Direction-adjustable beam forming method for vector small-aperture arbitrary planar array

Abstract

A direction-adjustable beam forming method for a vector small-aperture arbitrary planar array belongs to the field of signal processing, and comprises the following steps: constructing a guiding function; based on the differential beam pattern of the acoustic vector sensor, rewriting the differential beam pattern of the acoustic vector sensor by using a JAE approximate beam pattern, and simplifying the differential beam pattern of the acoustic vector sensor by using an Euler formula to obtain a simplified differential beam pattern of the acoustic vector sensor; calculating according to an n-order Bessel function to obtain an ideal N-order direction-adjustable difference beam pattern; designing the direction-adjustable beam former of each order, comparing a direction-adjustable difference beam pattern with an ideal difference beam pattern, and solving by using a least square method to obtain the optimal weight of each channel so as to realize the design of the direction-adjustable beam former; and the direction-adjustable beam former is used for completing direction-adjustable beam forming of any vector small-aperture planar array. According to the invention, the limitation of the array geometric structure on the performance of the direction-adjustable differential beam former is overcome, and the inherent white noise amplification problem of the traditional differential beam forming method is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a method for forming an adjustable beam with an arbitrary planar array of vector small apertures. Background Technique

[0002] Differential beamforming technology plays an important role in the field of signal processing and is widely used in fields such as target localization, speech enhancement, sonar, and radar. It has attracted attention due to its excellent spatial resolution ability and effective suppression of interference signals. However, the traditional differential beamforming method shows certain limitations in the detection performance in complex dynamic environments due to its dependence on the array structure and the fixed direction of the main lobe of the directivity.

[0003] Conventional differential beamforming methods are usually designed based on specific array structures, such as linear arrays, circular arrays, or spherical arrays. However, in practical applications, due to the limitations of device space and platform layout, specific array forms are difficult to meet the diverse scenario requirements. In addition, most traditional differential beamforming methods cannot flexibly adjust the direction and shape of the main lobe of the beam. When the direction of the target signal changes or the environmental conditions are complex, the performance of the differential beamforming method will be significantly reduced, and even the desired signal may be weakened.

[0004] In addition, under high-noise conditions, the anti-interference ability of the traditional differential beamforming method is weak. Especially in low signal-to-noise ratio scenarios, its array gain and sidelobe suppression performance are not sufficient to meet the actual application requirements. These limitations have become the main obstacles to the further development of traditional differential beamforming technology. Summary of the Invention

[0005] In order to solve the technical problems of signal suppression, white noise amplification, and limitation by the array geometry existing in the existing differential beamforming method, the present invention provides a method for forming an adjustable beam with an arbitrary planar array of vector small apertures. The present invention effectively solves the practical problems encountered in the application of the existing differential beamforming method. Especially in the case of limited platform size, the present invention can still achieve adjustable detection in a small-size arbitrary vector planar geometry, overcoming the drawback that the conventional array cannot achieve directivity adjustment.

[0006] The technical solution adopted by the present invention to solve the technical problems is as follows:

[0007] A method for forming an adjustable beam with an arbitrary planar array of vector small apertures provided by the present invention specifically includes the following steps:

[0008] (1) Determine the element spacing of the acoustic vector sensor array, obtain the array steering vector, and construct the steering function;

[0009] (2) Based on the differential beam pattern of the acoustic vector sensor, the JAE approximate beam pattern is used, that is, the mathematical expression of JAE is substituted into the differential beam pattern of the acoustic vector sensor, and at the same time, the order is restricted to rewrite the differential beam pattern of the acoustic vector sensor; the Euler formula is used to simplify the rewritten differential beam pattern of the acoustic vector sensor to obtain the simplified differential beam pattern of the acoustic vector sensor; the ideal N-order steerable differential beam pattern is calculated according to the n-order Bessel function.

[0010] (3) Design the steerable beamformer for each order, compare the steerable differential beam pattern with the ideal differential beam pattern, and use the least squares method to solve for the optimal weights of each channel to achieve the design of the steerable beamformer.

[0011] (4) Use the steerable beamformer to complete the steerable beamforming of the vector small aperture arbitrary planar array.

[0012] Further, in step (1), assuming that the array reference element coincides with the origin of the Cartesian coordinate system, the position of the m-th array reference element is:

[0013] r m =[r m cos(ψ m ),r m sin(ψ m )]

[0014] where r m represents the distance between the m-th array reference element and the origin of the Cartesian coordinate system, and ψ m represents the counterclockwise angle of the m-th array reference element relative to the positive half-axis of the x-axis of the Cartesian coordinate system.

[0015] For a far-field plane wave incident on an arbitrary planar array composed of M acoustic vector sensors, the received data is:

[0016] Y(ω)=d(ω,θ)X(ω)+V(ω)

[0017] where ω represents the angular frequency, θ represents the incident angle, X(ω) represents the source signal, Y(ω) is a 3M×1 column vector representing the array received data, V(ω) is a 3M×1 column vector representing the noise data received by each channel; d(ω,θ) represents the array steering vector.

