Meshless compressive beamforming for sound source identification compatible with arbitrary linear microphone arrays

Abstract

This invention discloses a gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays, comprising the following steps: 1) obtaining a noisy measurement sound pressure matrix P using a microphone array. ★ ;2) Establish a denoising mathematical model for microphone sound pressure measurement based on atomic norm minimization;3) Transform the denoising mathematical model into a semi-positive definite programming model using elliptic spherical wave functions;4) Convert the noisy sound pressure measurement matrix P ★ The input is fed into a positive semidefinite programming model, which is then solved to reconstruct the sound pressure generated by the sound source at the array microphones. 5) Based on the denoised sound pressure, the DOA of the sound source is estimated using the matrix bundle method, and the sound source intensity is quantized using the least squares method. This invention has no requirements on the microphone distribution and is compatible with any linear microphone array. When using a linear array with randomly distributed microphones for measurement, this invention can still accurately identify the sound source.

Description

Technical Field

[0001] This invention belongs to the field of sound field recognition technology, specifically a gridless compressed beamforming sound source recognition method compatible with arbitrary linear microphone arrays. Background Technology

[0002] Compressed beamforming is an effective method for estimating the direction-of-arrival (DOA) and quantizing the intensity of sound sources. Meshless compressed beamforming, based on compressed sensing theory and treating the target sound source region as a continuum, is a novel sound source identification method for extracting sound source information from microphone array measurement data.

[0003] Within the framework of linear microphone array measurements, numerous scholars have conducted extensive research on meshless compressed beamforming methods. However, this work is limited to uniform and sparse linear arrays and is not applicable to linear arrays with irregularly distributed microphones. This not only hinders the widespread application of meshless compressed beamforming methods but also blocks the possibility of improving the method's sound source identification performance by optimizing microphone distribution.

[0004] Therefore, a method for identifying sound sources using compressed beamforming with irregularly distributed microphones is needed. Summary of the Invention

[0005] The purpose of this invention is to provide a gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays, comprising the following steps:

[0006] 1) Obtain the noise-containing measurement sound pressure matrix P using a microphone array. ★ ;

[0007] 2) Establish a mathematical model for denoising the sound pressure signal measured by the microphone based on minimizing the atomic norm;

[0008] 3) The denoising mathematical model is transformed into a semidefinite programming model using the elliptic spherical wave function;

[0009] 4) The sound pressure matrix P containing noise was measured. ★ The input is fed into a positive semidefinite programming model, which is then solved to reconstruct the sound pressure generated by the sound source at the array microphones.

[0010] 5) Based on sound pressure The source DOA is estimated using the matrix bundle method, and the source intensity is quantized using the least squares method.

[0011] Furthermore, the steps for establishing a denoising mathematical model for microphone sound pressure measurement signals based on atomic norm minimization include:

[0012] 2.1) Let the intensity parameter of sound source i be... vector Where ||·||2 represents the l2 norm; Let ψ be the set of positive real numbers; ψ is the parameter. i ||2=1; The row vector is composed of the intensity of sound source i in each snapshot; It is the set of complex numbers; the superscript T indicates transpose;

[0013] 2.2) Establish a sound pressure model under the measurement framework of an arbitrary linear microphone array, namely:

[0014]

[0015] In the formula, Let L be the sound pressure matrix generated by L sound sources at M microphones in a snapshot; Each snapshot captures a row vector of sound pressure signals generated at microphone m, forming a single line vector. Parameter f i ≡sinθ i / 2∈[-1 / 2,1 / 2];x m Let m be the coordinates of microphone m; θ∈[-90°,90°] is the direction of arrival of the sound source wave. The imaginary unit; i = 1, 2, ..., I are the sound source indices; m = 1, 2, ..., M;

[0016] 2.3) Establish the atom set A of the sound pressure model under the measurement framework of an arbitrary linear microphone array, that is:

[0017]

[0018] In the formula, the parameters

[0019] 2.4) Based on the minimization of the atomic norm, a mathematical model for denoising the sound pressure signal measured by the microphone is established, namely:

[0020]

[0021] In the formula, ε is the atomic norm of the sound pressure P; inf represents the infimum; ε is the noise control parameter. This is for noise reduction.

