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

Abstract

The present invention is a three-dimensional beamforming method for a small-sized volume array based on an acoustic vector hydrophone. The present invention relates to the technical field of beamforming of a small-sized acoustic vector array. The present invention constructs a small-sized acoustic vector volume array with a vector hydrophone as a primitive, and constructs a receiving signal model; uses a differential method to obtain spatial gradients of various orders of sound pressure in different directions; extracts multipole modes in spatial gradients of various orders; uses multipole modes to synthesize spherical functions, extracts spherical harmonics of various orders of a three-dimensional sound field; and uses spherical functions to synthesize desired three-dimensional beams. The present invention uses the above-mentioned weighted vectors to perform weighted processing on a small-sized acoustic vector volume array to obtain any desired three-dimensional beam and realize three-dimensional beamforming, which not only solves the contradiction between high three-dimensional spatial gain in a very low frequency band and array aperture, but also meets the needs of three-dimensional space detection.

Description

Technical Field

[0001] The invention relates to the technical field of acoustic vector array beamforming, in particular to a small-size volume array three-dimensional beamforming method based on acoustic vector hydrophones. Background Art

[0002] In the low-frequency and very low-frequency working range, the Rayleigh limit of traditional sonar design seriously restricts the detection performance of underwater sonar arrays. The breakthrough in the research of small-size arrays with array spacing far less than half a wavelength provides a solution to this problem. In recent years, super-directional beamforming methods based on small-size sonar arrays have become a research hotspot, and a large number of design analyses and computer simulations have demonstrated the advantages of this type of array. However, the current small-size arrays, whether based on acoustic pressure hydrophones or vector hydrophones, are mainly studied 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.

[0003] As underwater detection develops towards the deep sea, the vertical direction contains rich acoustic field information, so it is necessary to make full use of the three-dimensional information of the acoustic field. However, so far, there is still a lack of small-sized arrays and their beamforming algorithms that work in the very low frequency band and are suitable for three-dimensional space detection in the field of underwater acoustics. Therefore, studying the three-dimensional beamforming algorithm of small-sized arrays is an urgent problem to be solved in practical engineering applications. Summary of the invention

[0004] In view of the problem that most small-sized array beams cannot be steered in three-dimensional space, the present invention invents a small-sized vector volume array beamforming algorithm based on vector hydrophones, especially a vector volume array in which the ratio of the spacing between adjacent array elements to the signal wavelength is within the range of d / 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:

[0005] A small-size volume array three-dimensional beamforming method based on acoustic vector hydrophones comprises the following steps:

[0006] Step 1: Construct a small-sized acoustic vector volume array with vector hydrophone as the primitive, and build a receiving signal model;

[0007] Step 2: Use the difference method to obtain the spatial gradients of various orders of sound pressure in different directions;

[0008] Step 3: Extract multipole modes in spatial gradients of various orders;

[0009] Step 4: Use multipole mode to synthesize spherical functions and extract spherical harmonics of each order in the three-dimensional sound field;

[0010] Step 5: Use the spherical function to synthesize the desired 3D beam.

[0011] Preferably, the step 1 is specifically:

[0012] Construct a small volume array based on vector hydrophone and establish a received signal model:

[0013]

[0014] Where θ and φ represent the elevation angle and azimuth angle, respectively; The operation represents the Kronecker product, The elements in the left vector represent the array element sound pressure, x, y and z velocity channel directivity, and the superscript T indicates 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), D=[sinθcosφ,sinθsinφ,cosθ] T , is the direction cosine vector of the signal with respect to each coordinate axis.

[0015] Preferably, the step 2 is specifically:

[0016] Perform differential approximation on the array velocity channel to obtain the velocity gradient of the sound field:

[0017]

[0018] in, It is approximated by using the μ direction velocity channel difference When the column vector of each receiving channel coefficient is α, β ,γ It is the constant coefficient brought about by the α+β+γ order difference approximation.

