_l,m,n是l+m+n阶差分近似时带来的常系数。in,

It is approximated by the difference of the vibration velocity channel in the μ direction

When , the column vector formed by the coefficients of each receiving channel, α _{l, m, n} is the constant coefficient brought by the l+m+n order difference approximation.

Preferably, the step 3 is specifically:

Extract the multipole modes in the spatial gradient that do not change with frequency, and determine the coefficients of each receiving channel when extracting the multipole modes of each order:

where Ψ _l,m,n =(D _x ) ^l (D _y ) ^m (D _z ) ⁿ is the multipole mode,

D _x =sinθcosφD _y =sinθsinφD _z =cosθ represents the directivity of x, y and z channels respectively, when μ=x, then D _μ Ψ _l,m,n =Ψ _l+1,m,n ,

Similarly, the expression of D _μ Ψ _l,m,n can be obtained when μ=y,z, F _n (k)=(ikd) ⁿ is the amplitude compensation factor of the n-order difference;

Ψ _l,m,n =r _l,m,n V(θ,φ)

Among them, r _l,m,n is the coefficient vector of each receiving channel when the multipole mode Ψ _l,m,n is obtained by using the vibration velocity channel based on the differential approximation. For all the multipole modes, it is written in matrix form as :

H _D =RV(θ,φ)

where H _D contains all multipole modes with l+m+n≤N, and R is the coefficient matrix composed of r _l,m,n :

R=[r _0,0,0 ^T ,r _1,0,0 ^T ,...,r _l,m,n ^T ...] ^T .

Preferably, the step 4 is specifically:

The spherical function is represented by the multipole modes of various orders, and the coefficients of the spherical function corresponding to the multipole modes are determined

是由各阶多极子模态H_D表示

时，各阶多极子模态系数构成的向量，将阶数n≤N的所有球函数

用多极子模态表示，并写成矩阵形式有：in,

is represented by the multipole modes H _D of various orders

When , the vector formed by the modal coefficients of multipoles of each order, all spherical functions of order n≤N

It is represented by a multipole mode and written in matrix form as follows:

b _Y (θ,φ)= _EHD

是由n≤N且|m|≤n的各阶球函数

构成的(N+1)²×1列向量，E是由多极子模态得到各阶球函数的系数所构成的系数矩阵表示为:in,

are spherical functions of various orders with n≤N and |m|≤n

The (N+1) ² × 1 column vector formed by E is the coefficient matrix formed by the coefficients of the spherical functions of each order obtained by the multipole mode, which is expressed as:

Preferably, the step 5 is specifically:

Expand the desired beam with the spherical function as the basis function, and obtain the coefficients of the spherical function of each order

According to the relationship between the beam pattern and the beamformer, the weighting coefficient vector of each receiving channel of the array is obtained when the desired beam pattern is synthesized

B _N (θ,φ)=w ^H (θ _s ,φ _s )V(θ,φ)=g ^H ERV(θ,φ)

The weighted coefficient vector is obtained to satisfy:

w ^H (θ _s , φ _s )=g ^H ER

A beam pattern that can be steered in a three-dimensional space can be formed by performing weighting processing on a small-sized vector volume array by using the above-mentioned weighting vector.

The present invention has the following beneficial effects:

The present invention uses the above weighting vector to perform weighting processing on the small-sized vector volume array to form a beam pattern that can be steered in three-dimensional space, and solves the problem that the existing small-sized array beams cannot be steered in three-dimensional space. The invention has the advantage of providing a three-dimensional beam forming method for a small-sized acoustic vector array in a very low frequency band, which not only solves the contradiction between the acquisition of high spatial gain in the very low frequency band and the array aperture, but also meets the needs of three-dimensional space detection. The invention connects the multipole mode with the spherical function, and realizes the array beam forming under the small aperture by synthesizing the spherical function with θ and φ as the variables through the multipole mode. According to the orthogonal completeness of spherical functions in three-dimensional space, the desired three-dimensional beams that can be steered in both elevation and azimuth angles are synthesized by spherical functions of various orders, so that the beamforming algorithm can meet the needs of three-dimensional space detection. The present invention utilizes the directivity of the vector hydrophone itself to extract the multipole modes of various orders shown in step (5) and the spherical harmonics of various orders shown in step (6). Therefore, compared with the commonly used acoustic field spherical harmonic decomposition beamforming method for spherical arrays, the present invention can extract higher order spherical harmonics under the condition of the same size and the same number of array elements to obtain higher array gain and narrower beam.