[0022] Furthermore, the steps for converting the denoised mathematical model into a semidefinite programming model using the ellipsoidal wave function include:

[0023] 3.1) Record Let c be the set of all square-integrable functions defined on the interval [-1, 1], given a real number c > 0;

[0024] Define operator in, for Any function within the range; let λ0, λ1, ..., λ a ... are operators F c eigenvalues; |λ a |≥|λ a+1 |;ψ a (z) is the corresponding eigenvalue λ a The a-order ellipsoidal wave function; The set of natural numbers;

[0025] For all parameters Given the parameter z∈[-1,1], we have:

[0026]

[0027] 3.2) Based on the a-order elliptic spherical wave function, the noise-reducing mathematical model is transformed into a positive semidefinite programming model, i.e.:

[0028]

[0029] In the formula, the parameters Parameter D x =max{x1,x2,…,x M}-min{x1,x2,…,x M};x m Let Q be the coordinates of microphone m; e is the first column of the M×M identity matrix; Q and E are both Hermitian matrices. The transformed Hermitian matrix; Q mn The elements of Q are at row m and column n; vector The vth element is ψ v-1 ((x m -x n ) / D x );vector The element in row w and column v is ψ v-1 ((wd-1) / d); parameter matrix matrix I d It is a d×d dimensional identity matrix; 0 d×1 Let be a d×1 dimensional zero vector; tr(·) denotes finding the trace of a matrix; Indicates a matrix as positive semi-definite; superscript " * "and" H " represent conjugate and conjugate transpose, respectively; It is the set of real numbers; These are auxiliary parameters; T is a matrix; u d’It is a complex number; d' = 1, 2, ..., d; u0 is a constant.

[0030] Furthermore, tools for solving semidefinite programming models include the SDPT3 solver in the CVX toolbox.

[0031] Furthermore, based on noise reduction pressure The steps for calculating and estimating the DOA of a sound source using the matrix bundle method and for quantizing the sound source intensity using the least squares method include:

[0032] 5.1) Let the matrix be... For parameters The corresponding Toeplitz matrix, for the matrix Eigenvalue decomposition yields:

[0033]

[0034] In the formula, It is a unitary matrix composed of eigenvectors; It is a diagonal matrix composed of eigenvalues;

[0035] 5.2) Let the estimated total number of sound sources be . Among them, the estimated total number of sound sources is the number of feature values ​​that are greater than a set threshold;

[0036] 5.3) Establish a matrix in, for A diagonal matrix composed of the square roots of eigenvalues ​​greater than a set threshold. for A matrix consisting of eigenvectors corresponding to eigenvalues ​​greater than a set threshold;

[0037] 5.4) Delete the last row of matrix Y to obtain matrix Y.

[0038] Delete the first row of matrix Y to obtain matrix Y.

[0039] Computation matrix bundle (Y) d ,Y u The generalized eigenvalues ​​of ) are denoted as

[0040] 5.5) Calculate the sound source Im(·) represents taking the imaginary part of the variable within the parentheses;

[0041] 5.6) Quantization of sound source intensity based on least squares method Right now:

[0042]

[0043] In the formula, the superscript " + " denotes pseudo-inverse; perceptual matrix

[0044] Furthermore, the microphones in the linear microphone array are arbitrarily distributed.

[0045] This method has no restrictions on the microphone distribution of the linear microphone array and is compatible with any linear microphone array.

[0046] The technical effect of this invention is beyond doubt. This invention first establishes a mathematical model for denoising the sound pressure signal measured by a microphone, constrained by minimizing the sparsity metric of the sound source distribution in the continuous domain. Then, it uses the elliptic spherical wave function to transform the denoising mathematical model into an equivalent positive semidefinite programming problem and solves it. Finally, it estimates the DOA and intensity of the sound source from the solution results based on the matrix bundle method and the least squares method, thereby identifying the sound source.

[0047] When using a uniform linear microphone array for measurement, this invention can effectively overcome the shortcomings of the DAS beamforming method, such as low low-frequency spatial resolution and inability to distinguish small sound sources; when using a linear array of randomly distributed microphones for measurement, this invention can still accurately identify sound sources.

[0048] Overall, the proposed meshless compressed beamforming method is not only accurate and effective, but also has no requirements on microphone distribution and is compatible with any linear microphone array. This invention contributes to the widespread application of meshless compressed beamforming methods and also provides the possibility of improving sound source identification performance by optimizing microphone distribution. Attached Figure Description

[0049] Figure 1 Analysis of the relationship between c, a, PSWF and its eigenvalues.

[0050] Figure 1 (a) shows the imaging curves of the 0th, 2nd, 3rd and 8th order PSWF when c = 30;

[0051] Figure 1 (b) is a contour plot showing the change of the eigenvalues' magnitudes as a function of c and a;

[0052] Figure 1 (c) is the curve of d as a function of c.

[0053] Figure 2 The results show the sound source identification results of the proposed method, the classical delay summation method, and existing meshless compressed beamforming methods limited to uniform linear arrays and sparse linear arrays when using a uniform linear microphone array.