[0018] The mathematical expression of the array steering vector is:

[0019]

[0020] where d p (ω,θ) represents the acoustic pressure array steering vector. b(θ) represents the array manifold of the vector array, b(θ) = [1 cosθ sinθ] T , represents the Kronecker product operation, r1,…,r M represents the distances between the first to the Mth array reference elements and the origin of the Cartesian coordinate system, j represents the imaginary unit, c represents the speed of sound, ψ1,…,ψ M represents the counterclockwise angles of the first to the Mth array reference elements with respect to the positive x-axis of the Cartesian coordinate system, T represents the transpose operation.

[0021] Further, in step (2), the mathematical expression of the differential beam pattern of the acoustic vector sensor is:

[0022] B M,N [w(ω),θ] = w H (ω)d(ω,θ)

[0023] The mathematical expression of the JAE is:

[0024]

[0025] where ω represents the angular frequency, θ represents the incident angle, w(ω) represents the weight vector, H represents the conjugate transpose, d(ω,θ) represents the array steering vector, c represents the speed of sound, j represents the imaginary unit, J n (·) represents the Bessel function of the nth order, r m represents the distance between the mth array reference element and the origin of the Cartesian coordinate system, ψ m represents the counterclockwise angle of the mth array reference element with respect to the positive x-axis of the Cartesian coordinate system.

[0026] The rewritten mathematical expression of the differential beam pattern of the acoustic vector sensor is:

[0027]

[0028] where N p is the truncation order, ω represents the angular frequency, θ represents the incident angle, w(ω) represents the weight vector, c represents the speed of sound, j represents the imaginary unit, J n (·) represents the Bessel function of the nth order, r m represents the distance between the mth array reference element and the origin of the Cartesian coordinate system, ψ m represents the counterclockwise angle of the mth array reference element with respect to the positive x-axis of the Cartesian coordinate system, represents the p-channel vibration velocity weight value of the mth acoustic vector sensor, represents the x-channel vibration velocity weight value of the mth acoustic vector sensor, Denotes the y-channel vibration velocity weight of the m-th acoustic vector sensor.

[0029] The Euler's formula is:

[0030] cosθ = (e jθ + e -jθ ) / 2 and sinθ = (e jθ - e -jθ ) / 2j

[0031] By setting W p = [W p,1 … W p,M T , W x = [W x,1 … W x,M T , W y = [W y,1 … W y,M T , the mathematical expression of the differential beam pattern of the simplified acoustic vector sensor is obtained as:

[0032]

[0033] where N p is the truncation order, ω represents the angular frequency, c represents the sound speed, j represents the imaginary unit, θ represents the incident angle, H represents the conjugate transpose, T represents the transpose operation, J n (·) represents the n-th order Bessel function, r1, …, r M represents the distances between the 1st array reference element to the M-th array reference element and the origin of the Cartesian coordinate system, ψ1, …, ψ M represents the counterclockwise angles of the 1st array reference element to the M-th array reference element with respect to the positive x-axis of the Cartesian coordinate system, α n represents the coefficient of the n-th element, represents the set of coefficients, w represents the weight vector, W p represents the set of weights for the p-channel, W x represents the set of weights for the x-channel, W y represents the set of weights for the y-channel.

[0034] The mathematical expression of the ideal N-order steerable differential beam pattern is:

[0035]

[0036] where N and θ s represent the order and the steering angle respectively, θ represents the incident angle, p N (θ) = [e​​​-jNθ … 1… e jNθ T ,b N (θ s )=[b -N (θ s ) … b N (θ s )] T , T represents the transpose operation, j represents the imaginary unit, a N,n represents the coefficient of the nth element of the Nth order, a N,0 represents the coefficient of the first element of the Nth order, b N,n represents the coefficient of the nth element of the Nth order a N,n after simplification, the coefficient of the nth element of the Nth order, b N,0 represents b after simplification N,n the coefficient of the first element of the Nth order.

[0037] Furthermore, in step (3), first design a first-order differential steerable beamformer: by setting the truncation order N p =0, the mathematical expression of the first-order steerable differential beam pattern is obtained as:

[0038]

[0039] Substitute N = 1 into the mathematical expression of the ideal Nth-order steerable differential beam pattern to obtain the ideal first-order steerable differential beam pattern, compare the ideal first-order steerable differential beam pattern with the above first-order steerable differential beam pattern and construct an equation:

[0040]

[0041] Use the least squares method to solve the weight values of each channel, and the weight expressions of each channel are obtained as:

[0042]

[0043] where, w represents the weight vector, θ represents the incident angle, θ s represents the steering angle, H represents the conjugate transpose, W p represents the set of weight values of the p channel, W x represents the set of weight values of the x channel, W y represents the set of weight values of the y channel, j represents the imaginary unit, b 1,-1 represents a for N,n after simplification b N,n′ the coefficient of the first element of the first order on the negative half axis, b 1,0 represents a for N,n after simplification b​N,n Coefficient of the first element in the first order on the positive semi - axis, b 1,1 Denote for a N,n Simplified b N,n′ Coefficient of the second element in the first order on the positive semi - axis, b N,n′ Denote for the coefficient a of the n - th element in the N - th order N,n Coefficient of the (n + 1)-th element in the N - th order on the positive semi - axis obtained after simplification.

