Constant beamwidth beamforming method based on vector combination array

Abstract

The present invention proposes a constant-beamwidth beamforming method based on a vector combination array. To address the problem of wideband signal reception by an underwater acoustic measurement array, a vector nested linear array and a circular sound pressure array are combined into a vector combination array, which can be used to measure broadband radiated noise from underwater acoustic targets. The present invention divides the constant-beamwidth beamforming method based on the combination array into three parts: measurement beamwidth calculation, vector nested array constant-beamwidth beamforming, and combined array constant-beamwidth beamforming. Utilizing the principle of nested arrays, frequency weighting is used to compensate for beamwidth variations at different frequencies. Specifically, a nested array is formed by constructing subarrays with varying spacing, and a method of linearly combining the directivity functions of the subarrays is used to ensure a constant mainlobe beamwidth. During signal processing, a single linear array is subdivided into multiple subarrays for computation, reducing both the complexity of the combination array and the number of processing channels.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic target measurement, in particular to a constant beamwidth beamforming method based on a vector combination array. Background Art

[0002] Measuring the noise radiated by underwater acoustic targets plays an important role in fields such as marine resource development and environmental protection. Analyzing the noise characteristics of underwater acoustic targets can be used for target identification and location. Because the noise radiated by underwater acoustic targets consists of a superposition of a line spectrum and a broadband continuous spectrum, research into broadband measurement methods for underwater acoustic target noise is necessary.

[0003] During the measurement of underwater acoustic targets, if the main beam of the measurement array is too wide relative to the measurement target, it will receive too much background noise and reduce the array gain; if the main beam is too narrow, it will not be able to completely cover the underwater acoustic target, and it will not be possible to obtain effective information on its radiated noise and the true sound source level. Therefore, it is very important to study a measurement system in which the main lobe beamwidth does not change with frequency.

[0004] Traditionally, the measurement of radiated noise from underwater moving targets mostly uses a single hydrophone method or a linear array method. The single hydrophone method is easy to implement and has a simple principle. It can perform normal measurements on targets with high sound source levels, but it cannot provide array gain and cannot suppress the interference of marine environmental noise, making it difficult to meet the needs of measuring radiated noise from low-noise underwater acoustic targets. The horizontal linear array has an obvious ability to suppress traffic noise in space, but does not have sufficient array gain to suppress sea surface environmental noise or seabed reflection noise, which will reduce the stability of the radiated noise measurement results under shallow water conditions. Although the vertical linear array can reduce the influence of sea surface noise and multipath interference, the array aperture is limited by the sea depth, which is not conducive to conducting broadband radiated noise tests in shallow waters. The planar array has directional measurement capabilities, but the application aperture is large in the low-frequency band and is not easy to deploy.

[0005] The constant beamwidth beamformer of the base array can be implemented in the frequency domain and the time domain. The core of the Chebyshev weighting method, spatial resampling method, and FIR method is to divide the broadband signal into different sub-bands, apply different weights to each sub-band, and maintain the consistency of the mainlobe width across the measurement band. However, most of these methods are implemented in the form of scalar linear arrays, which makes it difficult to avoid the "left and right ambiguity" problem that exists in linear array signal processing.

[0006] In summary, while traditional methods for measuring the radiated noise of underwater acoustic targets can achieve a constant beamwidth, they suffer from issues such as insufficient array gain, aperture limitations, and "port / starboard ambiguity" when dealing with low-noise targets and complex ocean environments, making it difficult to guarantee measurement accuracy and stability. These limitations are particularly pronounced in shallow waters and low-frequency applications. Summary of the Invention

[0007] Aiming at the problem of receiving wide-band signals by underwater acoustic measurement array, the present invention combines a vector nested linear array with an acoustic pressure circular array into a vector combination array, and proposes a constant beamwidth beamforming method, which can be used for measuring broadband radiated noise of underwater acoustic targets.

[0008] Vector hydrophones simultaneously pick up sound pressure and three mutually orthogonal particle velocity signals in the underwater sound field. Their particle velocity channels exhibit frequency-independent dipole directivity, enabling unambiguous targeting of targets across the entire spatial range, achieving performance equivalent to that of a four-element acoustic pressure array system. Compared to acoustic pressure arrays of the same configuration, vector arrays offer higher array gain and improved target detection and estimation capabilities.