[0054] Figure 2 (a) shows the distribution of a uniform linear array of microphones;

[0055] Figure 2 (b) The sound source identification results of the classical delay summation method and the existing meshless compressed beamforming method limited to uniform linear arrays and sparse linear arrays at 1500Hz;

[0056] Figure 2 (c) The sound source identification results of the classical delay summation method and the existing meshless compressed beamforming method limited to uniform linear arrays and sparse linear arrays at 3000Hz;

[0057] Figure 2 (d) shows the sound source identification results of the classical delay summation method and the existing meshless compressed beamforming method limited to uniform linear arrays and sparse linear arrays at 6000Hz.

[0058] Figure 2 (e) shows the sound source identification results at 12000Hz using the classical delay summation method and existing meshless compressed beamforming methods limited to uniform linear arrays and sparse linear arrays;

[0059] Figure 2 (f) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 1500Hz;

[0060] Figure 2 (g) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 3000Hz;

[0061] Figure 2 (h) represents the sound source identification results of the classical delay summation method and the method proposed in this invention at 6000Hz;

[0062] Figure 2 (i) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 12000Hz.

[0063] Figure 3 The results of sound source identification using the proposed method and the classical delay summation method when using a linear array of randomly distributed microphones;

[0064] Figure 3 (a) shows the distribution of random linear array microphones;

[0065] Figure 3 (b) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 1500Hz;

[0066] Figure 3 (c) The sound source identification results of the classical delay summation method and the method proposed in this invention at 3000Hz;

[0067] Figure 3(d) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 6000Hz;

[0068] Figure 3 (e) shows the sound source identification results of the classical delay summation method and the method proposed in this invention at 12000Hz. Detailed Implementation

[0069] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0070] Example 1:

[0071] See Figures 1 to 3 A gridless compressed beamforming sound source identification method compatible with any linear microphone array includes the following steps:

[0072] 1) Obtain the noise-containing measurement sound pressure matrix P using a microphone array. ★ ;

[0073] The microphones in the linear microphone array are arbitrarily distributed; that is, the microphones can be uniformly distributed or randomly distributed.

[0074] This method has no restrictions on the microphone distribution of the linear microphone array and is compatible with any linear microphone array.

[0075] 2) Establish a mathematical model for denoising the sound pressure signal measured by the microphone based on minimizing the atomic norm;

[0076] 3) The denoising mathematical model is transformed into a semidefinite programming model using the elliptic spherical wave function;

[0077] 4) The sound pressure matrix P containing noise was measured. ★ The input is fed into a positive semidefinite programming model, which is then solved to reconstruct the sound pressure generated by the sound source at the array microphones.

[0078] 5) Based on noise reduction pressure The source DOA is estimated using the matrix bundle method, and the source intensity is quantized using the least squares method.

[0079] The steps for establishing a denoising mathematical model for microphone sound pressure measurement signals based on atomic norm minimization include:

[0080] 2.1) Let the intensity parameter of sound source i be... vector Where ||·||2 represents the l2 norm; Let ψ be the set of positive real numbers; ψ is the parameter. i ||2=1; The row vector is composed of the intensity of sound source i in each snapshot; It is the set of complex numbers; the superscript T indicates transpose;

[0081] 2.2) Establish a sound pressure model under the measurement framework of an arbitrary linear microphone array, namely:

[0082]

[0083] In the formula, Let L be the sound pressure matrix generated by L sound sources at M microphones in a snapshot; Each snapshot captures a row vector of sound pressure signals generated at microphone m, forming a single line vector. Parameter f i ≡sinθ i / 2∈[-1 / 2,1 / 2];x m Let m be the coordinates of microphone m; θ∈[-90°,90°] is the direction of arrival of the sound source wave. is the imaginary unit; i = 1, 2, ..., I are the sound source indices;

[0084] 2.3) Establish the atom set of the sound pressure model under the measurement framework of an arbitrary linear microphone array, i.e.:

[0085]

[0086] 2.4) Based on the minimization of the atomic norm, a mathematical model for denoising the sound pressure signal measured by the microphone is established, namely:

[0087]

[0088] In the formula, ε is the atomic norm of the sound pressure P; inf represents the infimum; ε is the noise control parameter.