[0044] First design a first - order differential steerable beamformer, and then design a second - order differential steerable beamformer: By setting the truncation order N p = 1, the mathematical expression of the second - order steerable differential beam pattern is obtained as:

[0045]

[0046] Substitute N = 2 into the mathematical expression of the ideal N - order steerable differential beam pattern to obtain the ideal second - order steerable differential beam pattern, and compare the ideal second - order steerable differential beam pattern with the above - mentioned second - order steerable differential beam pattern and construct an equation:

[0047]

[0048] Use the least - squares method to solve the weight values of each channel, and the weight expressions of each channel are obtained as:

[0049]

[0050] Among them,

[0051]

[0052] b 2,-2 Denote for a N,n Simplified b N,n Coefficient of the second element in the second order on the negative semi - axis, b 2,-1 Denote for a N,n Simplified b N,n Coefficient of the first element in the second order on the negative semi - axis, b 2,0 Denote for a N,n Simplified b N,n Coefficient of the first element in the second order, b 2,1 Denote for a N,n Simplified b N,n′ Coefficient of the second element in the second order on the positive semi - axis, * represents conjugate operation, b 2,2 Denote for a N,n Simplified b N,n Coefficient of the third element in the second order on the positive semi - axis, b N,n′Denotes the coefficient a of the nth element of the Nth order N,n The coefficient of the (n + 1)th element of the Nth order after simplification, w represents the weight vector, θ represents the incident angle, θ s Denotes the steering angle, H represents the conjugate transpose, T represents the transpose operation, ψ1,…,ψ M Denotes the counterclockwise angles of the first to the Mth array reference elements relative to the positive x-axis of the Cartesian coordinate system, j represents the imaginary unit, W p Denotes the set of weight values for the p channel, W x Denotes the set of weight values for the x channel, W y Denotes the set of weight values for the y channel.

[0053] First, design a first-order differential steerable beamformer, then design a second-order differential steerable beamformer, and then design a third-order differential steerable beamformer: By setting the truncation order N p = 2, the mathematical expression of the third-order steerable differential beam pattern is obtained as:

[0054]

[0055] Substitute N = 3 into the mathematical expression of the ideal Nth-order steerable differential beam pattern to obtain the ideal third-order steerable differential beam pattern, compare the ideal third-order steerable differential beam pattern with the above third-order steerable differential beam pattern and construct an equation:

[0056]

[0057] Use the least squares method to solve the weight values of each channel, and the weight expressions of each channel are obtained as follows:

[0058]

[0059] Among them,

[0060]

[0061] b 3,-3 Denotes a N,n After simplification, b N,n The coefficient of the 3rd element of the 3rd order on the negative semi-axis, b 3,-2 Denotes a N,n After simplification, b N,n The coefficient of the 2nd element of the 3rd order on the negative semi-axis, b 3,1 Denotes a N,n After simplification, b N,n The coefficient of the 2nd element of the 3rd order on the positive semi-axis, b 3,2 Denotes a N,n After simplification, b N,n′Coefficient of the third element in the third order on the positive semi - axis, * represents the conjugate operation, b 3,3 represents the operation on a N,n After simplification, b N,n Coefficient of the fourth element in the third order on the positive semi - axis, b N,n′ Represents the coefficient a of the nth element in the Nth order N,n Coefficient of the (n + 1)th element in the Nth order on the positive semi - axis obtained after simplification, w represents the weight vector, θ s Represents the steering angle, w represents the incident angle, H represents the conjugate transpose, T represents the transpose operation, ψ1,…,ψ M Represents the counter - clockwise angles of the first to the Mth array reference elements relative to the positive semi - axis of the x - axis in the Cartesian coordinate system, j represents the imaginary unit, W p Represents the set of weight values for the p channel, W x Represents the set of weight values for the x channel, W y Represents the set of weight values for the y channel.

[0062] First, design a first - order differential steerable beamformer, a second - order differential steerable beamformer, and a third - order differential steerable beamformer, and finally design an N - order differential steerable beamformer: By setting the truncation order N p = N - 1, the mathematical expression of the N - order steerable differential beam pattern is obtained as:

[0063]

[0064] Use the least - squares method to solve the weight values of each channel, and the weight expressions of each channel are obtained as follows:

[0065]

[0066] where N≥2,

[0067]

[0068]

[0069] b N,-N represents the operation on a N,n After simplification, b N,n′ Coefficient of the Nth element in the Nth order on the negative semi - axis, b N,N-1 represents the operation on a N,n After simplification, b N,n′ Coefficient of the Nth element in the Nth order on the positive semi - axis, * represents the conjugate operation, b N,N represents the operation on a N,n After simplification, b N,n Coefficient of the (N + 1)th element in the Nth order on the positive semi - axis, b N,n′ Represents the coefficient a of the nth element in the Nth orderN,n The coefficient of the (n + 1)-th element of the N-th order on the positive semi-axis after simplification, W p Denotes the set of weight values of the p-channel, W x Denotes the set of weight values of the x-channel, W y Denotes the set of weight values of the y-channel, j represents the imaginary unit, w represents the weight vector, N and θ s Respectively denote the order and the steering angle, θ represents the incident angle, H represents the conjugate transpose, T represents the transpose operation, ψ1, …, ψ M Denote the counterclockwise angles of the first array reference element to the M-th array reference element relative to the positive semi-axis of the x-axis of the Cartesian coordinate system.