[0019] Preferably, the step 3 is specifically:

[0020] Extract the multipole modes that do not change with frequency in the spatial gradient, and determine the coefficients of each receiving channel when extracting multipole modes of each order:

[0021]

[0022] Among them, α,β,γ =(D x )α(D y ) β (D z ) γ is the multipole mode,

[0023] D x = sinθcosφDy = sinθsinφD z =cosθ represents the directivity of x, y and z channels respectively. When μ = x, then D μ Ψ α,β,γ =Ψ α+1,β,γ ,

[0024] Similarly, we can get μ=y,z when D μ Ψ α,β,γ The expression of F s (k1)=(ik1d) s is the amplitude compensation factor of the n-order difference;

[0025] Ψ α,β,γ =r α,β,γ V(θ,φ)

[0026] Among them, r α,β,γ The multipole mode Ψ is obtained by using the velocity channel based on the difference approximation α,β,γ When , the coefficient vectors of each receiving channel, for all multipole modes, are written in matrix form as:

[0027] H D =RV(θ,φ)

[0028] Among them, H D Contains all multipole modes α+β+γ≤N, R is composed of r α,β,γ The coefficient matrix formed is:

[0029] R=[r 0,0,0 ,r 1,0,0 ,...,r α,β,γ ...] T .

[0030] Preferably, the step 4 is specifically:

[0031] Represent the spherical function with multipole modes of various orders and determine the coefficients of the spherical function corresponding to the multipole mode

[0032]

[0033] in, is composed of the multipole modes H D express When the vector of modal coefficients of multipole sub-orders is formed, all spherical functions with order n≤N are It can be expressed in multipole mode and written in matrix form:

[0034] b Y (θ,φ)=EH D

[0035] in, It is composed of spherical functions Y of various orders with n≤N and |m|≤n n m (θ,φ) composed of (N+1) 2 ×1 column vector, E is the coefficient matrix composed of the coefficients of the spherical functions of each order obtained by the multipole mode and is expressed as:

[0036]

[0037] Preferably, the step 5 is specifically:

[0038] Use the spherical function as the basis function to expand the desired beam and obtain the coefficients of each order of spherical function

[0039]

[0040] According to the relationship between the beam pattern and the beamformer, the weight coefficient vector of each receiving channel of the array when synthesizing the desired beam pattern is obtained.

[0041] B N (θ,φ)=w H (θ s ,φ s )V(θ,φ)=g H ERV(θ,φ)

[0042] The weighted coefficient vector is obtained to satisfy:

[0043] w H (θ s ,φ s ) = g H ER

[0044] By using the above-mentioned weighted vectors to perform weighted processing on the small-sized vector volume array, a beam pattern that can be steered in three-dimensional space can be formed.

[0045] The present invention has the following beneficial effects:

[0046] The present invention uses the above-mentioned weighted vector to perform weighted processing on the small-sized vector volume array to form a beam pattern that can be steered in three-dimensional space, thereby solving the problem that the existing small-sized array beam cannot be steered in three-dimensional space. The advantage of the present invention is that it provides a three-dimensional beamforming method for a small-sized acoustic vector array in a very low frequency band, which not only solves the contradiction between obtaining high spatial gain in the very low frequency band and the array aperture, but also meets the needs of three-dimensional space detection. The present invention links the multipole mode with the spherical function, and synthesizes the spherical function with θ and φ as variables through the multipole mode, thereby realizing array beamforming under small aperture. According to the orthogonal completeness of the spherical function in three-dimensional space, the desired three-dimensional beam that can be steered in both the pitch angle and the azimuth angle is synthesized using spherical functions of various orders, so that the beamforming algorithm can meet the needs of three-dimensional space detection. The present invention uses the directivity of the vector hydrophone itself to extract the multipole modes of various orders as shown in step (5) and the spherical harmonics of various orders as shown in step (6). Therefore, compared with the commonly used sound field spherical harmonic decomposition beamforming method for spherical arrays, under the conditions of the same size and the same number of array elements, the present invention can extract higher-order spherical harmonics to obtain higher array gain and narrower beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the structure of a small-size vector array;