[0089] The steps to convert a denoised mathematical model into a semidefinite programming model using ellipsoidal wave functions include:

[0090] 3.1) Record Let c be the set of all square-integrable functions defined on the interval [-1, 1], given a real number c > 0;

[0091] Define operator in, for Any function within the range; let λ0, λ1, ..., λ a ... are operators F c eigenvalues; |λ a |≥|λ a+1|;ψ a (z) corresponds to λ a The a-order ellipsoidal wave function; The set of natural numbers;

[0092] For all and z∈[-1,1], there is:

[0093]

[0094] 3.2) Based on the a-order elliptic spherical wave function, the noise-reducing mathematical model is transformed into a positive semidefinite programming model, i.e.:

[0095]

[0096] In the formula, the parameters Parameter D x =max{x1,x2,…,x M}-min{x1,x2,…,x M}; e is the first column of the M×M dimensional identity matrix; Q and E are both Hermitian matrices; Q mn The elements of Q are at row m and column n; vector The vth element is ψ v-1 ((x m -x n ) / D x );vector The element in row w and column v is ψ v-1 ((wd-1) / d); parameter matrix matrix I d It is a d×d dimensional identity matrix; 0 d×1 Let be a d×1 dimensional zero vector; tr(·) denotes finding the trace of a matrix; This indicates a positive semi-definite matrix; the superscripts "*" and "H" represent conjugate and conjugate transpose, respectively. It is the set of real numbers; This is an auxiliary quantity.

[0097] Tools for solving semidefinite programming models include the SDPT3 solver in the CVX toolbox.

[0098] Based on noise reduction pressure The steps for estimating the DOA of a sound source using the matrix bundle method and quantizing the sound source intensity using the least squares method include:

[0099] 5.1) Let the matrix be... for The corresponding Toeplitz matrix, for the matrix Eigenvalue decomposition yields:

[0100]

[0101] In the formula, It is a unitary matrix composed of eigenvectors; It is a diagonal matrix composed of eigenvalues;

[0102] 5.2) Let the estimated total number of sound sources be . Among them, the estimated total number of sound sources is the number of feature values ​​that are greater than a set threshold;

[0103] 5.3) Establish a matrix in, for A diagonal matrix composed of the square roots of eigenvalues ​​greater than a set threshold. for A matrix consisting of eigenvectors corresponding to eigenvalues ​​greater than a set threshold;

[0104] 5.4) Delete the last row of matrix Y to obtain matrix Y.

[0105] Delete the first row of matrix Y to obtain matrix Y.

[0106] Computation matrix bundle (Y) d ,Y u The generalized eigenvalues ​​of ) are denoted as

[0107] 5.5) Calculate the sound source Im(·) represents taking the imaginary part of the variable within the parentheses;

[0108] 5.6) Quantization of sound source intensity based on least squares method Right now:

[0109]

[0110] In the formula, the superscript "+" indicates the pseudo-inverse; the perception matrix Example 2:

[0111] A meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is proposed. The theoretical basis of this method is as follows:

[0112] Within the measurement framework of an arbitrary linear microphone array (where the microphones do not need to be uniformly distributed), the sound pressure generated by the sound source at the microphone can be expressed as:

[0113]

[0114] in, Let L be the sound pressure matrix generated by L sound sources at M microphones in a single snapshot. Each snapshot of the sound source generates a row vector of sound pressure signals at microphone m; f i ≡sinθ i / 2∈[-1 / 2,1 / 2],x m Let θ be the coordinates of microphone m (unit: half wavelength), and θ∈[-90°, 90°] be the direction of arrival (DOA), which is the angle between the array axis (a straight line passing through the origin and perpendicular to the array) and the line connecting the origin and the sound source. is the imaginary unit; i = 1, 2, ..., I are the sound source indices; Let i be the row vector composed of the intensities of sound source i in each snapshot; For the set of complex numbers, the superscript "T" indicates transpose.

[0115] Noise interference exists At that time, the actual measured sound pressure It can be represented as:

[0116] P ★ =P+N (2)

[0117] Signal-to-noise ratio (SNR) is defined as SNR = 20log 10 (||P|| F / ||N|| F ), where ||·|| F Denotes the Frobenius norm, from which ||N|| can be determined. F =||P|| F 10 -SNR / 20 .

[0118] The above describes the process of measuring sound pressure signals using an array microphone, which forms the theoretical basis for sound source identification methods.

[0119] The specific steps of this method are as follows:

[0120] Step 1: Establish a mathematical model for denoising the sound pressure signal measured by the microphone based on minimizing the atomic norm;

[0121] make Where ||·||2 represents the l2 norm, Let ||ψ be the set of positive real numbers. i ||2=1. Then equation (1) can be rewritten as:

[0122]

[0123] In a continuous domain, each element of d(f) and ψ can be regarded as a continuous function of f.

[0124] The atom in the signal model shown in equation (3) is d(f)ψ. The set of atoms with infinite potential is:

[0125]

[0126] The mathematical model for denoising the sound pressure signal measured by the microphone is as follows:

[0127]

[0128] in, Let P be the atomic norm, used to measure the sparsity of the sound source distribution; inf represents the infimum; ε is the noise control parameter, usually taken as ||N||. F Solving this mathematical model can remove P. ★ Medium noise, reconstruction P.

