A design method of a robust vector array differential beamformer

Abstract

The application relates to a design method of a robust vector array differential beamformer, belonging to the field of sound signal processing, which comprises the following steps: setting system working parameters; transmitting a detection signal; judging whether a target signal is detected; receiving and preprocessing array signals; reconstructing full-array steering vectors by using Kronecker product operation; selecting an ideal differential beam pattern form, setting target direction distortionless response constraints and non-target direction response constraints; decoupling the system total weight vector into the Kronecker product form of spatial weight and channel weight by using the Kronecker product property, taking the white noise gain maximization as an objective criterion, and solving the optimal channel weight; constructing a weight approximation model based on the Maclaurin series expansion, solving the optimal spatial weight by using the least square method, synthesizing the system total weight vector, and realizing the design of a differential beamformer of any order. The application can significantly improve the robustness of the differential beamformer and effectively suppress spatial white noise.

Description

Technical Field

[0001] This invention relates to the field of acoustic signal processing technology, and more specifically to a design method for a robust vector array differential beamformer. Background Technology

[0002] Traditional Delay-and-sum (DAS) beamforming technology is widely used in sonar, radar, and wireless communication. Its core principle is to receive target signals within a specified angular range in space, suppress interference from other directions, and thus improve the output signal-to-noise ratio. Theoretical analysis has verified that DAS beamforming technology has good robustness, but it has inherent drawbacks such as large beamwidth and low array gain. With the rapid development of underwater vibration reduction and noise reduction technologies, and the continuous increase in the background noise level of the marine environment, target signals are easily submerged by marine environmental noise, significantly increasing the difficulty of underwater target detection. The array gain provided by traditional DAS beamforming technology can no longer meet the practical application requirements of underwater target detection.

[0003] To effectively improve array gain, researchers have proposed differential beamforming (DBS), which achieves frequency-independent directivity within a limited array space and offers superior array gain compared to traditional DAS beamforming methods; hence, it is also known as super-directivity technology. However, DBS suffers from severe white noise amplification, significantly impacting its robustness in practical applications and making it unsuitable for complex oceanographic scenarios. To overcome this white noise amplification problem, previous studies have improved robustness through beam approximation and least-norm (L2) solutions, but these methods exhibit array gain instability and oscillations at low frequencies. To address this issue, researchers have applied distortion-free constraints to the target direction, achieving a partial balance between white noise gain and directivity; however, this approach has limited effectiveness in improving white noise gain and fails to fundamentally solve the problem.

[0004] To further improve the robustness of differential directivity, researchers proposed an improved scheme for robust differential beamforming of acoustic vector sensors. Utilizing the inherent directivity advantages of the acoustic vector sensor's sound pressure and vibration velocity channels, and designing weights using beam approximation principles, this scheme can suppress white noise amplification while maintaining supergain characteristics. However, this improved scheme currently only derives low-order analytical forms and does not provide a complete arbitrary-order analytical solution, limiting its applicability. A subsequently proposed zero-point controllable arbitrary-order differential directivity algorithm, while achieving the design of an arbitrary-order differential beamformer, does not address the white noise amplification problem, and its robustness still needs further improvement, failing to meet the stable detection requirements in complex underwater noise environments.

[0005] Therefore, how to construct a vector array differential beamformer design method that can ensure stable gain across the entire frequency band, achieve flexible design of arbitrary order, and take into account high robustness is one of the technical problems that urgently need to be solved in this field. Summary of the Invention

[0006] To address the white noise amplification problem in existing differential beamforming techniques based on acoustic vector sensors, this invention provides a design method for a robust vector array differential beamformer. This invention significantly improves the robustness of the differential beamformer and effectively suppresses spatial white noise.