[0070] The beneficial effects of the present invention are:

[0071] For existing differential beamforming methods, especially when designing a steerable differential beamformer, the performance highly depends on the array configuration. Therefore, the present invention proposes a steerable beamforming method for a vector small-aperture arbitrary planar array, which can solve problems such as limited size of small platforms, strict restrictions on array configuration, and weak detection ability, thus realizing a fully steerable beamforming method for a sound vector sensor array with a small arbitrary geometric planar structure. The present invention accurately derives the mathematical expression form of the high-order directivity beam pattern of the vector array by means of the Jacobi-Anger Expansion formula (JAE). Due to the need for frequency independence, the present invention obtains the weight values of each channel by comparing the expansion of the corresponding order directivity expression into each sub-term with the ideal beam pattern to construct the high-order directivity expression in the ideal state. After completing the above steps, according to the requirements, for the selected order, the high-order directivity beam pattern of the vector array is carefully compared with the corresponding ideal steerable directivity expression and a simultaneous relationship is established. Finally, the least squares solution is used to calculate the weight values of each channel to realize the steerable beamforming method for a vector small-aperture arbitrary planar array.

[0072] The present invention overcomes the limitation of the array geometric structure on the performance of the steerable differential beamformer and solves the inherent white noise amplification problem of traditional differential beamforming methods. Description of the Drawings

[0073] Figure 1 Is a flowchart of a steerable beamforming method for a vector small-aperture arbitrary planar array provided by the present invention.

[0074] Figure 2 Is the implementation result diagram of the first-order differential steerable beamformer with a steering angle of 45° in the present invention.

[0075] Figure 3 Is the implementation result diagram of the first-order differential steerable beamformer with a steering angle of 90° in the present invention.

[0076] Figure 4 This is the implementation result diagram of the steerable beamformer with a first-order difference of the steering angle of 225° in the present invention.

[0077] Figure 5 This is the implementation result diagram of the steerable beamformer with a second-order difference of the steering angle of 45° in the present invention.

[0078] Figure 6 This is the implementation result diagram of the steerable beamformer with a second-order difference of the steering angle of 90° in the present invention.

[0079] Figure 7 This is the implementation result diagram of the steerable beamformer with a second-order difference of the steering angle of 225° in the present invention.

[0080] Figure 8 This is the implementation result diagram of the steerable beamformer with a third-order difference of the steering angle of 45° in the present invention.

[0081] Figure 9 This is the implementation result diagram of the steerable beamformer with a third-order difference of the steering angle of 225° in the present invention.

[0082] Figure 10 This is the implementation result diagram of the steerable beamformer with a third-order difference of the steering angle of 315° in the present invention. Detailed implementation manners

[0083] The present invention will be further described in detail below with reference to the accompanying drawings.

[0084] As Figure 1 shown, a method for steerable beamforming of a vector small-aperture arbitrary planar array provided by the present invention has the following specific implementation process:

[0085] Step S-1: Parameter and array design;

[0086] First, determine the working parameters, including the carrier angular frequency range, the number of elements of the Acoustic Vector Sensor (AVS), the value range of the element spacing, and the geometric shape of the planar array (such as circular, square, cross-shaped, or any irregular shape), etc. These parameters will directly affect the performance and effect of subsequent beamforming. For example, the carrier angular frequency determines the frequency characteristics of the signal, the number of elements of the acoustic vector sensor and the element spacing affect the resolution and directivity of the array, and the geometric shape of the planar array is closely related to the signal reception and processing method.

[0087] Step S-2: Signal transmission preparation;

[0088] Use a signal generator to generate a detection signal that meets specific frequency range and waveform requirements.

[0089] Step S-3: Signal Transmission;

[0090] Transmit the processed detection signal to the target area by means of a transmitting transducer.

[0091] Step S-4: Sound Source Detection and Confirmation;

[0092] Continuously detect the target area to determine whether a reflected signal or a scattered signal from the target is received; if no signal is detected, continue the detection according to the set time interval or detection strategy until the signal source is successfully detected.

[0093] Step S-5: Signal Acquisition and Preprocessing;

[0094] Use a receiving transducer to collect the signal of the target in the sound field. During the collection process, attention should be paid to the performance parameters such as the sensitivity and directivity of the receiving transducer to ensure that the target signal can be accurately received and noise interference can be minimized as much as possible.

[0095] Perform preprocessing operations such as amplification and filtering on the collected target signal. The amplification operation can increase the intensity of the signal for subsequent processing; the filtering operation is used to remove the noise and interference components in the signal. For example, a band-pass filter is used to select the frequency range where the target signal is located, and an adaptive filter is used to suppress the environmental noise, etc., to improve the quality of the signal.

[0096] Step S-6: Beamforming Processing;

[0097] During this process, obtain the weights and directivities of each channel by constructing a steering vector, selecting an ideal N-order beamforming pattern, and setting an appropriate steering angle. The specific implementation process is as follows:

[0098] S6.1: Determine the element spacing of the acoustic vector sensor array, obtain the array steering vector, and construct a steering function;

[0099] Specifically, assuming that the reference element of the array coincides with the origin of the Cartesian coordinate system, the position of the m-th array reference element can be expressed as:

[0100] r m =[r m cos(ψ m ),r m sin(ψ m )]

[0101] where r m represents the distance between the m-th array reference element and the origin of the Cartesian coordinate system, and ψ m represents the counterclockwise angle of the m-th array reference element relative to the positive x-axis of the Cartesian coordinate system.