Description of drawings

Fig. 1 is a schematic diagram of the structure of a small-sized vector array;

Figure 2 is a schematic diagram of the second-order differential approximate vibration velocity gradient;

Fig. 3 is a flow chart of the content of the invention;

Fig. 4 is a 3rd order beam diagram of a small size vector array;

Figure 5 is the change of the 3rd order beam pattern of the small-sized vector array with d/λ, Figure 5-(a) is the azimuth beam pattern; Figure 5-(b) The elevation angle beam pattern;

Figure 6 shows the variation of gain with d/λ under different modal orders of small-sized vector arrays, Figure 6-(a) Array gain, Figure 6-(b) White noise gain

Detailed ways

The present invention is described in detail below with reference to specific embodiments.

Specific embodiment one:

A three-dimensional beamforming method for a small-sized volume array based on an acoustic vector hydrophone, comprising the following steps:

Step 1: Construct a small-sized acoustic vector volume array with the vector hydrophone as the primitive, and construct the received signal model;

The step 1 is specifically:

Construct a small-sized volume array based on vector hydrophones, and establish a received signal model:

运算表示克罗内克积，

左侧向量中的元素分别代表阵元声压、x、y和z振速通道指向性，上标T表示转置；a(θ,φ)是阵列声压通道的导向矢量，

其中L_h＝[x_h,y_h,z_h]是第h号阵元(h＝1,2,...M)空间位置，g＝[sinθcosφ,sinθsinφ,cosθ]^T，是信号对每个坐标轴的方向余弦向量。Among them, θ and φ represent the pitch angle and azimuth angle, respectively;

The operation represents the Kronecker product,

The elements in the vector on the left represent the directivity of the array element sound pressure, x, y and z vibration velocity channels respectively, and the superscript T represents the transposition; a(θ, φ) is the steering vector of the array sound pressure channel,

where L _h =[x _h ,y _h ,z _h ] is the spatial position of the h-th array element (h=1,2,...M), g=[sinθcosφ,sinθsinφ,cosθ] ^T , is the signal pair for each The direction cosine vector of each axis.

Step 2: Use the difference method to obtain the high-order vibration velocity gradient;

The step 2 is specifically:

The differential approximation operation is performed on the array vibration velocity channel to obtain the high-order vibration velocity gradient of the sound field:

是用μ方向振速通道差分近似

时，各接收通道系数构成的列向量，α_l,m,n是l+m+n阶差分近似时带来的常系数。Among them, p ₀ is the sound pressure response of the reference array element,

It is approximated by the difference of the vibration velocity channel in the μ direction

When , the column vector formed by the coefficients of each receiving channel, α _{l, m, n} is the constant coefficient brought by the l+m+n order difference approximation.

Step 3: Extract the multipole modes in each vibration velocity gradient;

The step 3 is specifically:

Extract the multipole modes in the vibration velocity gradient that do not change with frequency, and determine the coefficients of each receiving channel when extracting the multipole modes of each order:

where Ψ _l,m,n =(D _x ) ^l (D _y ) ^m (D _z ) ⁿ is the multipole mode,

D _x =sinθcosφD _y =sinθsinφD _z =cosθ represents the directivity of x, y and z channels respectively, when μ=x, then D _μ Ψ _l,m,n =Ψ _l+1,m,n ,

Similarly, the expression of D _μ Ψ _l,m,n can be obtained when μ=y,z, F _n (k)=(ikd) ⁿ is the amplitude compensation factor of the n-order difference;

Ψ _l,m,n =r _l,m,n V(θ,φ)

Among them, r _l,m,n is the coefficient vector of each receiving channel when the multipole mode Ψ _l,m,n is obtained by using the vibration velocity channel based on the differential approximation. For all the multipole modes, it is written in matrix form as :

H _D =RV(θ,φ)

Among them, H _D contains all multipole modes of l+m+n≤N, and R is the coefficient matrix composed of r _l,m,n :

R=[r _0,0,0 ^T ,r _1,0,0 ^T ,...,r _l,m,n ^T ...] ^T .