[0048] Figure 2 It is a schematic diagram of the second-order difference approximate velocity gradient;

[0049] Figure 3 It is a flowchart of the invention content;

[0050] Figure 4 It is the 3rd order beam pattern of a small size vector array;

[0051] Figure 5 is the variation of the third-order beam pattern of a small-size vector array with d / λ, Figure 5 -(a) is the azimuth beam pattern; Figure 5 -(b) elevation beam pattern;

[0052] Figure 6 is the gain variation with d / λ under different modal orders of small-sized vector array, Figure 6 -(a) array gain, Figure 6 -(b) White noise gain DETAILED DESCRIPTION

[0053] The present invention is described in detail below in conjunction with specific embodiments. Specific embodiment one:

[0055] A small-size volume array three-dimensional beamforming method based on acoustic vector hydrophones comprises the following steps:

[0056] Step 1: Construct a small-sized acoustic vector volume array with vector hydrophone as the primitive, and build a receiving signal model;

[0057] The step 1 is specifically as follows:

[0058] Construct a small volume array based on vector hydrophone and establish a received signal model:

[0059]

[0060] Where θ and φ represent the elevation angle and azimuth angle, respectively; The operation represents the Kronecker product, The elements in the left vector represent the array element sound pressure, x, y and z velocity channel directivity, and the superscript T indicates 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), D=[sinθcosφ,sinθsinφ,cosθ] T , is the direction cosine vector of the signal with respect to each coordinate axis.

[0061] Step 2: Use the difference method to obtain the high-order velocity gradient;

[0062] The step 2 is specifically as follows:

[0063] Perform differential approximation on the array velocity channel to obtain the high-order velocity gradient of the sound field:

[0064]

[0065] Where p0 is the sound pressure response of the reference array element, It is approximated by the difference of the velocity channel in the μ direction When the column vector of each receiving channel coefficient is α, β ,γ It is the constant coefficient brought about by the α+β+γ order difference approximation.

[0066] Step 3: Extract the multipole modes in each order of velocity gradient;

[0067] The step 3 is specifically as follows:

[0068] Extract the multipole modes that do not change with frequency in the velocity gradient, and determine the coefficients of each receiving channel when extracting multipole modes of each order:

[0069]

[0070] Among them, α,β,γ=(D x )α(D y ) β (D z ) γ is the multipole mode,

[0071] D x = sinθcosφD y = sinθsinφD z =cosθ represents the directivity of x, y and z channels respectively. When μ = x, then D μ Ψ α,β,γ =Ψ α+1,β,γ ,

[0072] Similarly, we can get μ=y,z when D μ Ψ α,β,γ The expression of F s (k1)=(ik1d) s is the amplitude compensation factor of the n-order difference;

[0073] Ψ α,β,γ =r α,β,γ V(θ,φ)

[0074] Among them, r α,β,γ The multipole mode Ψ is obtained by using the velocity channel based on the difference approximation α,β,γ When , the coefficient vectors of each receiving channel, for all multipole modes, are written in matrix form as:

[0075] H D =RV(θ,φ)

[0076] Among them, H D Contains all multipole modes α+β+γ≤N, R is composed of r α,β,γ The coefficient matrix formed is:

[0077] R=[r 0,0,0 ,r 1,0,0 ,...,r α,β,γ ...] T .