[0007] The technical solution adopted by this invention to solve the technical problem is as follows:

[0008] This invention provides a design method for a robust vector array differential beamformer, comprising the following steps:

[0009] Step S101: Set system operating parameters and initialize the array;

[0010] Step S102: Transmit a detection signal;

[0011] Step S103: Determine whether a target signal is detected. If no target signal is detected, return to step S102; if a target signal is detected, proceed to step S104.

[0012] Step S104: Array signal reception and preprocessing;

[0013] Step S105: Reconstruct the full array steering vector using the Kronecker product operation;

[0014] Step S106: Select the ideal differential beam pattern and set the distortion-free response constraint in the target direction and the response constraint in the non-target direction;

[0015] Step S107: Using the Kronecker product property, the total weight vector of the system is decoupled into the Kronecker product form of spatial weights and channel weights, and the optimal channel weights are solved with the goal of maximizing white noise gain.

[0016] Step S108: Construct a weight approximation model based on the McLaurin series expansion, solve for the optimal spatial weights using the least squares method, synthesize the total weight vector of the system, and realize the design of an arbitrary-order differential beamformer.

[0017] Furthermore, in step S104, spatial sound field information is acquired through each acoustic vector sensor in the array to obtain a multidimensional raw data signal, which includes sound pressure components and mutually orthogonal particle velocity components; the multidimensional raw data signal is then subjected to bandpass filtering, amplification and normalization processing in sequence.

[0018] Furthermore, in step S105, the full array guiding vector Guided vector by acoustic pressure array With acoustic vector sensor guide vector The Kronecker product is constructed, denoted as , This represents the Kronecker product operation. Let θ be the angular frequency and θ be the incident angle of the signal.

[0019] Furthermore, in step S105, the frequency domain representation of the received signal is determined based on the full array steering vector: assuming the target signal is incident from the end-fire direction, the frequency domain representation of the received signal is as follows:

[0020] ;

[0021] in, Angular frequency, Indicates the target signal. and These represent the received signal and noise vector of the acoustic vector sensor, respectively. and These represent the received signal and noise vector received by the m-th element of the uniform linear array, respectively. , , These represent the received signals of the sound pressure channel of the m-th array element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively. , , These represent the noise levels of the sound pressure channel of the m-th element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively.

[0022] Using conventional filtering methods, the filter output is expressed as:

[0023] ;

[0024] Among them, superscript Represents the conjugate transpose operator; This represents the filter weighting coefficients corresponding to the differential beamformer, i.e., the total system weight vector; This represents the weights corresponding to each component channel of the m-th element in a uniform linear array. , and These represent the sound pressure component weight, the particle velocity component weight in the x-axis direction, and the particle velocity component weight in the y-axis direction of the m-th element of the uniform linear array, respectively.

[0025] Furthermore, in step S106, the differential beam pattern is defined as follows: superscript Represents the conjugate transpose operator; This represents the filter weighting coefficients corresponding to the differential beamformer, i.e., the total system weight vector; Represents the full array steering vector. θ is the angular frequency, and θ is the signal incident angle;

[0026] Ensure that the target signal satisfies the distortion-free response constraint in the target direction and the response constraint in the non-target direction, i.e.:

[0027] ;

[0028] The mathematical expression for an ideal Nth-order differential beam pattern is:

[0029] ;

[0030] in, The coefficients are real, and .

[0031] Furthermore, in step S107, based on the Kronecker product property, the white noise gain is... Represented as:

[0032] ;in The white noise gain of the acoustic pressure array. For the white noise gain of a monophonic vector sensor, For spatial weights, For channel weights, superscript This represents the conjugate transpose operator. The acoustic pressure array steering vector, The guide vector for the acoustic vector sensor. express 3D identity matrix .