[0009] The technical solution of the present invention is:

[0010] A constant beamwidth beamforming method based on a vector combination array includes the following steps:

[0011] Step 1: Calculate the measurement beam width;

[0012] The main lobe width of the measurement beam is calculated based on the height of the underwater acoustic target and the distance between the measurement point and the target;

[0013] Step 2: Form a vector nested array constant beamwidth beam response;

[0014] Step 2.1: Divide the set working frequency bandwidth into K frequency sub-bands. Adjacent frequency sub-bands have the same frequency endpoint value. For a certain frequency sub-band [f l ~f h ], a set of vector nested linear arrays is formed by two linear arrays with different array element spacings;

[0015] Step 2.2: Calculate the beam response B of the low-frequency linear array L (f,θ);

[0016] Step 2.3: Calculate the beam response B of the high-frequency linear array H (f,θ);

[0017] Step 2.4: Perform frequency weighting on the beam responses of the high-frequency linear array and the low-frequency linear array respectively to obtain the beam response output result B(f,θ) of the set of vector nested linear arrays.

[0018] Step 2.5: Based on the beam response output of the vector nested linear array obtained in step 2.4, calculate the constant beamwidth beam response B of the vector nested linear array. vector (f,θ);

[0019] Step 3: Form the combined array constant beamwidth beam response:

[0020] Step 3.1: Calculate the beam response B of a circular sound pressure array with a radius of r, formed by N equally spaced array elements. circle (θ);

[0021] Step 3.2: Calculate the array steering vectors of the sound pressure circular array and the vector nested linear array in the combined array;

[0022] Step 3.3: Calculate the received signals of each element of the sound pressure circular array and each element of the vector nested linear array in the combined array, and then calculate the mutual coordination direction of the combined array;

[0023] Step 3.4: Calculate the beam response of the combined array based on the steering vector of the combined array;

[0024] Step 3.5: Construct a low-frequency combination array and a high-frequency combination array respectively; the low-frequency combination array is composed of a low-frequency linear array and a sound pressure circular array, and the high-frequency combination array is composed of a high-frequency linear array and a sound pressure circular array;

[0025] Step 3.6: Calculate the beam responses of the low-frequency combined array and the high-frequency combined array respectively;

[0026] Step 3.7: Calculate the frequency weighting function of the combined array, and obtain the constant beamwidth beam response of the combined array in the frequency sub-band based on the frequency weighting function of the combined array.

[0027] Furthermore, the main lobe width of the measurement beam in step 1 is expressed as:

[0028]

[0029] Where H is the height of the underwater acoustic target itself; L is the distance between the measurement point and the target.

[0030] Furthermore, in step 2.2, according to the low frequency f l The design spacing is d l =λ l / 2 M-element linear array is used as the low-frequency linear array SA1 of the vector nested linear array, where λ l For low frequency f l The corresponding wavelength, M is the set value, the beam response of the low-frequency linear array is B L (f,θ) is:

[0031]

[0032] Where θ is the measurement beam scanning angle; θ p is the known desired direction of the main beam; f is the frequency of the received target signal;

[0033] In step 2.3, according to the high frequency f h The design spacing is dh =λ h / 2 M-element linear array is used as the high-frequency linear array SA2 of the vector nested linear array, where λ h For high frequency f h Corresponding wavelength, beam response B of high-frequency linear array H (f,θ) is:

[0034]

[0035] The beam response output result B(f,θ) of the set of vector nested linear arrays obtained in step 2.4 is:

[0036] B(f,θ)=L(f)B L (f,θ)+H(f)B H (f,θ)

[0037] Where L(f) and H(f) are the frequency weighting coefficients of the low-frequency linear array and the high-frequency linear array, respectively.

[0038] Furthermore, the low-frequency linear array frequency weighting coefficient L(f) and the high-frequency linear array frequency weighting coefficient H(f) are calculated according to the formula

[0039]

[0040]

[0041] Calculated.

[0042] Furthermore, in step 2.5, the vector nested linear array constant beamwidth beam response B vector (f,θ) is:

[0043]

[0044] Furthermore, in step 3.1, the beam response B of the sound pressure circular array circle (θ) is:

[0045] B circle (θ)=|w H (θ)a(θ)|=|a H (θ p )Q -1 a(θ)|

[0046] Where w(θ)=Q -1 a(θ p ) is the weight vector under the condition of maximum array gain; a(θ) is the scanning vector; Q is the normalized noise covariance matrix; a(θ p ) is the circular array steering vector.