Step 4: Use the multipole mode to synthesize the spherical function to extract the spherical harmonics of each order of the three-dimensional sound field;

The step 4 is specifically:

The spherical function is represented by the multipole modes of various orders, and the coefficients of the spherical function corresponding to the multipole modes are determined

是由各阶多极子模态H_D表示

时，各阶多极子模态系数构成的向量，将阶数n≤N的所有球函数

用多极子模态表示，并写成矩阵形式有：in,

is represented by the multipole modes H _D of various orders

When , the vector formed by the modal coefficients of multipoles of each order, all spherical functions of order n≤N

It is represented by a multipole mode and written in matrix form as follows:

b _Y (θ,φ)= _EHD

是由n≤N且|m|≤n的各阶球函数

构成的(N+1)²×1列向量，E是由多极子模态得到各阶球函数的系数所构成的系数矩阵表示为:in,

are spherical functions of various orders with n≤N and |m|≤n

The (N+1) ² × 1 column vector formed by E is the coefficient matrix formed by the coefficients of the spherical functions of each order obtained by the multipole mode, which is expressed as:

Step 5: Use spherical function synthesis to steer the desired three-dimensional beam in three-dimensional space.

The step 5 is specifically:

Expand the desired beam pattern with the spherical function as the basis function, and obtain the coefficients of the spherical function of each order

According to the relationship between the beam pattern and the beamformer, the weighting coefficient vector of each receiving channel of the array is obtained when the desired beam pattern is synthesized

B _N (θ,φ)=w ^H (θ _s ,φ _s )V(θ,φ)=g ^H ERV(θ,φ)

The weighted coefficient vector is obtained to satisfy:

w ^H (θ _s , φ _s )=g ^H ER

A beam pattern that can be steered in a three-dimensional space can be formed by performing weighting processing on a small-sized vector volume array by using the above-mentioned weighting vector.

Specific embodiment two:

Take the small-sized vector matrix shown in Figure 1 as an example. The small-scale array studied includes No. 1 to No. 11 array elements, which form a volume array. The No. 5 array element at the center of the array is also a reference array element. The reference sound pressure response p ₀ =p ₅ , which is adjacent to any adjacent coordinate axis. The distance between the two array elements of is d and satisfies kd<<1.

As shown in Figure 3, put the array into the water with relatively good free field conditions, and hoist it to a deep depth, and put the sound source into the water at the same time. The distance r between the sound source and the center of the array satisfies the acoustic far-field conditions. The signal generator is adjusted to generate a CW pulse signal to obtain the received signal of the array.

The steering vector form of the received signal is obtained as:

The superscript T represents the transposition, and a(θ, φ) is the steering vector of the sound pressure channel of the array, which is expressed as:

where L _h =[x _h ,y _h ,z _h ] is the spatial position of the hth array element (h=1,2,...11), g=[sinθcosφ,sinθsinφ,cosθ] ^T , is the signal pair for each The direction cosine vector of each coordinate axis takes the No. 5 array element at the center of the array as the reference array element.