[0033] Furthermore, in step S107, due to the ideal differential beam pattern of the single-sound vector sensor... If the order is 1, then the ideal differential beam pattern of the monoacoustic vector sensor will be... Represented as:

[0034] ;

[0035] in, , , All coefficients are real coefficients;

[0036] By weighting the guide vector of the monoacoustic vector sensor using channel weights, the beam response of the monoacoustic vector sensor, i.e., the approaching differential beam pattern, can be obtained. for:

[0037] ;

[0038] in, Indicates the channel weights of a monophonic vector sensor, superscript Representing the conjugate operator, compared with the ideal differential beam pattern of a single-sound vector sensor. Approaching Differential Beamform have to: , , The white noise gain of the monophonic vector sensor The denominator is expressed as:

[0039] ;

[0040] Combining the target direction distortion-free response constraint Rewrite the above formula as follows: A quadratic function of one variable:

[0041] ;

[0042] For the variables in the above formula Differentiate:

[0043] ;

[0044] Analyze the above formula to determine the white noise gain of the monophonic vector sensor. denominator extremum:

[0045] ;

[0046] After analysis and calculation, the function is in For a non-monotonic function, the minimum point is at Obtained, at this time The white noise gain of the monophonic vector sensor The maximum value is 3, in which case:

[0047] ;

[0048] At this time, the channel weights of the monophonic vector sensor are:

[0049] ;

[0050] To maximize the white noise gain of the differential beamformer, the ideal differential beam pattern for the monoacoustic vector sensor should be:

[0051] .

[0052] Furthermore, in step S108, when the ideal differential beam pattern of the monoacoustic vector sensor is taken... At that time, the ideal differential beam pattern of the acoustic pressure array should be of order N-1, that is:

[0053] ;

[0054] Among them, any All are real coefficients, and At this point, the overall differential beam pattern of the vector array is represented as:

[0055] ;

[0056] Ideal Nth-order differential beam pattern The mathematical expression is as follows:

[0057] ;

[0058] Global differential beam pattern using vector array Compared to the ideal Nth-order differential beam pattern By approximating, we obtain and The relationship between them is as follows:

[0059] ;

[0060] Solving the above equation yields:

[0061] ;

[0062] According to the above formula, when hour, and The following relationship exists:

[0063] ;

[0064] Combination When N=1, the solution is obtained. The possible values ​​are as follows:

[0065] ;

[0066] when When, the solution is obtained The possible values ​​are as follows:

[0067] ;

[0068] in, real numbers For free variables, .

[0069] Furthermore, in step S108, the approach differential beam pattern is obtained by weighting the acoustic pressure array steering vector using spatial weights. :

[0070] ;

[0071] According to Maclaurin's series expansion of exponential functions, we have:

[0072] ;

[0073] This will approach the differential beam pattern. Rewritten as:

[0074] ;

[0075] in, If we restrict the order n in the above equation to expand it to order N-1, then:

[0076] ;

[0077] because Comparison of approaching differential beam patterns Ideal differential beam pattern with acoustic pressure array The calculation formula is as follows:

[0078] ;

[0079] make : ,get , for 3D matrix , It is an N-dimensional diagonal matrix. for Dimensional vector.

[0080] Furthermore, in step S108, the least squares method is used to... The calculation yielded the following:

[0081] ;

[0082] Due to the matrix with vector If all elements in the set are real numbers, then:

[0083] ;

[0084] The weights of the vector array differential beamformer with maximum white noise gain are:

[0085] ;

[0086] in, for Zero-dimensional vector.

[0087] The beneficial effects of this invention are:

[0088] This invention provides a robust vector array differential beamformer design method. It reconstructs the full array steering vector using Kronecker product operations, decouples the total system weight vector, and solves for the optimal channel weights based on white noise gain maximization analysis. Simultaneously, based on the McLaurin series expansion theory and combined with the least squares method, it derives the optimal spatial weights that satisfy the distortion-free end-fire direction constraint, and finally synthesizes the total system weight vector, thereby realizing the design of an arbitrary order differential beamformer.