[0047] Furthermore, the circular array steering vector a(θ p ) is expressed as:

[0048]

[0049] Where λ is the wavelength of the received signal and n is the number of the nth array element.

[0050] Furthermore, in step 3.2, the array steering vectors of the sound pressure circular array and the vector nested linear array in the combined array are:

[0051]

[0052]

[0053] Among them, a circle_n (θ) is the steering vector of the nth element of the sound pressure circular array; a v_m (θ) is the steering vector of the mth element of the vector nested linear array; d is the element spacing;

[0054] The received signals of each element of the sound pressure circular array and each element of the vector nested linear array in the combined base array in step 3.3 are:

[0055] x circle_n (t) = a circle_n (θ s )s(t)+n pn (t)

[0056] x line_m (t) = a v_m (θ s )s(t)+n vm (t)

[0057] Among them, x circle_n (t) is the sound pressure hydrophone receiving signal corresponding to the nth array element in the sound pressure circular array; x line_m (t) is the vector hydrophone receiving signal corresponding to the mth array element in the vector nested linear array; s(t) is the far-field incident signal, n pn (t) and n vm (t) is the noise signal;

[0058] The beam response of the combined array in step 3.4 is:

[0059] B(θ s )=w H (θ s )a c (θ s )

[0060] Among them, w(θ s ) is the weight vector, ac (θ s ) is the steering vector of the combined array.

[0061] Furthermore, the steering vector a of the combined matrix c (θ s )for:

[0062]

[0063] a circle (θ s )=[a circle_1 (θ s ),...,a circle_n (θ),...,a circle_N (θ s )] T

[0064] a v (θ s )=[a v_1 (θ s ),...,a v_m (θ),...,a v_M (θ s )] T .

[0065] Further,

[0066] The beam response B of the low-frequency combined array in step 3.6 L (f,θ) and the beam response of the high-frequency combined array B H (f,θ) is:

[0067] B L (f,θ)=B circle (f,θ)B L (f,θ)

[0068] B H (f,θ)=B circle (f,θ)B H (f,θ)

[0069] The frequency weighting function of the combined matrix in step 3.7 is:

[0070]

[0071] Beneficial effects

[0072] This invention achieves broadband constant-beamwidth beamforming by combining a vector nested linear array with an acoustic pressure circular array. From an array design perspective, this combination leverages the advantages of both. First, the vector hydrophone array, with its four receiving channels, can capture and combine directional underwater acoustic target radiated noise signals. A single vector hydrophone not only achieves unambiguous directionality across the entire space, but also boasts performance comparable to that of a four-element acoustic pressure array sonar system. Furthermore, compared to acoustic pressure arrays of the same configuration, the vector nested array exhibits stronger immunity to "port / starboard ambiguity" and higher processing gain. Second, the uniform circular array, with its unique geometric properties, can receive signals from all directions in space without blind spots, effectively avoiding signal ambiguity caused by improper formation or layout. It also effectively suppresses ocean background noise and significantly improves array gain. From a beamforming perspective, this invention leverages the principle of nested arrays, using frequency weighting to compensate for beamwidth variations at different frequencies. Specifically, the nested array is constructed by constructing subarrays with varying spacing, and a linear combination of the subarray directivity functions is employed to ensure a constant mainlobe beamwidth. During the signal processing process, this algorithm subdivides a single linear array into multiple different sub-arrays for calculation, which not only reduces the complexity of the combined array, but also reduces the number of processing channels. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is the combined matrix diagram of the present invention;

[0074] Figure 2 The directivity diagrams of the two sub-arrays in the embodiment of the present invention are shown in FIG. 1 , where (a) is the directivity diagram of the low-frequency sub-array and (b) is the directivity diagram of the high-frequency sub-array.

[0075] Figure 3 : The constant beamwidth beam pattern of the nested linear array according to the embodiment of the present invention, wherein (a) is the constant beamwidth beam pattern of the scalar nested linear array, and (b) is the constant beamwidth beam pattern of the vector nested linear array;

[0076] Figure 4 : is the directivity diagram of the sound pressure circular array according to an embodiment of the present invention;

[0077] Figure 5 The directivity diagrams of the low-frequency combination array and the high-frequency combination array according to an embodiment of the present invention are shown in FIG. 1 , wherein (a) is the directivity diagram of the low-frequency combination array, and (b) is the directivity diagram of the high-frequency combination array.