[0129] Step 2: Solve the positive semidefinite programming problem of the noise-reduced mathematical model;

[0130] This invention utilizes Prolate Spheroidal Wave Functions (PSWF) to transform the denoising mathematical model into an equivalent semidefinite programming problem for solution.

[0131] remember Let F be the set of all square-integrable functions defined on the interval [-1, 1]. Given a real number c > 0, let the operator F... c : Defined as in, for Any function within. The PSWF used in this invention is the operator F. c The characteristic function of λ. Let λ0, λ1, ..., λ a ... are operators F c eigenvalues, |λ a |≥|λ a+1 |,ψ a (z) corresponds to λ a The characteristic function, i.e., the a-order PSWF, For the set of natural numbers, for all And z∈[-1,1],

[0132]

[0133] The value of PSWF is a real number, typically ψ a (z) is standardized

[0134] Calculate the PSWF and eigenvalues ​​for different values ​​of c and a. Figure 1(a) The imaging curves of PSWF are given as examples of c=30 and a=0, 2, 3, 8. Figure 1 (b) presents a contour plot showing the magnitude of the eigenvalues ​​as a function of c and a. Clearly, for a specific c, when a is sufficiently large, |λ a | is almost 0, which is consistent with the property that "the magnitude of eigenvalues ​​decays rapidly to zero as the order increases". Let When a > 2d, |λ a | Almost 0 (less than 10) -3 ).based on Figure 1 (b) The values ​​of d under different c values ​​can be searched, such as Figure 1 (c) shows the solid line marked with "○". The fitted relationship between d and c is as follows:

[0135]

[0136] in, This indicates that the value is rounded to the nearest integer in the direction of positive infinity. The relationship shown in equation (7) is as follows: Figure 1 (c) is shown by the solid line.

[0137] Based on PSWF, the atomic norm minimization shown in equation (5) can be transformed into the following positive semidefinite programming problem:

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] ||P ★ -P|| F ≤ε (8)

[0144] in, (corresponding to the parameter c in equation (7) being equal to πD) x ), D x =max{x1,x2,…,x M}-min{x1,x2,…,x M}, e is the first column of an M×M dimensional identity matrix, Q and E are both Hermitian matrices, Q mn Given the m rows and n columns of Q, calculate Q. mn Need to use and h mn The vth element is ψ v-1 ((xm -x n ) / D x The element in row w and column v of Φ is ψ. v-1 ((wd-1) / d), calculate Need to use and I d It is a d×d dimensional identity matrix, 0 d×1 Let tr be a d×1 dimensional zero vector, and tr(·) denotes finding the trace of the matrix. To indicate that the matrix is ​​positive semi-definite, the superscript " * "and" H "represents conjugate and conjugate transpose, respectively." It is the set of real numbers; For auxiliary quantities. The semidefinite programming problem shown in equation (8) can be solved using the SDPT3 solver in the CVX toolbox.

[0145] Step 3: Source DOA estimation and intensity quantization

[0146] The solution of equation (8) and As input, the source DOA can be estimated based on the matrix bundle method, and the source intensity can be quantized based on the least squares method. The specific steps are as follows:

[0147] 1) Record for The corresponding Toeplitz matrix, eigenvalue decomposition

[0148]

[0149] in, The unitary matrix formed by the eigenvectors. Let be a diagonal matrix composed of eigenvalues. The estimated total number of sound sources is the number of eigenvalues ​​greater than a set threshold, denoted as . remember for A diagonal matrix formed by the square roots of the larger eigenvalues. for Let the matrix consisting of the eigenvectors corresponding to the larger eigenvalues ​​be...

[0150] 2) Delete the last row of Y to get Delete the first row of Y Computation matrix bundle (Y) d ,Y u The generalized characteristics of ) are worth Thus, the sound source is obtained. Im(·) means taking the imaginary part of the variable inside the parentheses.

[0151] 3) Calculate the perception matrix based on the estimated source DOA. Quantizing sound source intensity based on least squares method for

[0152]

[0153] Among them, the superscript " + "Indicates a false rebellion."

[0154] Example 3:

[0155] The basic execution steps of the meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays are as follows:

[0156] Input: Measure sound pressure Array microphone coordinates (unit: half wavelength), noise control parameter ε

[0157] D is calculated from the coordinates of the array microphones. x And d, calculate Φ and {h mn |m,n=1,2,…,M}.

[0158] 2. Calculation Construct matrices J1 and J2.