According to the multipole principle, the approximate vibration velocity gradient is obtained:

中元素及如何确定α_l,m,n，以图1所示的11元矢量体积阵进行说明。以x、y和z方向的所有2阶振速梯度为例(即x、y和z方向的所有3阶声压梯度)，给出所用阵元及其系数，具体情况如图2所示。图2中红色、蓝色和绿色分别表示差分所用通道为该阵元的x、y和z通道，白色代表该次差分中未使用该阵元；若接收通道系数为正数，该阵元边框为实线，若为负数则边框为虚线。在所有使用的阵元左上角均标有差分时该阵元通道的系数，即

中元素的值，为了简洁，未使用的白色阵元所有接收通道系数均为0，图中不标注。阵元下方带’#’标注的数字表示阵元编号.To elaborate

The elements in and how to determine α _l,m,n are explained with the 11-element vector volume matrix shown in Figure 1. Taking all the second-order vibration velocity gradients in the x, y and z directions as examples (that is, all the third-order sound pressure gradients in the x, y and z directions), the used array elements and their coefficients are given, as shown in Figure 2. In Figure 2, red, blue, and green indicate that the channel used for the differential is the x, y, and z channels of the array element, respectively, and white indicates that the array element is not used in this difference; if the receiving channel coefficient is a positive number, the border of the array element It is a solid line, if it is a negative number, the border is a dashed line. The coefficient of the array element channel when the upper left corner of all used array elements is marked with difference, namely

The value of the element in , for the sake of brevity, all the receiving channel coefficients of the unused white array elements are 0, and are not marked in the figure. The number marked with '#' below the array element indicates the array element number.

Obtain the multipole mode from the spatial gradient:

F _n (k)=(ikd) ⁿ , if μ=x, then D _μ Ψ _l,m,n =Ψ _l+1,m,n . Similarly, when μ=y,z, D _μ Ψ _{l, m,n} expression.

Ψ _l,m,n =r _l,m,n V(θ,φ)

为例:r _l,m,n is the coefficient vector of each receiving channel when the multipole mode Ψ _l,m,n is obtained based on the differential approximation, as shown in Figure 2.

For example:

此公式改了,但word并未显示批注,务必以此公式为准.

This formula has been changed, but word does not display comments, so this formula must prevail.

仅用了y振速通道进行差分近似，所以此时其余通道的系数均为0。对于所有多极子模态，可写成矩阵形式:where 0 _m,n represents an all-zero matrix with m rows and n columns, because

Only the y vibration velocity channel is used for differential approximation, so the coefficients of the other channels are all 0 at this time. For all multipole modes, it can be written in matrix form:

H _D =RV(θ,φ)

where H _D is all multipole modes including l+m+n≤N _. For ease of understanding, the multipole modes in HD are arranged from small to large according to the value of l+m+n. For l+m The multipole modes with the same +n are arranged according to the priority l>m>n, that is, the item with a larger l is given priority, the item with a smaller l is given later, and m and n are deduced in turn. If _N =2, then HD contains all multipole modes with l+m+n≤2:

H _D = [Ψ _0,0,0 ,Ψ _1,0,0 ,Ψ _0,1,0 ,Ψ _0,0,1 ,Ψ _2,0,0 ,Ψ _1,1,0 ,Ψ _{1,0 ,1} ,Ψ _0,2,0 ,Ψ _0,1,1 ,Ψ _0,0,2 ] ^T

At this time, the multipole modes in HD are arranged according to the above rules. When _N takes a larger value, _HD can be obtained according to the relationship between the vibration velocity gradient and the multipole modes described above, and R is given by Coefficient matrix composed of r _l,m,n :

R=[r _0,0,0 ^T ,r _1,0,0 ^T ,...,r _l,m,n ^T ...] ^T

The spherical function is represented by a multipole mode:

是由各阶多极子模态H_D表示

时，各阶多极子模态系数构成的向量，以

为例:in,

is represented by the multipole modes H _D of various orders

When , the vector formed by the multipole modal coefficients of each order is given by

For example:

用多极子模态表示，并写成矩阵形式有Convert all spherical functions of order n≤N

It is represented by a multipole mode and written in matrix form as

b _Y (θ,φ)= _EHD

是由n≤N且|m|≤n的各阶球函数

构成的(N+1)²×1列向量，E是由多极子模态得到各阶球函数的系数所构成的系数矩阵，可以表示为:in

are spherical functions of various orders with n≤N and |m|≤n

The (N+1) ² × 1 column vector formed by E is the coefficient matrix formed by the coefficients of the spherical functions of each order obtained by the multipole mode, which can be expressed as:

Expand the desired beam pattern series with the spherical function as the basis function:

According to the relationship between the beam pattern and the beamformer, the weighting vector of the beamformer is obtained:

B _N (θ,φ)=w ^H (θ _s ,φ _s )V(θ,φ)=g ^H ERV(θ,φ)

The weighting vector of the beamformer is obtained as:

w ^H (θ _s , φ _s )=g ^H ER

Using the above weighting vector to weight the small-sized vector volume array can form a beam pattern that can be steered in three-dimensional space, which provides a reliable and effective method for solving the contradiction between the high three-dimensional spatial gain of the very low frequency band and the array aperture. .

First, the steerability of the method of the present invention in three-dimensional space is verified. In the case of dλ=120, let the beam point to (45°, 45°), the result is shown in Figure 4, it can be accurately pointed in the case of small size desired direction.

Next, verify its range of use. Taking the highest order spherical harmonic N=3 that can be extracted by the array as an example, the expected pointing angle is (90°, 180°). The changes of , in Fig. 5-(a) and (b), the curves marked with black "x" are the sectional views of the desired beam pattern at azimuth and elevation angles, respectively. According to Fig. 5-(a) and (b), it can be seen that when dλ≤16 in the present invention, the main lobe width of the beam pattern remains basically unchanged, and although the side lobes gradually increase, the error from the ideal beam pattern is small. , with the continuous increase of d/λ, due to the increase of the error introduced by the differential approximation at this time, the beam pattern is seriously distorted, and the performance of the beamforming algorithm decreases.

Finally, the gain and robustness of the present invention are verified. When the 1-3 order spherical harmonics are extracted from the array shown in Fig. 1 for beamforming, the variation trend of the array gain with d/λ is shown in Fig. 6-(a). , where the black dotted line is the theoretical array gain of the corresponding order, and the red solid line represents the variation of the simulated array gain with d/λ. From the simulation results, it can be seen that the small-size vector volume array and its beamforming algorithm established in this paper have high array gain. Taking N=3, dλ=120 as an example, the array gain can reach 12dB at this time, and at d/ Under the condition of λ≤16, the array gain and the corresponding dotted line basically coincide and remain unchanged, which means that the algorithm can obtain high gain in a wider low frequency band. However, it can be seen from Figure 6-(b) that as the frequency decreases, the WNG will decrease rapidly. At this time, the array will be more sensitive to the amplitude and phase errors and self-noise of the primitives, and the robustness of the entire system will be worse. At the same time, comparing the array gain and white noise gain with different orders N, it can be seen that with the increase of the maximum spherical harmonic order N, the array gain gradually increases, and the white noise gain gradually decreases.

The above is only a preferred embodiment of a small-size volume array 3D beamforming method based on an acoustic vector hydrophone, and the protection scope of a small-size acoustic vector volume array-based 3D beamforming method is not limited to the above implementation. For example, all technical solutions under this idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims (6)

1. A small-size volume array three-dimensional beam forming method based on acoustic vector hydrophones is characterized by comprising the following steps: the method comprises the following steps:

step 1: constructing a small-size acoustic vector volume array with vector hydrophones as elements, and constructing a received signal model;

step 2: obtaining the spatial gradients of each order of sound pressure in different directions by using a difference method;

and step 3: extracting multipole modes in each order of spatial gradient;

and 4, step 4: synthesizing a spherical function by utilizing a multipole mode, and extracting spherical harmonics of each order of a three-dimensional sound field;

and 5: the desired three-dimensional beam is synthesized using a spherical function.