[0078] Figure 6 1 and 2 are combined array constant beamwidth beam patterns in two linear array cases according to an embodiment of the present invention, wherein (a) is a combined array constant beamwidth beam pattern, and (b) is a vector combined array constant beamwidth beam pattern. DETAILED DESCRIPTION

[0079] The present invention proposes a constant beamwidth beamforming method based on a combined array consisting of a vector nested linear array and an acoustic pressure circular array. This method not only has the characteristics of being resistant to 180-degree ambiguity, but also can achieve broadband constant beamwidth beamforming while achieving greater array gain.

[0080] The first part of the present invention calculates the optimal main beam width by measuring the size of the target and the distance between the measurement array and the target. This width is the -3dB beam width used subsequently. The second part constructs a vector nested linear array, uses the -3dB beam width calculated in the first part as the target width, and adopts a linear combination method to achieve constant beamwidth beamforming of the array. The third part constructs a combined array consisting of the vector nested linear array and the acoustic pressure circular array, adopts a conventional beamforming method to obtain the directivity function of the acoustic pressure circular array, and then combines the acoustic pressure circular array with the low-frequency sub-array and high-frequency sub-array constructed in the second part to construct a combined array. After obtaining two directivity functions, the linear combination method is used to achieve constant beamwidth of the combined array.

[0081] The present invention specifically comprises the following steps:

[0082] Step 1: Calculate the measurement beamwidth:

[0083] The main lobe width of the measurement beam is calculated based on the height H of the underwater acoustic target and the distance L between the measurement point and the target:

[0084]

[0085] Step 2: Form the vector nested array constant beamwidth beam response:

[0086] Step 2.1: Divide the set working frequency bandwidth into K frequency sub-bands, and adjacent frequency sub-bands have the same frequency endpoint value; for a certain frequency sub-band [f l ~f h ], a set of vector nested linear arrays is formed by two linear arrays with different array element spacings, and the beam responses of the low-frequency linear array and the high-frequency linear array of the vector nested linear array corresponding to the frequency sub-band are obtained through steps 2.2 and 2.3.

[0087] Step 2.2: According to the low frequency f l The design spacing is d l =λ l / 2 M-element linear array is used as the low-frequency linear array SA1 of the vector nested linear array, where λ l For low frequency f l The corresponding wavelength, M is the set value, calculate the beam response B of the low-frequency linear array L (f,θ) is:

[0088]

[0089] Where θ is the measurement beam scanning angle; θ p is the known desired direction of the main beam; f is the frequency of the received target signal.

[0090] Step 2.3: According to the high frequency f h The design spacing is d h =λ h / 2 M-element linear array is used as the high-frequency linear array SA2 of the vector nested linear array, where λ h For high frequency f h Corresponding wavelength, calculate the beam response B of the high-frequency linear array H (f,θ) is:

[0091]

[0092] Step 2.4: After assigning appropriate amplitude weights to the high-frequency linear array and the low-frequency linear array, a linear combination is performed. That is, the beam responses of the high-frequency linear array and the low-frequency linear array are frequency-weighted to obtain the beam response output of the nested linear array group:

[0093] B(f,θ)=L(f)B L (f,θ)+H(f)B H (f,θ) (4)

[0094] Where L(f) and H(f) are the frequency weighting coefficients of the low-frequency linear array and the high-frequency linear array, respectively;

[0095] The specific frequency weighting coefficient is calculated as follows:

[0096] The beam response B(f,θ) obtained after frequency weighting should satisfy:

[0097]

[0098] Where D(f,θ c ) is the directivity factor;

[0099] The frequency weighting functions corresponding to the low-frequency linear array SA1 and the high-frequency linear array SA2 are solved as follows:

[0100]

[0101] If we assume that θ p = 0, that is, when the target is in the horizontal direction of the array, then take

[0102]

[0103] Where c is the underwater sound speed;

[0104] It can be seen that L(f) and H(f) are a set of frequency filters that weight the beam responses of the two linear arrays according to the frequency variation.

