A non-synchronous measurement technique in a multi-point out-of-plane low-frequency sound source 3D imaging method

Abstract

This invention discloses an asynchronous measurement technique for 3D imaging of multi-point, non-planar low-frequency sound sources. It utilizes two 64-channel 3D spherical arrays for asynchronous measurement, proposing a unique dual-cylindrical spiral ascent and rotation movement method to achieve 3D point source imaging within low-frequency sound sources. This method differs from previous directional methods. It employs an asynchronous measurement technique involving the centers of two spherical arrays following a designed dual-cylindrical spiral parallel ascent trajectory and the array's rotation, applied to 3D imaging of multi-point, non-planar low-frequency sound sources. This results in a larger and denser array. To a certain extent, the asynchronous measurement method combining the dual-cylindrical spiral trajectory and rotation further improves the density of synthesized microphones compared to cylindrical trajectory asynchronous measurement methods and spherical array center revolution-rotation asynchronous measurement methods. The method is stable and efficient.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for 3D imaging of multi-point heterogeneous low-frequency sound sources using asynchronous measurement technology. Background Technology

[0002] Non-synchronous measurement (NSM) is an effective method for achieving low-frequency sound localization performance through sequential scanning of the sound field. It achieves larger and denser aperture arrays by moving a single planar array. Evidence suggests that non-synchronous measurement of moving microphone arrays can improve the accuracy of sound source localization in a two-dimensional plane. However, existing methods can only perform sound source imaging at frequencies above 2000 Hz. In noise source identification and localization, sound source imaging studies generally use planar arrays to image in a two-dimensional plane. Non-synchronous measurement mainly involves planar movement. The non-synchronous measurement method for two-dimensional planar arrays sequentially moves the planar array, scans the spatially distributed sound sources, and approximately obtains measurements of large-aperture and high-density microphone arrays. Then, traditional beamforming algorithms are used for imaging to locate the sound source.

[0003] Currently, the asynchronous measurement method of 3D spherical microphone arrays in three-dimensional planar imaging still follows the method of planar arrays in far-field two-dimensional planar imaging. It adopts horizontal movement, which improves the spatial resolution of CBF to a certain extent, but has not made any innovation in 3D space. However, the existing literature has not yet shown the feature of using the rotation of the 3D spherical array combined with the revolution of the center of the 3D spherical array as the movement trajectory. Summary of the Invention

[0004] The purpose of this invention is to provide a non-synchronous measurement technology for 3D imaging of multi-point heterogeneous low-frequency sound sources. This technology utilizes a 3D spiral orbit trajectory at the center of a 3D sphere array combined with the rotation of the sphere array, achieving true high resolution of point sound sources. This is beneficial for large-scale, long-distance measurements and allows for intelligent automated measurements using mechanical devices.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for 3D imaging of multi-point, non-planar low-frequency sound sources using asynchronous measurement technology, comprising the following steps:

[0006] S01: The 3D double helix orbit trajectory of the center movement of the 3D spherical microphone array is constructed using the double helix formula. Then, combined with the characteristics of the rotation of the 3D spherical microphone array, 3D double helix orbit-rotation-3D asynchronous measurement is performed.

[0007] S02: Conventional asynchronous measurement achieves a larger and denser aperture array by moving a single planar array. 3D double helix revolution-rotation-3D asynchronous measurement is designed for the special double helix revolution trajectory with evenly distributed polar angles (3D double helix arc trajectory). Based on the center of the 3D spherical array, the 3D spherical microphone array is moved, and the 3D spherical microphone is further rotated with equal polar angles, so that different positions correspond to different microphone distributions. The advantage is that it exceeds the constraints defined by the measurement using a single fixed planar array. At the same time, the parallel upward revolution of the 3D double cylindrical helix achieves a complementary effect and improves the longitudinal sound source resolution imaging in a certain spatial domain.

[0008] S03: Imaging of multi-point heterogeneous sound sources can be achieved by using beamforming algorithms and multi-signal classification algorithms for asynchronous cylindrical measurements. First, two 3D spherical arrays are used to rotate and move along a 3D double helix orbital trajectory to collect signals at each point and preprocess the signals. Then, a cross-spectral matrix is ​​constructed and filled using a fast iterative threshold shrinkage algorithm. Finally, imaging is performed using either beamforming algorithms or multi-signal classification algorithms for asynchronous cylindrical measurements.