[0102] For a far-field plane wave incident on an arbitrary planar array composed of M acoustic vector sensors, the received data can be expressed as:

[0103] Y(ω) = d(ω,θ)X(ω) + V(ω)

[0104] where ω represents the angular frequency, θ represents the angle of incidence, X(ω) represents the source signal, Y(ω) is a 3M×1 column vector representing the array received data, and V(ω) is a 3M×1 column vector representing the noise data received by each channel; the array steering vector where d p (ω,θ) represents the acoustic pressure array steering vector, b(θ) represents the vector array manifold, b(θ) = [1 cosθ sinθ] T , represents the Kronecker product operation, r1,…,r M represent the distances between the first array reference element to the Mth array reference element and the origin of the Cartesian coordinate system, j represents the imaginary unit, c represents the speed of sound, ψ1,…,ψ M represent the counterclockwise angles of the first array reference element to the Mth array reference element relative to the positive x-axis of the Cartesian coordinate system, and T represents the transpose operation. The array steering vector plays a key role in beamforming, which describes the response characteristics of the array to incident signals in different directions.

[0105] S6.2: Select the appropriate difference beam pattern of the acoustic vector sensor and expand the expression of the ideal difference beam pattern of the acoustic vector sensor;

[0106] Specifically, based on the difference beam pattern B M,N [w(ω),θ] = w H (ω)d(ω,θ), where w(ω) represents the weight vector and H represents the conjugate transpose; represent the weights of each channel of the M acoustic vector sensors. Use the Jacobi-Anger Expansion formula (JAE) to approximate the beam pattern. The mathematical expression of JAE is as follows:

[0107]

[0108] where c represents the speed of sound, J n (·) represents the nth-order Bessel function, and n is a real coefficient.

[0109] Substitute the mathematical expression of JAE into the difference beam pattern B M,N [w(ω),θ] = w H (ω)d(ω,θ), and limit the order n, using the truncation order Np Replace ∞, and rewrite the differential beam pattern of the acoustic vector sensor as:

[0110]

[0111] where, represents the p-channel vibration velocity weight of the m-th acoustic vector sensor, represents the x-channel vibration velocity weight of the m-th acoustic vector sensor, represents the y-channel vibration velocity weight of the m-th acoustic vector sensor.

[0112] Using Euler's formula cosθ = (e jθ + e -jθ ) / 2 and sinθ = (e jθ - e -jθ ) / 2j to simplify the above formula, and at the same time set W p = [W p,1 … W p,M T , W x = [W x,1 … W x,M T , W y = [W y,1 … W y,M T , W p represents the set of weights for the p-channel, W x represents the set of weights for the x-channel, W y represents the set of weights for the y-channel, and we can obtain:

[0113]

[0114] where, represents the set of coefficients.

[0115] At the same time, using the finite order m p to replace ∞, the mathematical expression of the n-th order Bessel function can be obtained as:

[0116]

[0117] Then the mathematical expression of the ideal N-th order steerable differential beam pattern is:

[0118]

[0119] where, N and θ s represent the order and steering angle respectively, p N (θ) = [e -jNθ … 1 … e​​​jNθ T , b N (θ s ) = [b -N (θ s ) … b N (θ s )] T , a N,n represents the coefficient of the nth element of the Nth order, a N,0 represents the coefficient of the first element of the Nth order, b N,n represents the coefficient of the nth element of the Nth order a N,n the coefficient of the (n + 1)th element of the positive half-axis of the Nth order after simplification, b N,0 represents a N,n after simplification b N,n the coefficient of the first element of the positive half-axis of the Nth order.

[0120] S6.3: Design the steerable beamformer for each order, compare the steerable difference beam pattern with the ideal difference beam pattern, and use the least squares method to solve for the optimal weights of each channel, thereby realizing the design of the steerable beamformer;

[0121] The specific operation steps are as follows:

[0122] S6.3.1: Design the first-order differential steerable beamformer;

[0123] When designing the first-order differential steerable beamformer, the truncated order N p = 0 can be set to obtain the mathematical expression of the first-order steerable difference beam pattern as:

[0124]

[0125] Substitute N = 1 into the mathematical expression of the ideal Nth-order steerable difference beam pattern to obtain the ideal first-order steerable difference beam pattern, compare the ideal first-order steerable difference beam pattern with the above first-order steerable difference beam pattern and construct an equation. The mathematical expression of this process is as follows:

[0126]

[0127] Use the least squares method to solve for the weight values of each channel, and obtain the weight expressions of each channel as follows:

[0128]

[0129] Among them, b 1,-1 represents a N,n after simplification b N,n ​Coefficient of the first element in the negative half-axis of the first order, b 1,0 Denote for a N,n b after simplification N,n Coefficient of the first element in the first order of the positive half-axis, b 1,1 Denote for a N,n b after simplification N,n′ Coefficient of the second element in the first order of the positive half-axis.