[0089] This invention, by introducing the Kronecker product operator, theoretically derives the constraint criterion for maximizing white noise gain in the differential beamforming design of vector array differential beamformers. Simultaneously, by combining McLaurin series expansion and the least squares method, it derives analytical solutions for differential beamformers of arbitrary order. This invention not only provides complete analytical solutions for high-order differential beamformers but also significantly improves the white noise gain of the system while maintaining the array's hyperdirectivity, effectively suppressing spatial white noise and significantly enhancing the robustness and target detection performance of miniaturized array systems in complex, high-noise environments. This invention effectively alleviates the problems of limited order design and severe white noise amplification in beamforming technology, providing an efficient engineering implementation scheme for the design of differential beamformers under high-order conditions.

[0090] Compared to conventional acoustic pressure array differential beamforming technology, the white noise gain of this invention can be increased by up to 4.8dB, and its overall performance is also superior to existing differential beamforming technology. It effectively suppresses spatial white noise, enabling the differential beamformer to maintain superdirectivity while possessing better robustness, and significantly improving the working performance of the array system in complex noise environments. Attached Figure Description

[0091] Figure 1 A flowchart illustrating a design method for a robust vector array differential beamformer provided by this invention.

[0092] Figure 2 To set the number of array elements And the spacing between array elements The diagram shows the implementation effect of a first-order differential beamformer. Among them, (a) is the differential beam pattern, and (b) is a comparison diagram of white noise gain (WNG).

[0093] Figure 3 To set the number of array elements And the spacing between array elements The diagram shows the implementation effect of the second-order differential beamformer. Among them, (a) is the differential beam pattern, and (b) is a comparison diagram of white noise gain (WNG).

[0094] Figure 4 To set the number of array elements And the spacing between array elements The diagram shows the implementation effect of the third-order differential beamformer. Among them, (a) is the differential beam pattern, and (b) is a comparison diagram of white noise gain (WNG). Detailed Implementation

[0095] The present invention will be further described in detail below with reference to the accompanying drawings.

[0096] See Figure 1 As shown, the present invention provides a design method for a robust vector array differential beamformer, the specific implementation process of which is as follows:

[0097] Step S101: Set system operating parameters;

[0098] Consider a plane wave signal located in the far sound field incident on a uniform linear array (ULA) consisting of M acoustic vector sensors (AVS). The ULA is placed along the x-axis, with an adjacent element spacing of δ, and the spacing between adjacent elements is much smaller than half the signal wavelength, i.e.:

[0099]

[0100] in, The highest frequency of the corresponding signal wavelength, c is the speed of sound, and f is the frequency of the target signal.

[0101] The system operating parameters are determined and the array is initialized. These parameters mainly include the target signal frequency f, the number of AVS elements M in the array, and the spacing between adjacent elements δ. This step provides precise basic physical parameters for subsequent full-array steering vector reconstruction based on the Kronecker product.

[0102] Step S102: Transmit a detection signal;

[0103] Transmit a detection signal, ensuring that the detection signal meets specific frequency range and waveform requirements, and that the bandwidth satisfies the narrowband assumption. Repeat this step periodically until the target signal is detected.

[0104] Step S103: Determine whether a target signal is detected. If no target signal is detected, return to step S102; if a target signal is detected, proceed to step S104.

[0105] Step S104: Array signal reception and preprocessing;

[0106] Spatial sound field information is acquired by individual acoustic vector sensors in a uniform linear array, resulting in a multidimensional raw data signal containing sound pressure components and mutually orthogonal particle velocity components. To eliminate DC bias in the signal and suppress high-frequency noise, the multidimensional raw data signal is sequentially subjected to bandpass filtering, amplification, and normalization.

[0107] Step S105: Reconstruct the full array steering vector using the Kronecker product operation;

[0108] Taking the first acoustic vector sensor as a reference point, the Scalar Pressure Array (SPA) steering vector... It can be determined as follows:

[0109]

[0110] in, , Here, ω is the angular frequency, and θ is the angle of incidence of the signal. (Superscript) This indicates the transpose operation.