[0078] Step 4: Use multipole mode to synthesize spherical functions and extract spherical harmonics of each order in the three-dimensional sound field;

[0079] The step 4 is specifically as follows:

[0080] Represent the spherical function with multipole modes of various orders and determine the coefficients of the spherical function corresponding to the multipole mode

[0081]

[0082] in, is composed of the multipole modes H D express When the vector of modal coefficients of multipole sub-orders is formed, all spherical functions with order n≤N are It can be expressed in multipole mode and written in matrix form:

[0083] b Y (θ,φ)=EH D

[0084] in, It is composed of spherical functions of various orders with n≤N and |m|≤n Composed of (N+1) 2 ×1 column vector, E is the coefficient matrix composed of the coefficients of the spherical functions of each order obtained by the multipole mode and is expressed as:

[0085]

[0086] Step 5: Use spherical function synthesis to steer the desired three-dimensional beam in three-dimensional space.

[0087] The step 5 is specifically as follows:

[0088] Use the spherical function as the basis function to expand the desired beam pattern and obtain the coefficients of each order of spherical function

[0089]

[0090] According to the relationship between the beam pattern and the beamformer, the weight coefficient vector of each receiving channel of the array when synthesizing the desired beam pattern is obtained.

[0091] B N (θ,φ)=w H (θ s ,φ s )V(θ,φ)=g H ERV(θ,φ)

[0092] The weighted coefficient vector is obtained to satisfy:

[0093] w H (θ s ,φ s ) = g H ER

[0094] By using the above-mentioned weighted vectors to perform weighted processing on the small-sized vector volume array, a beam pattern that can be steered in three-dimensional space can be formed. Specific embodiment 2:

[0096] by Figure 1Take the small-sized vector array shown in the figure as an example. The small-sized array studied includes array elements 1 to 11, which form a volume array. The array center is array element 5, which is also the reference array element. The reference sound pressure response is p0=p5. The distance between any two adjacent array elements along the coordinate axis is d and satisfies kd<<1.

[0097] according to Figure 3 As shown, the array is placed in a water area with relatively good free field conditions and suspended to a deeper depth. At the same time, the sound source is placed in the water, and the distance r between the sound source and the center of the array meets the acoustic far field condition. The signal generator is adjusted to generate a CW pulse signal to obtain the array's receiving signal.

[0098] First, the steerability of the method of the present invention in three-dimensional space is verified. When d / λ=1 / 20, the beam is directed to (45°, 45°). The results are as follows: Figure 4 As shown, it can accurately point to the desired direction in a small size.

[0099] Secondly, we verify its application range. Taking the highest order spherical harmonic N=3 that the array can extract as an example, the expected pointing angle is (90°, 180°), and analyze the changes of the beam pattern in azimuth and elevation with d / λ respectively. Figure 5 - In (a) and (b), the curves marked with black “×” are the cross-sectional views of the desired beam pattern at azimuth and elevation angles, respectively. Figure 5 -(a) and (b) show that, in the case of d / λ≤1 / 6, the main lobe width of the beam pattern remains basically unchanged. Although the side lobe gradually increases, the error with the ideal beam pattern is small. As d / λ continues to increase, the error introduced by the differential approximation increases, the beam pattern is seriously distorted, and the performance of the beamforming algorithm is reduced.

[0100] Finally, the gain and robustness of the present invention are verified. Figure 1 When the array shown in the figure extracts 1st-3rd order spherical harmonics for beamforming, the variation trend of array gain with d / λ is as follows: Figure 6 -(a), where the black dashed line is the theoretical array gain of the corresponding order, and the red solid line represents the simulated array gain as a function of d / λ. From the simulation results, it can be seen that the small-sized vector volume array and its beamforming algorithm established in this paper have a higher array gain. Taking N=3 and d / λ=1 / 20 as an example, the array gain can reach 12dB. Under the condition of d / λ≤1 / 6, the array gain basically coincides with the corresponding dashed line and remains unchanged, which means that the algorithm can obtain high gain in a wider low-frequency band. However, due to Figure 6-(b) As can be seen, as the frequency decreases, 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 also be worse. At the same time, by comparing the array gain and white noise gain under different orders N, it can be seen that: as the maximum spherical harmonic order N increases, the array gain gradually increases, and the white noise gain gradually decreases.