[0105] Step 2.5: Perform combined signal processing on the vector hydrophone sound pressure channel and the three velocity channels, where the orthogonal joint velocity is expressed as:

[0106]

[0107] Among them, s(t) is the far-field incident signal, (p(t)+v c (t))v c (t) Normalized directivity of this combination Signal processing applied to vector nested linear arrays.

[0108] Since the vector array beamforming conforms to the product theorem, that is, the vector array beam response is equal to the product of the non-directional beam response (i.e., B(f,θ) obtained in step 2.4) and the vector array's own directivity function, the constant beamwidth beam response of the vector nested linear array can be calculated as:

[0109]

[0110] Step 3: Form the combined array constant beamwidth beam response:

[0111] Step 3.1: N equally spaced array elements form a sound pressure circle array with a radius of r. The position vector of the nth array element relative to the coordinate origin (center of the circle) is p n =[rcosα,rsinα], where α is the angle between the array element and the coordinate origin relative to the x-axis, and the beam response B of the sound pressure circular array is calculated. circle (θ), the specific steps are:

[0112] Under far-field plane wave conditions, θ p If the desired direction of the main beam is the direction of the circular array, the received signal can be expressed as:

[0113] X=a(θ p )s(t)+n(t) (10)

[0114] Where s(t) is the far-field incident signal; n(t) is the received noise; a(θ p ) is the circular array steering vector, expressed as:

[0115]

[0116] Where, λ is the wavelength of the received signal; n is the number of the nth array element;

[0117] Array gain (AG) is defined as the ratio of the output signal-to-noise ratio of the base array to the output signal-to-noise ratio of the reference array element. max =a(θ p ) H Q-1 a(θ p ), the beam response of the acoustic pressure circular array is:

[0118] B circle (θ)=|w H (θ)a(θ)|=|a H (θ p )Q -1 a(θ)| (12)

[0119] Where w(θ)=Q -1 a(θ p ) is the weighting vector under the maximum array gain condition; a(θ) is the scanning vector; Q is the normalized noise covariance matrix.

[0120] Step 3.2: Calculate the sound pressure in the combined array. The array steering vectors of the circular array and the vector nested linear array are:

[0121]

[0122] Among them, a circle_n (θ) is the steering vector of the nth element of the sound pressure circular array; a v_m (θ) is the steering vector of the mth element of the vector nested linear array; d is the element spacing.

[0123] Step 3.3: Calculate the sound pressure in the combined array, the received signal of each element in the circular array, and the received signal of each element in the vector nested linear array:

[0124]

[0125] Among them, x circle_n (t) is the sound pressure hydrophone receiving signal corresponding to the nth array element in the sound pressure circular array; x line_m (t) is the vector hydrophone receiving signal corresponding to the mth array element in the nested linear array; s(t) is the far-field incident signal, n pn (t) and n vm (t) is the noise signal;

[0126] Then, calculate the mutual coordination direction R of the combined matrix:

[0127]

[0128] Among them, a circle (θ s )=[a circle_1 (θ s ),...,a circle_n (θ),...,a circle_N (θ s )] T ,

[0129] a v (θ s )=[a v_1 (θ s ),...,a v_m (θ),...,a v_M (θ s )] T and a c (θ s ) is the steering vector of the combined matrix; σ s is the signal power, σ nm is the noise power.

[0130] Step 3.4: According to the conventional beamforming algorithm, the weight vector is w = a (θ s ) / MN, the beam response of the combined array is calculated as:

[0131] B(θ s )=w H (θ s )a c (θ s ) (16)

[0132] Step 3.5: Similar to Step 2.2 and Step 2.3, construct the low-frequency combination array and the high-frequency combination array respectively, where the low-frequency combination array CA1 is composed of the array element spacing d l The low-frequency vector linear array and the sound pressure circular array are combined, and the high-frequency combination base array CA2 is composed of array elements with a spacing of d h The high-frequency vector linear array and the sound pressure circular array are combined. The horizontal linear array and the horizontal circular array are placed independently. The positions are as shown in the attached figure. Figure 1 As shown, the horizontal linear array is fixed in the middle of the water body by buoys and bottom sinking devices, and the circular array is placed horizontally on one side of the linear array. A rectangular coordinate system is drawn in the underwater environment. The linear array and the circular array have distances on the z-axis and x-axis, and the direct distance between the two arrays is known.