[0159] by J1, J2, Φ, {h mn |m,n=1,2,…,M}、P ★ Given ε as input, solve the positive semidefinite program shown in equation (8) to obtain... and

[0160] by and As input, estimate the source DOA and quantify the source intensity according to the three steps in step 3.

[0161] Example 4:

[0162] An experiment was conducted on a meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays, the contents of which are as follows:

[0163] To analyze and verify the sound source identification performance of the method of the present invention, simulation experiments were conducted, and the results were compared with classical Delay And Sum (DAS) beamforming and existing gridless compressed beamforming methods limited to uniform linear arrays and sparse linear arrays (Y.Li, Y.Chi, Off-the-grid line spectrum denoising and estimation with multiple measurement vectors, IEEE Transactions on Signal Processing. 64(5)(2016) 1257-1269.).

[0164] Assuming five sound sources with DOAs of -50°, -10°, 0°, 20°, and 70°, and intensities of 100dB, 97dB, 97dB, 94dB, and 99dB respectively (refer to 2×10⁻⁶). -5 Pa). The total number of microphones was set to 36, the total number of data snapshots to 10, and the measured signal SNR to 20dB. Using... Figure 2 (a) shows the sound source identification results obtained by measuring a uniform linear microphone array as follows: Figure 2 (b)-(i) are shown.

[0165] In each diagram, the matchstick marked with "○" indicates the actual sound source, and the matchstick marked with "○" indicates the actual sound source. The matchstick represents the output of the meshless compressed beamforming method, while the curve represents the output of the classical delay-summation beamforming method. Both the matchstick and the curve have a maximum value of 0 dB because they are both scaled to their own maximum output value in dB. The maximum value marked above the graph is the reference value for the meshless compressed beamforming method (2×10). -5 The maximum output value that Pa can scale to dB. Figure 2 (b)-(e) employ previously existing meshless compressed beamforming methods limited to uniform linear arrays and sparse linear arrays. Figure 2 (f)-(i) Using the method proposed in this paper, the output results of the two are basically the same. Figure 2 (b) and Figure 2 (f) corresponds to a frequency of 1500Hz. Figure 2 (c) and Figure 2 (g) corresponds to a frequency of 3000Hz. Figure 2 (d) and Figure 2 (h) corresponds to a frequency of 6000Hz. Figure 2 (e) and Figure 2 (i) Corresponding to a frequency of 12000Hz. At 1500Hz, 3000Hz, and 6000Hz, both meshless compressed beamforming methods accurately identified all sound sources, overcoming the shortcomings of the DAS beamforming method, which has low low-frequency spatial resolution and cannot distinguish small, separated sound sources. At the high frequency of 12000Hz, due to the influence of the regular distribution of microphones, both the DAS and meshless compressed beamforming methods exhibit aliasing, meaning that the output results contain spurious sources with intensity equivalent to the real sound sources.

[0166] Figure 3 (a) A linear array of randomly distributed microphones is presented. Measurements using this array yield the following sound source identification results: Figure 3 (b)-(e) show that the proposed method accurately identified all sound sources at all four frequencies. This demonstrates that the proposed meshless compressed beamforming method is not only correct and effective, but also has no requirements on microphone distribution and is compatible with any linear microphone array. This contributes to the widespread application of meshless compressed beamforming methods and also provides the possibility of improving sound source identification performance by optimizing microphone distribution.

[0167] Example 5:

[0168] A gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays includes the following steps:

[0169] 1) Obtain the noise-containing measurement sound pressure matrix P using a microphone array. ★ ;

[0170] 2) Establish a mathematical model for denoising the sound pressure signal measured by the microphone based on minimizing the atomic norm;

[0171] 3) The denoising mathematical model is transformed into a semidefinite programming model using the elliptic spherical wave function;

[0172] 4) The sound pressure matrix P containing noise was measured. ★ The input is fed into a positive semidefinite programming model, which is then solved to reconstruct the sound pressure generated by the sound source at the array microphones.

[0173] 5) Based on sound pressure The source DOA is estimated using the matrix bundle method, and the source intensity is quantized using the least squares method.