2. The small-size volume array three-dimensional beam forming method based on the acoustic vector hydrophone, as recited in claim 1, wherein: the step 1 specifically comprises the following steps:

constructing a small-size volume array based on a vector hydrophone, and establishing a received signal model:

wherein θ and φ represent a pitch angle and an azimuth angle, respectively;

the operation represents the kronecker product,

elements in the left vector respectively represent array element sound pressure, x, y and z vibration velocity channel directivity, and superscript T represents transposition; a (theta, phi) is a guide vector of the array sound pressure channel,

wherein L is_h＝[x_h,y_h,z_h]Is the spatial position of the h-th array element (h 1, 2.. M), g [ [ sin θ cos Φ, sin θ sin Φ, cos θ [ ]]^TAnd is the direction cosine vector of the signal to each coordinate axis.

3. The method for forming the three-dimensional beam of the small-size volume array based on the acoustic vector hydrophone as claimed in claim 2, wherein the method comprises the following steps: the step 2 specifically comprises the following steps:

carrying out difference approximation operation on the array vibration velocity channel to obtain a high-order vibration velocity gradient of the sound field:

wherein,

is obtained by differential approximation of mu-direction vibration velocity channel

While receiving a column vector of channel coefficients, α_l,m,nIs a constant coefficient brought by l + m + n order differential approximation.

4. The method for forming the three-dimensional beam of the small-size volume array based on the acoustic vector hydrophone as claimed in claim 3, wherein the method comprises the following steps: the step 3 specifically comprises the following steps:

extracting a multipole mode which does not change along with the frequency in the vibration velocity gradient, and determining the coefficient of each receiving channel when extracting the multipole mode of each order:

therein, Ψ_l,m,n＝(D_x)^l(D_y)^m(D_z)ⁿIs a multipole mode, D_x＝sinθcosφD_y＝sinθsinφD_zCos θ represents the directivity of x, y and z channels, respectively, and when μ ═ x, D represents_μΨ_l,m,n＝Ψ_l+1,m,n，

For the same reason, mu-y, z is D_μΨ_l,m,nExpression of (1), F_n(k)＝(ikd)ⁿAn amplitude compensation factor that is an nth order difference;

Ψ_l,m,n＝r_l,m,nV(θ,φ)

wherein r is_l,m,nThe multi-pole mode psi is obtained by using the vibration velocity channel based on the difference approximation_l,m,nIn the process, the coefficient vector of each receiving channel is written into a matrix form for all multipole modes:

H_D＝RV(θ,φ)

wherein H_DAll multipole modes comprising l + m + N ≦ N, R being represented by R_l,m,nThe coefficient matrix is formed by:

R＝[r_0,0,0 ^T,r_1,0,0 ^T,...,r_l,m,n ^T...]^T。

5. the method for forming the three-dimensional beam of the small-size volume array based on the acoustic vector hydrophone as claimed in claim 4, wherein the method comprises the following steps: the step 4 specifically comprises the following steps:

expressing the spherical function by each order of multipole mode, and determining the coefficient of the spherical function corresponding to the multipole mode

Wherein,

is composed of multiple pole modes H_DTo represent

Then, the vector formed by the multi-pole mode coefficients of each order is the spherical function with the order N less than or equal to N

Expressed in a multipole mode and written in matrix form:

b_Y(θ,φ)＝EH_D

wherein,

is a spherical function of each order consisting of N less than or equal to N and m less than or equal to N

Formed (N +1)²X 1 column vector, E is a coefficient matrix formed by coefficients of the spherical functions of each order obtained from the multipole mode, and is represented as:

6. the method for forming the three-dimensional beam of the small-size volume array based on the acoustic vector hydrophone as claimed in claim 5, wherein the method comprises the following steps: the step 5 specifically comprises the following steps:

spreading the desired beam with the spherical function as the basis function to obtain the coefficient of each order of spherical function

According to the relation between the beam pattern and the beam former, the weighting coefficient vector of each receiving channel of the array when synthesizing the expected beam pattern is obtained

B_N(θ,φ)＝w^H(θ_s,φ_s)V(θ,φ)＝g^HERV(θ,φ)

The obtained weighting coefficient vector satisfies:

w^H(θ_s,φ_s)＝g^HER

and carrying out weighting processing on the small-size vector volume array by using the weighting vector to obtain any desired three-dimensional beam, thereby realizing three-dimensional beam forming.

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