[0133] Step 3.6: Similar to steps 2.2 and 2.3, calculate the beam response B of the low-frequency combination array. L (f,θ) and the beam response of the high-frequency combined array B H (f,θ):

[0134]

[0135] Step 3.7: Similar to step 2.4, calculate the frequency weighting function of the combined matrix as:

[0136]

[0137] The constant beamwidth beam response of the combined array within the frequency sub-band is obtained based on the frequency weighting function of the combined array.

[0138] The following takes an octave as an example and further describes the constant beamwidth beamforming method of the present invention in conjunction with the accompanying drawings. In this example, the combined array is composed of a 7-element vector nested linear array and an 8-element sound pressure circular array. The combined array array diagram is shown in the attached figure. Figure 1 As shown, the specific steps are:

[0139] Step 1: Calculate the measurement beamwidth:

[0140] The measurement distance is 50m, the underwater acoustic target parameter H is 12m, and the optimal main lobe width for measurement is 14 according to formula (1).

[0141] Step 2: Form the vector nested array constant beamwidth beam response:

[0142] The signal processing frequency band is 1000Hz~2000Hz, which is converted into a sub-band. Two vector nested sub-arrays are constructed. The array element spacing between the low-frequency sub-array and the high-frequency sub-array is d l =λ l / 2=0.75 and d h =λ h / 2=0.375.

[0143] According to formula (2) and (3), the directivity function of the low-frequency sub-array and the beam response of the high-frequency sub-array are calculated respectively. The directivity diagrams of the two sub-arrays are shown in the attached figure. Figure 2 shown.

[0144] The frequency weighting function is calculated according to formula (6), and then the frequency weighting function calculated by formula (6) is substituted into formula (4) to obtain the beam response output result of the vector nested linear array.

[0145] The constant beamwidth beam response of the vector nested linear array is calculated according to formula (9), as shown in the attached figure. Figure 3 shown.

[0146] Step 3: Forming a combined array constant beamwidth wave

[0147] The beam response of the 8-element sound pressure circular array is calculated according to formula (12). The radius of the sound pressure circular array is 0.5m, and its directivity diagram is shown in the attached figure. Figure 4 shown.

[0148] According to formula (17), the beam response of the low-frequency combined array and the beam response of the high-frequency combined array are calculated respectively. The directivity diagrams of the two combined arrays are shown in the attached figure. Figure 5 shown.

[0149] Step 3.3: Calculate the frequency weighting function of the combined array according to formula (18) and obtain the constant beamwidth beam patterns of the combined array in the two linear array cases, as shown in the attached figure. Figure 6 shown.

[0150] The foregoing description is merely an embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of the claims.

Claims

1. A constant beamwidth beamforming method based on a vector combination array, characterized in that: The following steps are involved: Step 1: Calculate the measurement beam width; The main lobe width of the measurement beam is calculated based on the height of the underwater acoustic target and the distance between the measurement point and the target; Step 2: Form a vector nested array constant beamwidth beam response; Step 2.1: Divide the set working frequency bandwidth into K frequency sub-bands. Adjacent frequency sub-bands have the same frequency endpoint value. For a certain frequency sub-band [f l ~f h ], a set of vector nested linear arrays is formed by two linear arrays with different array element spacings; Step 2.2: Calculate the beam response B of the low-frequency linear array L (f,θ); Step 2.3: Calculate the beam response B of the high-frequency linear array H (f,θ); Step 2.4: Perform frequency weighting on the beam responses of the high-frequency linear array and the low-frequency linear array respectively to obtain the beam response output result B(f,θ) of the set of vector nested linear arrays. Step 2.5: Based on the beam response output of the vector nested linear array obtained in step 2.4, calculate the constant beamwidth beam response B of the vector nested linear array. vector (f,θ); Step 3: Form the combined array constant beamwidth beam response: Step 3.1: Calculate the beam response B of a circular sound pressure array with a radius of r, formed by N equally spaced array elements. circle (θ); Step 3.2: Calculate the array steering vectors of the sound pressure circular array and the vector nested linear array in the combined array; Step 3.3: Calculate the received signals of each element of the sound pressure circular array and each element of the vector nested linear array in the combined array, and then calculate the mutual coordination direction of the combined array; Step 3.4: Calculate the beam response of the combined array based on the steering vector of the combined array; Step 3.5: Construct a low-frequency combination array and a high-frequency combination array respectively; the low-frequency combination array is composed of a low-frequency linear array and a sound pressure circular array, and the high-frequency combination array is composed of a high-frequency linear array and a sound pressure circular array; Step 3.6: Calculate the beam responses of the low-frequency combined array and the high-frequency combined array respectively; Step 3.7: Calculate the frequency weighting function of the combined array, and obtain the constant beamwidth beam response of the combined array in the frequency sub-band based on the frequency weighting function of the combined array.

2. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: The main lobe width of the measurement beam in step 1 is expressed as: Where H is the height of the underwater acoustic target itself; L is the distance between the measurement point and the target.

3. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: In step 2.2, according to the low frequency f l The design spacing is d l =λ l / 2 M-element linear array is used as the low-frequency linear array SA1 of the vector nested linear array, where λ l For low frequency f l The corresponding wavelength, M is the set value, the beam response of the low-frequency linear array is B L (f,θ) is: Where θ is the measurement beam scanning angle; θ p is the known desired direction of the main beam; f is the frequency of the received target signal; In step 2.3, according to the high frequency f h The design spacing is d h =λ h / 2 M-element linear array is used as the high-frequency linear array SA2 of the nested linear array group, where λ h For high frequency f h Corresponding wavelength, beam response B of high-frequency linear array H (f,θ) is: The beam response output result B(f,θ) of the set of vector nested linear arrays obtained in step 2.4 is: B(f,θ)=L(f)B L (f,θ)+H(f)B H (f,θ) Where L(f) and H(f) are the frequency weighting coefficients of the low-frequency linear array and the high-frequency linear array, respectively.

4. The constant beamwidth beamforming method based on a vector combination array according to claim 3, wherein: The low-frequency linear array frequency weighting coefficient L(f) and the high-frequency linear array frequency weighting coefficient H(f) are calculated according to the formula Calculated.

5. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: In step 2.5, the vector nested linear array constant beamwidth beam response B vector (f,θ) is:

6. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: In step 3.1, the beam response B of the sound pressure circular array circle (θ) is: B circle (θ)=|w H (θ)a(θ)|=|a H (i p )Q -1 a(θ)| Where w(θ)=Q -1 a(θ p ) is the weight vector under the condition of maximum array gain; a(θ) is the scanning vector; Q is the normalized noise covariance matrix; a(θ p ) is the circular array steering vector.

7. The constant beamwidth beamforming method based on a vector combination array according to claim 6, characterized in that: The circular array steering vector a(θ p ) is expressed as: Where λ is the wavelength of the received signal and n is the number of the nth array element.

8. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: In step 3.2, the array steering vectors of the sound pressure circular array and the vector nested linear array in the combined array are: Among them, a circle_n (θ) is the steering vector of the nth element of the sound pressure circular array; a v_m (θ) is the steering vector of the mth element of the vector nested linear array; d is the element spacing; The received signals of each element of the sound pressure circular array and each element of the vector nested linear array in the combined base array in step 3.3 are: x circle_n (t)=a circle_n (θ s )s(t)+n pn (t) x line_m (t)=a v_m (θ s )s(t)+n vm (t) Among them, x circle_n (t) is the sound pressure hydrophone receiving signal corresponding to the nth array element in the sound pressure circular array; x line_m (t) is the vector hydrophone receiving signal corresponding to the mth array element in the vector nested linear array; s(t) is the far-field incident signal, n pn (t) and n vm (t) is the noise signal; The beam response of the combined array in step 3.4 is: B(θ s )=w H (i s )a c (i s ) Among them, w(θ s ) is the weight vector, a c (θ s ) is the steering vector of the combined array.

9. The constant beamwidth beamforming method based on a vector combination array according to claim 1, wherein: The steering vector a of the combined array c (θ s )for: a circle (i s )=[a circle_1 (i s ),...,a circle_n (θ),...,a circle_N (i s )] T a v (i s )=[a v_1 (i s ),...,a v_m (θ),...,a v_M (i s )] T 。 10. The constant beamwidth beamforming method based on vector combination array according to claim 1, characterized in that: The beam response B of the low-frequency combined array in step 3.6 L (f,θ) and the beam response of the high-frequency combined array B H (f,θ) is: B L (f,θ)=B circle (f,θ)B L (f,θ) B H (f,θ)=B circle (f,θ)B H (f,θ) The frequency weighting function of the combined matrix in step 3.7 is:

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