[0111] Taking a two-dimensional acoustic vector sensor as an example, the single acoustic vector sensor guides the vector. It can be determined as follows:

[0112]

[0113] Where 1 represents the sound pressure component. and These represent the velocity components along the x-axis and y-axis, respectively.

[0114] Guided vector by acoustic pressure array With acoustic vector sensor guide vector The Kronecker product constructs the full array guiding vector. ,Right now:

[0115]

[0116] in, This represents the Kronecker product operation.

[0117] The frequency domain representation of the received signal is determined based on the full array steering vector. Specifically, it is assumed that the target signal is incident from the end-fire direction (i.e., the signal incident angle). The received signal in the frequency domain is then represented as:

[0118]

[0119] in, This represents the target signal, each with a length of 3M. and Let represent the received signal and noise vector of the acoustic vector sensor, respectively. and Let and represent the received signal and noise vector received by the m-th element of the uniform linear array, respectively. , , These represent the received signals of the sound pressure channel of the m-th array element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively. , , These represent the noise levels of the sound pressure channel of the m-th array element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively.

[0120] Using conventional filtering methods, the filter output is expressed as:

[0121]

[0122] Among them, superscript Represents the conjugate transpose operator; This represents the filter weighting coefficients corresponding to a differential beamformer with a length of 3M, which is the total weight vector of the system. This represents the weights corresponding to each component channel of the m-th element in a uniform linear array, where... , and These represent the sound pressure component weight, the particle velocity component weight in the x-axis direction, and the particle velocity component weight in the y-axis direction of the m-th element of the uniform linear array, respectively.

[0123] Step S106: Select the ideal differential beam pattern and set the distortion-free response constraint in the target direction and the response constraint in the non-target direction;

[0124] Specifically, the differential beammap is used to describe the sensitivity of the differential beamformer to the response of targets at different incident angles, and its specific definition is as follows:

[0125]

[0126] in, This represents the overall beam response of the system.

[0127] To ensure the target signal is distortion-free in the end-fire direction, constraints are set to ensure that the differential beamformer's response in the end-fire direction meets the distortion-free response constraint, i.e. The differential beamformer's response is less than 1 in all other directions, thus ensuring that the target signal satisfies the distortion-free response constraint in the target direction and the response constraint in non-target directions. Its mathematical expression is as follows:

[0128]

[0129] Based on the accuracy requirements and interference suppression needs of the detection mission, the mathematical expression for the Nth-order differential beam pattern is as follows:

[0130]

[0131] Among them, any The coefficients are real, and .

[0132] Step S107: Using the Kronecker product property, the total weight vector of the system is decoupled into the Kronecker product of spatial weights and channel weights, and the optimal channel weights are solved with the goal of maximizing white noise gain (WNG).

[0133] Based on full array steering vector The Kronecker product construction property decomposes the total weight vector of the system into spatial weights. With channel weights The Kronecker product form is:

[0134]

[0135] At this time, the overall beam response of the system Represented as:

[0136]

[0137] in, For acoustic pressure array beam response, This is the beam response of a monoacoustic vector sensor.

[0138] White noise gain (WNG) is a metric for evaluating the robustness of a differential beamformer. It describes the degree to which a uniform linear array suppresses white noise, and its specific definition is as follows:

[0139]

[0140] in, , express 3D identity matrix .

[0141] Based on the Kronecker product property, the white noise gain Represented as:

[0142]

[0143] The white noise gain of the acoustic pressure array is expressed as:

[0144]

[0145] The white noise gain of a monophonic vector sensor is expressed as:

[0146]

[0147] When the white noise gain of the sound pressure array When fixed, the white noise gain of a monophonic vector sensor The range of values ​​directly affects the white noise gain improvement of the vector array compared to the acoustic pressure array.

[0148] Due to the ideal differential beam pattern of the monoacoustic vector sensor If the order is 1, then the ideal differential beam pattern of the monoacoustic vector sensor will be... Represented as:

[0149]

[0150] in, , , All are real coefficients.