[0174] Example 6:

[0175] A meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is described in Example 5. The steps for establishing a denoising mathematical model of the microphone's measured sound pressure signal based on atomic norm minimization include:

[0176] 2.1) Let the intensity parameter of sound source i be... vector Where ||·||2 represents the l2 norm; Let ψ be the set of positive real numbers; ψ is the parameter. i ||2=1; The row vector is composed of the intensity of sound source i in each snapshot; It is the set of complex numbers; the superscript T indicates transpose;

[0177] 2.2) Establish a sound pressure model under the measurement framework of an arbitrary linear microphone array, namely:

[0178]

[0179] In the formula, Let L be the sound pressure matrix generated by L sound sources at M microphones in a snapshot; Each snapshot captures a row vector of sound pressure signals generated at microphone m, forming a single line vector. Parameter f i ≡sinθ i / 2∈[-1 / 2,1 / 2];x m Let m be the coordinates of microphone m; θ∈[-90°,90°] is the direction of arrival of the sound source wave. The imaginary unit; i = 1, 2, ..., I are the sound source indices; m = 1, 2, ..., M;

[0180] 2.3) Establish the atom set A of the sound pressure model under the measurement framework of an arbitrary linear microphone array, that is:

[0181]

[0182] In the formula, the parameters

[0183] 2.4) Based on the minimization of the atomic norm, a mathematical model for denoising the sound pressure signal measured by the microphone is established, namely:

[0184]

[0185] In the formula, ε is the atomic norm of the sound pressure P; inf represents the infimum; ε is the noise control parameter. This is for noise reduction.

[0186] Example 7:

[0187] A gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is described in Example 5. The step of converting the denoising mathematical model into a semidefinite programming model using an ellipsoidal wavefunction includes:

[0188] 3.1) Record Let c be the set of all square-integrable functions defined on the interval [-1, 1], given a real number c > 0;

[0189] Define operator in, for Any function within the range; let λ0, λ1, ..., λ a ... are operators F c eigenvalues; |λ a |≥|λ a+1 |;ψ a (z) is the corresponding eigenvalue λ a The a-order ellipsoidal wave function; The set of natural numbers;

[0190] For all parameters Given the parameter z∈[-1,1], we have:

[0191]

[0192] 3.2) Based on the a-order elliptic spherical wave function, the noise-reducing mathematical model is transformed into a positive semidefinite programming model, i.e.:

[0193]

[0194] In the formula, the parameters Parameter D x =max{x1,x2,…,x M}-min{x1,x2,…,x M};x m Let Q be the coordinates of microphone m; e is the first column of the M×M identity matrix; Q and E are both Hermitian matrices. The transformed Hermitian matrix; Q mn The elements of Q are at row m and column n; vector The vth element is ψ v-1 ((x m -x n ) / D x );vector The element in row w and column v is ψ v-1 ((wd-1) / d); parameter matrix matrix I d It is a d×d dimensional identity matrix; 0 d×1 Let be a d×1 dimensional zero vector; tr(·) denotes finding the trace of a matrix; Indicates a matrix as positive semi-definite; superscript " * "and" H" represent conjugate and conjugate transpose, respectively; It is the set of real numbers; These are auxiliary parameters; T is a matrix; u d’ It is a complex number; d' = 1, 2, ..., d; u0 is a constant.

[0195] Example 8:

[0196] The main content of the meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is described in Example 5. The tool for solving the semidefinite programming model includes the SDPT3 solver in the CVX toolbox.

[0197] Example 9:

[0198] A meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is described in Example 5, whereby it is based on noise reduction compression... The steps for calculating and estimating the DOA of a sound source using the matrix bundle method and for quantizing the sound source intensity using the least squares method include:

[0199] 5.1) Let the matrix be... For parameters The corresponding Toeplitz matrix, for the matrix Eigenvalue decomposition yields:

[0200]

[0201] In the formula, It is a unitary matrix composed of eigenvectors; It is a diagonal matrix composed of eigenvalues;

[0202] 5.2) Let the estimated total number of sound sources be . Among them, the estimated total number of sound sources is the number of feature values ​​that are greater than a set threshold;

[0203] 5.3) Establish a matrix in, for A diagonal matrix composed of the square roots of eigenvalues ​​greater than a set threshold. for A matrix consisting of eigenvectors corresponding to eigenvalues ​​greater than a set threshold;

[0204] 5.4) Delete the last row of matrix Y to obtain matrix Y.

[0205] Delete the first row of matrix Y to obtain matrix Y.

[0206] Computation matrix bundle (Y)d ,Y u The generalized eigenvalues ​​of ) are denoted as

[0207] 5.5) Calculate the sound source Im(·) represents taking the imaginary part of the variable within the parentheses;

[0208] 5.6) Quantization of sound source intensity based on least squares method Right now:

[0209]

[0210] In the formula, the superscript " + " denotes pseudo-inverse; perceptual matrix

[0211] Example 10:

[0212] A gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays is described in Example 5, wherein the microphones in the linear microphone array are arbitrarily distributed.

[0213] This method has no restrictions on the microphone distribution of the linear microphone array and is compatible with any linear microphone array.