[0101] The above is only a preferred implementation of a small-size volume array three-dimensional beamforming method based on an acoustic vector hydrophone. The protection scope of a small-size volume array three-dimensional beamforming method is not limited to the above embodiment. 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, several 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

1. A small-size volume array three-dimensional beamforming method based on acoustic vector hydrophones, characterized by: The following steps are involved: Step 1: Construct a small-sized acoustic vector volume array with vector hydrophone as the primitive, and construct a receiving signal model V(θ,φ), where θ and φ represent the elevation angle and azimuth angle respectively; Step 2: Use the difference method to obtain the spatial gradients of various orders of sound pressure in different directions; The step 2 is specifically as follows: Perform differential approximation on the array velocity channel to obtain the high-order velocity gradient of the sound field: in, It is approximated by using the μ direction velocity channel difference When the column vector of each receiving channel coefficient is α, β ,γ It is the constant coefficient brought by the α+β+γ order difference approximation; Step 3: Extract multipole modes in spatial gradients of various orders; The step 3 is specifically as follows: Extract the multipole modes that do not change with frequency in the velocity gradient, and determine the coefficients of each receiving channel when extracting multipole modes of each order: Among them, α,β,γ =(D x )α(D y ) β (D z ) γ 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 α,β,γ =Ψ α+1,β,γ , Similarly, we can get μ=y,z when D μ Ψ α,β,γ The expression of F s (k1)=(ik1d) s is the amplitude compensation factor of the s-order difference; P α,β,γ =r α,β,γ V(θ,φ) Among them, r α,β,γ The multipole mode Ψ is obtained by using the velocity channel based on the difference approximation α,β,γ When , the coefficient vectors of each receiving channel, for all multipole modes, are written in matrix form as: H D =RV(θ,φ) Among them, H D Contains all multipole modes α+β+γ≤N, R is composed of r α,β,γ The coefficient matrix formed is: R＝[r 0,0,0 ,r 1,0,0 ,...,r α,β,γ ...] T ； Step 4: Use multipole mode to synthesize spherical functions and extract spherical harmonics of each order in the three-dimensional sound field; The step 4 is specifically as follows: Represent the spherical function with multipole modes of various orders and determine the coefficients of the spherical function corresponding to the multipole mode in, is composed of the multipole modes H D express When the vector of modal coefficients of multipole sub-orders is formed, all spherical functions with order n≤N are It can be expressed in multipole mode and written in matrix form: b Y (θ,φ)=EH D Among them, b Y (θ,φ)=[Y0 0 (θ,φ),Y1 -1 (θ,φ),...,Y N N (θ,φ)] T , is the spherical function Y of each order with n≤N and m≤n n m (θ,φ) composed of (N+1) 2 ×1 column vector, E is the coefficient matrix composed of the coefficients of the spherical functions of each order obtained by the multipole mode and is expressed as: Step 5: Use spherical functions to synthesize the desired three-dimensional beam; The step 5 is specifically as follows: Using the spherical function as the basis function, the desired beam B N (θ, φ) expansion, to obtain the coefficients g of the spherical functions of each order H According to the relationship between the beam pattern and the beamformer, the weight coefficient vector of each receiving channel of the array when synthesizing the desired beam pattern is obtained. B N (θ,φ)=w H (i s ,f 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 IS By using the above-mentioned weighted coefficient vector to perform weighted processing on the small-size vector volume array, any desired three-dimensional beam can be obtained, thereby realizing three-dimensional beam forming.

2. The method for three-dimensional beamforming of a small volume array based on acoustic vector hydrophone according to claim 1, characterized in that: The step 1 is specifically as follows: Construct a small volume array based on vector hydrophone and establish a received signal model: in, The operation represents the Kronecker product, The elements in the left vector represent the array element sound pressure, x, y and z velocity channel directivity, and the superscript T indicates 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), D=[sinθcosφ,sinθsinφ,cosθ] T , is the direction cosine vector of the signal with respect to each coordinate axis.

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