[0151] By weighting the guide vector of the monoacoustic vector sensor using channel weights, the beam response of the monoacoustic vector sensor, i.e., the approaching differential beam pattern, can be obtained. Represented as:

[0152]

[0153] in, Indicates the channel weights of a monophonic vector sensor, superscript Representing the conjugate operator, compared with the ideal differential beam pattern of a single-sound vector sensor. Approaching Differential Beamform We can obtain, , , The white noise gain of the monophonic vector sensor The denominator can be expressed as:

[0154]

[0155] Combining the target direction distortion-free response constraint Rewrite the above formula as follows: For a quadratic function of variable 1, we can obtain:

[0156]

[0157] For the variables in the above formula Taking the derivative, we get:

[0158]

[0159] Analyze the above formula to determine the white noise gain of the monophonic vector sensor. denominator extremum:

[0160]

[0161] After analysis and calculation, the function is in For a non-monotonic function, the minimum point is at Obtained, at this time The white noise gain of the monophonic vector sensor The maximum value is 3, in which case:

[0162]

[0163] At this time, the channel weights of the monophonic vector sensor are:

[0164]

[0165] To maximize the white noise gain of the differential beamformer, the ideal differential beam pattern for the monoacoustic vector sensor should be:

[0166]

[0167] Step S108: Construct a weight approximation model based on the McLaurin series expansion, solve for the optimal spatial weights using the least squares method, and synthesize the total weight vector of the system to realize the design of an arbitrary order differential beamformer.

[0168] When the ideal differential beam pattern of the monoacoustic vector sensor is taken At that time, the ideal differential beam pattern of the acoustic pressure array should be of order N-1, that is:

[0169]

[0170] Among them, any All are real coefficients, and At this point, the overall differential beam pattern of the vector array can be represented as:

[0171]

[0172] Ideal Nth-order differential beam pattern The mathematical expression is as follows:

[0173]

[0174] Global differential beam pattern using vector array Compared to the ideal Nth-order differential beam pattern By approximating, we obtain and The relationship between them is as follows:

[0175]

[0176] Solving the above equation, we get:

[0177]

[0178] According to the above formula, when hour, and The following relationship exists:

[0179]

[0180] Combination When N=1, the solution is obtained. The possible values ​​are as follows:

[0181]

[0182] when When, the solution is obtained The possible values ​​are as follows:

[0183]

[0184] in, real numbers For free variables, In practical applications, free variables can be uniquely determined based on requirements. The value of is determined to obtain the optimal differential beam pattern.

[0185] For an acoustic pressure array, the approximate differential beam pattern is obtained by weighting its acoustic pressure array steering vector using spatial weights. , is represented as:

[0186]

[0187] According to Maclaurin's series expansion of exponential functions, we have:

[0188]

[0189] Then approaching differential beam pattern It can be rewritten as:

[0190]

[0191] in, To represent factorial operation, If we restrict the order n in the above equation to expand it to order N-1, then:

[0192]

[0193] because Comparison of approaching differential beam patterns Ideal differential beam pattern with acoustic pressure array The calculation formula can be obtained as follows:

[0194]

[0195] make : We can obtain: ;in, for dimensional matrix, where the th The elements are , , It is an N-dimensional diagonal matrix. for Dimensional vector.

[0196] Using the least squares method Calculations show that:

[0197]

[0198] Due to the matrix with vector If all elements in the set are real numbers, then:

[0199]

[0200] The weights of the vector array differential beamformer with maximum white noise gain are:

[0201]

[0202] in, for Zero-dimensional vector.

[0203] Step S109: Beamforming output;

[0204] The weight vector obtained in step S108 is applied to the array received signal to synthesize the radiation pattern, achieving a distortion-free signal response in the end-fire direction while maximizing white noise gain. The complete differential beam pattern has high spatial directivity and strong background noise suppression capability.