[0130] S6.3.2: Design a second-order differential steerable beamformer;

[0131] When designing a second-order differential steerable beamformer, the truncated order N p = 1 can be set to obtain the mathematical expression of the second-order steerable differential beam pattern as:

[0132]

[0133] Substitute N = 2 into the mathematical expression of the ideal N-order steerable differential beam pattern to obtain the ideal second-order steerable differential beam pattern. Compare the ideal second-order steerable differential beam pattern with the above second-order steerable differential beam pattern and construct an equation. The mathematical expression of this process is as follows:

[0134]

[0135] Use the least squares method to solve the weight values of each channel, and obtain the weight expressions of each channel as follows:

[0136]

[0137] Among them,

[0138]

[0139]

[0140] b 2,-2 Denote for a N,n b after simplification N,n Coefficient of the second element in the second order of the negative half-axis, b 2,-1 Denote for a N,n b after simplification N,n Coefficient of the first element in the second order of the negative half-axis, b 2,0 Denote for a N,n b after simplification N,n Coefficient of the first element in the second order of the positive half-axis, b 2,1 Denote for a N,n b after simplification N,n Coefficient of the second element in the second order of the positive half-axis, b 2,2′ Denote for aN,n Simplified b N,n′ Coefficient of the third element in the second order on the positive semi - axis.

[0141] S6.3.3: Design a third - order differential steerable beamformer;

[0142] When designing a third - order differential steerable beamformer, by setting the truncation order N p = 2, the mathematical expression of the third - order steerable differential beam pattern is:

[0143]

[0144] Substituting N = 3 into the mathematical expression of the ideal N - order steerable differential beam pattern, the ideal third - order steerable differential beam pattern can be obtained. Comparing the ideal third - order steerable differential beam pattern with the above - mentioned third - order steerable differential beam pattern and constructing an equation, the mathematical expression of this process is as follows:

[0145]

[0146] Using the least - squares method to solve the weight values of each channel, the weight expressions of each channel are obtained as follows:

[0147]

[0148] Among them,

[0149]

[0150] b 3,-3 represents the result of simplifying a N,n Simplified b N,n Coefficient of the third element in the third order on the negative semi - axis, b 3,-2 represents the result of simplifying a N,n Simplified b N,n Coefficient of the second element in the third order on the negative semi - axis, b 3,1 represents the result of simplifying a N,n Simplified b N,n Coefficient of the second element in the third order on the positive semi - axis, b 3,2 represents the result of simplifying a N,n Simplified b N,n′ Coefficient of the third element in the third order on the positive semi - axis, b 3,3 represents the result of simplifying a N,n Simplified b N,n′ Coefficient of the fourth element in the third order on the positive semi - axis.

[0151] S6.3.4: Design an N - order differential steerable beamformer;

[0152] When designing an N - order differential steerable beamformer, the truncated order N can be set p = N - 1, and the mathematical expression of the N - order steerable differential beam pattern is obtained as follows:

[0153]

[0154] Using the least - squares method to solve the weight values of each channel, the weight expressions of each channel are obtained as follows:

[0155]

[0156] where N≥2,

[0157]

[0158]

[0159] b N,-N′ represents the coefficient of the N - th element of the N - th order on the negative semi - axis of a after simplification, b N,n represents the coefficient of the N - th element of the N - th order on the positive semi - axis of a after simplification, b N,n′ represents the coefficient of the (N + 1)-th element of the N - th order on the positive semi - axis of a after simplification. N,N-1 represents the coefficient of the N - th element of the N - th order on the negative semi - axis of a after simplification, b N,n represents the coefficient of the N - th element of the N - th order on the positive semi - axis of a after simplification, b N,n′ represents the coefficient of the (N + 1)-th element of the N - th order on the positive semi - axis of a after simplification. N,N represents the coefficient of the N - th element of the N - th order on the negative semi - axis of a after simplification, b N,n represents the coefficient of the N - th element of the N - th order on the positive semi - axis of a after simplification, b N,n represents the coefficient of the (N + 1)-th element of the N - th order on the positive semi - axis of a after simplification.

[0160] So far, the design of the N - order differential steerable beamformer is completed.

[0161] S6.4: Use the designed steerable beamformer to complete the steerable beamforming of an arbitrary planar array with a vector small aperture.

[0162] Step S - 7: Result output and application;

[0163] In practical applications (such as sonar detection, radar positioning, speech enhancement, etc.), this method can support functions such as target detection, tracking, recognition, and communication, providing strong technical support for applications in related fields.

[0164] In the present invention, Figure 2 —4 is the beam pattern of the first - order differential beamformer at steering angles of 45°, 90°, and 225°, Figure 5 —7 is the beam pattern of the second - order differential beamformer at steering angles of 45°, 90°, and 225°, Figure 8— 10 are the beam patterns of the third-order difference beamformer at steering angles of 45°, 225°, and 315°. Among them, the solid line is the target beam pattern, and the dashed line is the predicted beam pattern. The figure shows that at different orders and different steering angles, the beam pattern of the beamformer is very close to the target beam pattern.

[0165] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A vector small aperture arbitrary plane array steerable beamforming method, characterized in that: The following steps are involved: (1) Determine the array element spacing of the acoustic vector sensor array, obtain the array steering vector, and construct a steering function; (2) Based on the differential beam pattern of the acoustic vector sensor, the JAE approximates the beam pattern, that is, the mathematical expression of JAE is substituted into the differential beam pattern of the acoustic vector sensor, and the order is restricted to rewrite the differential beam pattern of the acoustic vector sensor; The differential beam pattern of the rewritten acoustic vector sensor is simplified by using the Euler formula to obtain a simplified differential beam pattern of the acoustic vector sensor; an ideal N-order steerable differential beam pattern is obtained by calculating according to an n-order Bessel function; (3) Design steerable beamformers of various orders, compare the steerable differential beam pattern with the ideal differential beam pattern, and use the least squares method to obtain the optimal weight of each channel to achieve the steerable beamformer design; (4) Use a steerable beamformer to complete vector small aperture arbitrary planar array steerable beamforming.

2. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (1), assuming that the array reference element coincides with the origin of the Cartesian coordinate system, the position of the mth array reference element is: r m =[r m cos(ψ m ),r m sin(ψ m )] Among them, r m represents the distance between the mth array reference element and the origin of the Cartesian coordinate system, ψ m represents the counterclockwise angle of the mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system; For a far-field plane wave incident on an arbitrary planar array consisting of M acoustic vector sensors, the received data is: Y(ω)=d(ω,θ)X(ω)+V(ω) Where ω represents the angular frequency, θ represents the incident angle, X(ω) represents the source signal, Y(ω) is a 3M×1 dimensional column vector representing the array received data, V(ω) is a 3M×1 dimensional column vector representing the noise data received by each channel; d(ω,θ) represents the array steering vector; The mathematical expression of the array steering vector is: Among them, d p (ω,θ) represents the sound pressure array steering vector, b(θ) represents the vector array flow pattern, b(θ)=[1cosθsinθ] T , represents the Kronecker product operation, r1,…,r M represents the distance between the 1st array reference element to the Mth array reference element and the origin of the Cartesian coordinate system, j represents the imaginary unit, c represents the speed of sound, ψ1,…,ψ M represents the counterclockwise angle from the 1st array reference element to the Mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system, and T represents the transpose operation.

3. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (2), the mathematical expression of the differential beam pattern of the acoustic vector sensor is: B M,N [w(ω),θ]=w H (ω)d(ω,θ) The mathematical expression of the JAE is: Where ω represents the angular frequency, θ represents the incident angle, w(ω) represents the weight vector, H represents the conjugate transpose, d(ω,θ) represents the array steering vector, c represents the speed of sound, and J n (·) represents the nth-order Bessel function, r m represents the distance between the mth array reference element and the origin of the Cartesian coordinate system, ψ m Represents the counterclockwise angle of the mth array reference element relative to the positive x-axis of the Cartesian coordinate system.

4. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (2), the mathematical expression of the differential beam pattern of the rewritten acoustic vector sensor is: Among them, N p is the cutoff order, ω represents the angular frequency, θ represents the incident angle, w(ω) represents the weight vector, c represents the speed of sound, j represents the imaginary unit, and J n (·) represents the nth-order Bessel function, r m represents the distance between the mth array reference element and the origin of the Cartesian coordinate system, ψ m It represents the counterclockwise angle of the mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system. represents the p-channel velocity weight of the m-th acoustic vector sensor, represents the x-channel velocity weight of the m-th acoustic vector sensor, Represents the y-channel velocity weight of the m-th acoustic vector sensor.

5. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (2), the Euler formula is: cosθ=(e jθ +e -jθ ) / 2 sum sinθ=(e jθ -e -jθ ) / 2j By setting W p =[W p,1 …W p,M ] T ,W x =[W x,1 …W x,M ] T , W y =[W y,1 …W y,M ] T , the mathematical expression of the simplified differential beam pattern of the acoustic vector sensor is: Among them, N p is the truncation order, ω is the angular frequency, c is the speed of sound, j is the imaginary unit, θ is the incident angle, H is the conjugate transpose, T is the transpose operation, and J n (·) represents the nth-order Bessel function, r1,…,r M represents the distance between the 1st array reference element to the Mth array reference element and the origin of the Cartesian coordinate system, ψ1,…,ψ M represents the counterclockwise angle from the 1st array reference element to the Mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system, α n represents the coefficient of the nth element, p Np represents a set of coefficients, w represents a weight vector, W p represents the weight set of p channels, W x Represents the weight set of the x channel, W y Represents the weight set of the y channel.

6. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (2), the mathematical expression of the ideal N-order steerable differential beam pattern is: Among them, N and θ s denote the order and the steering angle respectively, θ denotes the incident angle, p N (θ)=[e -jNθ … 1 …e jNθ ] T , b N (θ s )=[b -N (θ s ) … b N (θ s )] T , T represents the transposition operation, j represents the imaginary unit, a N,n Represents the coefficient of the nth element of the Nth order, = a N,0 Indicates the coefficient of the first element of the Nth order, b N,n Represents the coefficient a of the nth element of order N N,n After simplification, we get the coefficient of the Nth order n+1th element of the positive semi-axis, b N,0 Indicates a N,n After simplification, the positive semi-axis b N,n' The coefficient of the first element of the Nth order.

7. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (3), a first-order differential steerable beamformer is designed: by setting the truncation order N p =0, the mathematical expression of the first-order steerable differential beam pattern is: Substituting N=1 into the mathematical expression of the ideal N-order steerable differential beam pattern, we obtain the ideal first-order steerable differential beam pattern. The ideal first-order steerable differential beam pattern is compared with the above first-order steerable differential beam pattern and the equation is constructed: The least square method is used to solve the weight value of each channel, and the weight expression of each channel is obtained as follows: Where w represents the weight vector, θ represents the incident angle, and θ s represents the steering angle, H represents the conjugate transpose, W p represents the weight set of p channels, W x Represents the weight set of the x channel, W y represents the weight set of the y channel, j represents the imaginary unit, b 1,-1 Indicates a N,n After simplification N,n' The coefficient of the first element of the first order on the negative semiaxis, b 1,0 Indicates a N,n After simplification N,n The coefficient of the first element of the first order on the positive semi-axis, b 1,1 Indicates a N,n After simplification N,n' The coefficient of the second element of the first order on the positive semi-axis, b N,n' Represents the coefficient a of the nth element of order N N,n The coefficient of the n+1th element of the Nth order on the positive semiaxis obtained after simplification.