Claims

1. A gridless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays, characterized in that, Includes the following steps: Step 1) Obtain the sound pressure measurement matrix containing noise using a microphone array. ; Step 2) Establish a denoising mathematical model for the microphone's sound pressure measurement signal based on minimizing the atomic norm; Step 3) Use the ellipsoidal wave function to convert the noise-reducing mathematical model into a semidefinite programming model; Step 4) Measure the sound pressure matrix containing noise. The input is fed into a positive semidefinite programming model, which is then solved to reconstruct the sound pressure generated by the sound source at the array microphones. ; Step 5) Based on sound pressure The matrix bundle method is used to calculate and estimate the DOA of the sound source, and the least squares method is used to quantize the sound source intensity. The steps for establishing a denoising mathematical model for microphone sound pressure measurement signals based on atomic norm minimization include: Step 2.1) Let No. 1 sound source intensity parameters ,vector ;in, express Norm; The set of positive real numbers; parameters ; Take photos for each person The row vector composed of the intensity of the sound source; It is the set of complex numbers; the superscript T indicates transpose; Step 2.2) Establish the sound pressure model under the measurement framework of an arbitrary linear microphone array, that is: (1) In the formula, for A quick snapshot of the sound source The sound pressure matrix generated at each microphone; Each quick shot captures the sound source. A row vector composed of sound pressure signals generated at the microphone; vector ;parameter ; for The coordinates of the microphone; Indicates the direction of arrival of the sound source wave; The imaginary unit; For the sound source index; m = 1, 2, ..., M; Step 2.3) Establish the atom set of the sound pressure model under the measurement framework of arbitrary linear microphone array. ,Right now: (2) In the formula, the parameter f ; Step 2.4) Establish a denoising mathematical model for the microphone's measured sound pressure signal based on minimizing the atomic norm, i.e.: (3) In the formula, sound pressure The atomic norm; Indicates the infimum; These are noise control parameters; For noise reduction; The steps to convert a denoised mathematical model into a semidefinite programming model using ellipsoidal wave functions include: Step 3.1) Record To define in the interval The set of all square-integrable functions on the given real number. ; Define operator ;in, for Any function within; denoted as For operators eigenvalues; ; For the corresponding eigenvalues of Elliptic spherical wave function; The set of natural numbers; For all parameters and parameters ,have: (4) Step 3.2) Based on The order elliptic spherical wave function transforms the noise-reducing mathematical model into a positive semidefinite programming model, namely: (5) In the formula, the parameters ;parameter ;x m for The coordinates of the microphone; for The first column of the 3D identity matrix; and All are Hermitian matrices; This is the transformed Hermitian matrix; For of OK Column elements; vector The The elements are ;vector of OK Column elements are ;parameter ; matrix ;matrix ; for 3D identity matrix; for Zero-dimensional vector; This indicates finding the trace of a matrix; Indicates a matrix as positive semi-definite; superscript " "and" " represent conjugate and conjugate transpose, respectively; It is the set of real numbers; These are auxiliary parameters; T is a matrix; For complex numbers; d' = 1, 2, ..., d; It is a constant.

2. The meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays according to claim 1, characterized in that, Tools for solving semidefinite programming models include the SDPT3 solver in the CVX toolbox.

3. The meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays according to claim 1, characterized in that, Based on noise reduction pressure The steps for calculating and estimating the DOA of a sound source using the matrix bundle method and quantizing the sound source intensity using the least squares method include: Step 1) Denote the matrix For parameters The corresponding Toeplitz matrix, for the matrix Eigenvalue decomposition yields: (6) In the formula, It is a unitary matrix composed of eigenvectors; It is a diagonal matrix composed of eigenvalues; Step 2) Record the estimated total number of sound sources as The estimated total number of sound sources is the number of feature values ​​greater than a set threshold. Step 3) Establish the matrix ;in, for A diagonal matrix composed of the square roots of eigenvalues ​​greater than a set threshold. for A matrix consisting of eigenvectors corresponding to eigenvalues ​​greater than a set threshold; Step 4) Delete the matrix The last line yields the matrix. ; Deleting matrix The first row yields the matrix. ; Computational matrix bundle The generalized eigenvalues ​​are denoted as ; Step 5) Calculate the DOA of the sound source. ; This indicates taking the imaginary part of the variable within the parentheses; Step 6) Quantize the sound source intensity based on the least squares method ,Right now: (7) In the formula, the superscript " " denotes pseudo-inverse; perceptual matrix .

4. The meshless compressed beamforming sound source identification method compatible with arbitrary linear microphone arrays according to claim 1, characterized in that, The microphones in a linear microphone array are arbitrarily distributed.

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