[0205] In this invention, the number of array elements And the spacing between array elements The implementation effects of the first-order differential beamformer, second-order differential beamformer, and third-order differential beamformer are shown in the following diagrams. Figure 2 , Figure 3and Figure 4 As shown in Figure (a), the differential beamformation obtained by this invention (dashed line) closely matches the theoretical beamformation (solid line), achieving a distortion-free response in the target end-fire direction and effectively suppressing sidelobes in other directions. The white noise gain (WNG) comparison figure (b) shows that, compared to traditional acoustic pressure arrays (SPAs), the vector array differential beamformer with maximum white noise gain designed in this invention achieves a significant improvement in white noise gain (WNG) performance. These results fully demonstrate the superiority and feasibility of this invention in improving system robustness and suppressing spatially uncorrelated background noise.

[0206] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a robust vector array differential beamformer, characterized in that, Includes the following steps: Step S101: Set system operating parameters and initialize the array; Step S102: Transmit a detection signal; Step S103: Determine whether a target signal is detected. If no target signal is detected, return to step S102; if a target signal is detected, proceed to step S104. Step S104: Array signal reception and preprocessing; Step S105: Reconstruct the full array steering vector using the Kronecker product operation; Step S106: Select the ideal differential beam pattern and set the distortion-free response constraint in the target direction and the response constraint in the non-target direction; Step S107: Using the Kronecker product property, the total weight vector of the system is decoupled into the Kronecker product form of spatial weights and channel weights, and the optimal channel weights are solved with the goal of maximizing white noise gain. Step S108: Construct a weight approximation model based on the McLaurin series expansion, solve for the optimal spatial weights using the least squares method, synthesize the total weight vector of the system, and realize the design of an arbitrary-order differential beamformer.

2. The design method for a robust vector array differential beamformer according to claim 1, characterized in that, In step S104, spatial sound field information is obtained through each sound vector sensor in the array to obtain a multidimensional raw data signal, which includes sound pressure components and mutually orthogonal particle velocity components. The multidimensional raw data signal is sequentially subjected to bandpass filtering, amplification, and normalization.

3. The design method for a robust vector array differential beamformer according to claim 1, characterized in that, In step S105, the full array guiding vector Guided vector by acoustic pressure array With acoustic vector sensor guide vector The Kronecker product is constructed, denoted as , This represents the Kronecker product operation. Let θ be the angular frequency and θ be the incident angle of the signal.

4. The design method of a robust vector array differential beamformer according to claim 1, characterized in that, In step S105, the frequency domain representation of the received signal is determined based on the full array steering vector: Assuming the target signal is incident from the end-fire direction, the frequency domain representation of the received signal is as follows: ； in, Angular frequency, Indicates the target signal. and These represent the received signal and noise vector of the acoustic vector sensor, respectively. and These represent the received signal and noise vector received by the m-th element of the uniform linear array, respectively. , , These represent the received signals of the sound pressure channel of the m-th array element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively. , , These represent the noise levels of the sound pressure channel of the m-th element, the particle velocity channel along the x-axis, and the particle velocity channel along the y-axis, respectively. Using conventional filtering methods, the filter output is expressed as: ； Among them, superscript Represents the conjugate transpose operator; This represents the filter weighting coefficients corresponding to the differential beamformer, i.e., the total system weight vector; This represents the weights corresponding to each component channel of the m-th element in a uniform linear array. , and These represent the sound pressure component weight, the particle velocity component weight in the x-axis direction, and the particle velocity component weight in the y-axis direction of the m-th element of the uniform linear array, respectively.