8. The method for steerable beamforming of a vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (3), a first-order differential steerable beamformer is designed first, and then a second-order differential steerable beamformer is designed: by setting the truncation order N p =1, the mathematical expression of the second-order steerable differential beam pattern is: Substituting N=2 into the mathematical expression of the ideal N-order steerable differential beam pattern, we obtain the ideal second-order steerable differential beam pattern. The ideal second-order steerable differential beam pattern is compared with the above second-order steerable differential beam pattern and the equation is constructed: The least square method is used to solve the weight value of each channel, and the weight expression of each channel is obtained as follows: in, b 2,-2 Indicates a N,n After simplification N,n The coefficient of the second element of the second order on the negative semiaxis, b 2,-1 Indicates a N,n After simplification N,n The coefficient of the first element of the second order on the negative semiaxis, b 2,0 Indicates a N,n After simplification N,n The coefficient of the first element of the second order on the positive semi-axis, b 2,1 Indicates a N,n After simplification N,n The coefficient of the second element of the second order of the positive semi-axis. * indicates the conjugate operation. b 2,2 After simplification, b N,n The coefficient of the third element of the second order on the positive semi-axis, b N,n' Represents the coefficient a of the nth element of order N N,n After simplification, we get the coefficient of the Nth order n+1th element of the positive semi-axis, w represents the weight vector, θ represents the incident angle, and θ s represents the steering angle, H represents the conjugate transpose, T represents the transpose operation, ψ1,…,ψ M represents the counterclockwise angle from the first array reference element to the Mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system, j represents the imaginary unit, W p represents the weight set of p channels, W x Represents the weight set of the x channel, W y Represents the weight set of the y channel.

9. The method for steerable beamforming of vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (3), a first-order differential steerable beamformer is designed first, a second-order differential steerable beamformer is designed, and then a third-order differential steerable beamformer is designed: by setting the truncation order N p =2, the mathematical expression of the third-order steerable differential beam pattern is: Substituting N=3 into the mathematical expression of the ideal N-order steerable differential beam pattern, we obtain the ideal third-order steerable differential beam pattern. The ideal third-order steerable differential beam pattern is compared with the above third-order steerable differential beam pattern and the equation is constructed: The least squares method is used to solve the weight value of each channel, and the weight expression of each channel is as follows: in, b 3,-3 Indicates a N,n After simplification N,n The coefficient of the third element of the third order on the negative semiaxis, b 3,-2 Indicates a N,n After simplification N,n The coefficient of the second element of the third order on the negative semi-axis, b 3,1 Indicates a N,n After simplification N,n The coefficient of the second element of the third order on the positive semi-axis, b 3,2 Indicates a N,n After simplification N,n' The coefficient of the third element of the third order on the positive half axis. * indicates the conjugate operation. b 3,3 Indicates a N,n After simplification N,n The coefficient of the 4th element of the 3rd order on the positive half axis, b N,n' Represents the coefficient a of the nth element of order N N,n The coefficient of the Nth order n+1th element of the positive semi-axis obtained after simplification, w represents the weight vector, θ s represents the steering angle, w represents the incident angle, H represents the conjugate transpose, T represents the transpose operation, ψ1,…,ψ M represents the counterclockwise angle from the first array reference element to the Mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system, j represents the imaginary unit, W p represents the weight set of p channels, W x Represents the weight set of the x channel, W y Represents the weight set of the y channel.

10. The method for steerable beamforming of vector small aperture arbitrary plane array according to claim 1, characterized in that: In step (3), firstly, a first-order differential steerable beamformer, a second-order differential steerable beamformer, and a third-order differential steerable beamformer are designed, and finally an N-order differential steerable beamformer is designed: by setting the truncation order N p =N-1, and the mathematical expression of the N-order steerable differential beam pattern is: The least squares method is used to solve the weight value of each channel, and the weight expression of each channel is as follows: Where N ≥ 2, b N,-N Indicates a N,n After simplification N,n' The coefficient of the Nth element of the Nth order on the negative semiaxis, b N,N-1 Indicates a N,n After simplification N,n' The coefficient of the Nth element of the Nth order on the positive axis. * indicates the conjugate operation. b N,N Indicates a N,n After simplification N,n The coefficient of the N+1th element of the Nth order, b N,n Represents the coefficient a of the nth element of order N N,n The coefficient of the Nth order n+1th element of the positive semi-axis obtained after simplification, W p represents the weight set of p channels, W x Represents the weight set of the x channel, W y represents the weight set of the y channel, j represents the imaginary unit, w represents the weight vector, N and θ s denote the order and the steering angle respectively, θ denotes the incident angle, H denotes the conjugate transpose, T denotes the transpose operation, ψ1,…,ψ M Represents the counterclockwise angle from the 1st array reference element to the Mth array reference element relative to the positive half axis of the x-axis of the Cartesian coordinate system.

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