5. The design method for a robust vector array differential beamformer according to claim 1, characterized in that, In step S106, the differential beam pattern is defined as follows: superscript Represents the conjugate transpose operator; This represents the filter weighting coefficients corresponding to the differential beamformer, i.e., the total system weight vector; Represents the full array steering vector. θ is the angular frequency, and θ is the signal incident angle; Ensure that the target signal satisfies the distortion-free response constraint in the target direction and the response constraint in the non-target direction, i.e.: ； The mathematical expression for an ideal Nth-order differential beam pattern is: ； in, The coefficients are real, and .

6. The design method for a robust vector array differential beamformer according to claim 1, characterized in that, In step S107, based on the Kronecker product property, the white noise gain is... Represented as: ;in The white noise gain of the acoustic pressure array. For the white noise gain of a monophonic vector sensor, For spatial weights, For channel weights, superscript This represents the conjugate transpose operator. The acoustic pressure array steering vector, The guide vector for the acoustic vector sensor. express 3D identity matrix .

7. The design method for a robust vector array differential beamformer according to claim 1, characterized in that, In step S107, due to the ideal differential beam pattern of the single-sound vector sensor... If the order is 1, then the ideal differential beam pattern of the monoacoustic vector sensor will be... Represented as: ； in, , , All coefficients are real coefficients; By weighting the guide vector of the monoacoustic vector sensor using channel weights, the beam response of the monoacoustic vector sensor, i.e., the approaching differential beam pattern, can be obtained. for: ； in, Indicates the channel weights of a monophonic vector sensor, superscript Representing the conjugate operator, compared with the ideal differential beam pattern of a single-sound vector sensor. Approaching Differential Beamform have to: , , The white noise gain of the monophonic vector sensor The denominator is expressed as: ； Combining the target direction distortion-free response constraint Rewrite the above formula as follows: A quadratic function of one variable: ； For the variables in the above formula Differentiate: ； Analyze the above formula to determine the white noise gain of the monophonic vector sensor. denominator extremum: ； After analysis and calculation, the function is in For a non-monotonic function, the minimum point is at Obtained, at this time The white noise gain of the monophonic vector sensor The maximum value is 3, in which case: ； At this time, the channel weights of the monophonic vector sensor are: ； To maximize the white noise gain of the differential beamformer, the ideal differential beam pattern for the monoacoustic vector sensor should be: 。 8. The design method of a robust vector array differential beamformer according to claim 7, characterized in that, In step S108, when the ideal differential beam pattern of the monoacoustic vector sensor is taken... At that time, the ideal differential beam pattern of the acoustic pressure array should be of order N-1, that is: ； Among them, any All are real coefficients, and At this point, the overall differential beam pattern of the vector array is represented as: ； Ideal Nth-order differential beam pattern The mathematical expression is as follows: ； Global differential beam pattern using vector array Compared to the ideal Nth-order differential beam pattern By approximating, we obtain and The relationship between them is as follows: ； Solving the above equation yields: ； According to the above formula, when hour, and The following relationship exists: ； Combination When N=1, the solution is obtained. The possible values ​​are as follows: ； when When, the solution is obtained The possible values ​​are as follows: ； in, real numbers For free variables, .

9. The design method of a robust vector array differential beamformer according to claim 8, characterized in that, In step S108, the approaching differential beam pattern is obtained by weighting the acoustic pressure array steering vector using spatial weights. : ； According to Maclaurin's series expansion of exponential functions, we have: ； This will approach the differential beam pattern. Rewritten as: ； in, To represent factorial operation, If we restrict the order n in the above equation to expand it to order N-1, then: ； because Comparison of approaching differential beam patterns Ideal differential beam pattern with acoustic pressure array The calculation formula is obtained as follows: ； make : ,get , for 3D matrix , It is an N-dimensional diagonal matrix. for Dimensional vector.

10. The design method of a robust vector array differential beamformer according to claim 9, characterized in that, In step S108, the least squares method is used to... The calculation yielded the following: ； Due to the matrix with vector If all elements in the set are real numbers, then: ； The weights of the vector array differential beamformer with maximum white noise gain are: ； in, for Zero-dimensional vector.

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