[0009] As a further description of the above technical solution:

[0010] In step S01, the 3D imaging method for the sound source utilizes a non-synchronous measurement method that combines a 3D double-helix revolution of points with the rotation of a spherical array. This is an improvement on the non-synchronous measurement method in real-world scenarios. The 3D double-helix revolution is used to make the array larger and denser, while for a single fixed array, the rotation is used to transform the originally sparse array into a dense array, while retaining the pattern of a 3D spherical array. The formulas for the 3D double-helix revolution trajectory of the center of the spherical array and the rotation of the spherical array are as follows:

[0011]

[0012]

[0013] θ1=θ1+ω1*t

[0014] θ2=θ2+ω2*t

[0015]

[0016] Where, x 11 The x-axis displacement of the spiral 1 is represented by its revolution around the sun, and the y-axis displacement is represented by its revolution around the sun. 11 The x-axis represents the displacement of the spiral 1 around the y-axis. 12 The x-axis displacement of the spiral 2 revolutions, y-axis displacement 12Let θ1 represent the y-axis displacement of the spiral 2's revolution, z1 represent the z-axis displacement, r1 represent the distance from the center of the sphere array's trajectory, θ1 represent the 3D spiral's revolution angle range, x2 represent the x-axis displacement of rotation, y2 represent the y-axis displacement of rotation, z2 represent the z-axis displacement of rotation, and r2 represent the distance from the center of the sphere array to the microphone. θ1 represents the rotation elevation angle, θ2 represents the rotation plane angle range, ω1 represents the angular velocity of the 3D spiral revolution of the sphere array, ω2 represents the angular velocity of the sphere array rotation, and t represents time.

[0017] As a further description of the above technical solution:

[0018] In step S02, for low-frequency multi-point eccentric sound sources, assuming the sound source is a steady-state sound source, the sound source is distributed in various corners, while the 3D spherical array (with M microphones) is positioned at equal angles.

[0019] γ, 3D spiral revolution combined with constant angle γ rotation to move to It identifies several locations and collects signals from each location.

[0020] As a further description of the above technical solution:

[0021] In step S03, for low-frequency multi-point heterogeneous sound sources, the imaging method using beamforming algorithm and cylindrical asynchronous measurement multi-signal classification algorithm is as follows;

[0022] S03.1: Assuming the sound source is a steady-state sound source, the sound source is distributed in various corners, while the 3D spherical array (with M microphones) moves along a 3D double helix orbital trajectory with equal angle γ, combined with equal angle γ rotation. Each location is identified, and signals are collected from each location.

[0023] S03.2: Assuming a Q-uncorrelated far-field narrowband signal exists on the source plane, therefore, in the asynchronous cylindrical measurement, the {l}th... th The data vector received at positions (l = 1, ..., L) can be represented in the frequency domain as:

[0024] P {l} =G {l} S+E {l}

[0025] Where S = [s1, ..., s Q ] T ∈c Qx1 P represents the far-field narrowband uncorrelated signal in the frequency domain; P is the received signal vector; E represents the uncertainty of the model, including noise interference and model approximation.

[0026] S03.3: Assume that the noise is an independent and identically distributed (iid) random variable following a complex Gaussian distribution; This is the guide vector for the spatial array;

[0027]

[0028] in, t and t′ represent the position vector of the sound source and the signal emission time, respectively. t and t represent the position vector of the receiver and the signal reception time, respectively; |·| represents the magnitude of the vector; and δ(.) represents the Dirac function.

[0029] S03.4: Filling the spectral matrix according to its specific construction and algorithm can be represented as follows: The second step of the asynchronous cylindrical measurement is covariance matrix completion. Using the asynchronous cylindrical measurement, the small covariance matrix of each measurement position in the orbital trajectory can be obtained. The received signal data vector P {l} The covariance matrix is ​​expressed as:

[0030]

[0031] in, It is the covariance matrix of uncorrelated sources. q th The power of the source;

[0032] S03.5: A block diagonal matrix can be obtained directly. The composite covariance matrix representing missing terms has its off-diagonal blocks empty, replaced by zeros due to the lack of phase relationships between consecutive positions. Then, a complete composite covariance matrix is ​​obtained. The matrix can be obtained. Finally, the covariance matrix needs to be analyzed. The goal of continuing with fast eigenvalue decomposition of sparse symmetric matrices is to enable the algorithm to perform fast and accurate imaging.

[0033] S03.6: The covariance matrix completion problem can be formulated as a constrained optimization problem. The fast iterative shrinkage threshold analysis algorithm is used to solve the constrained optimization problem. Compared with simultaneous measurement, the algorithm inevitably leads to matrix completion errors. A complete optimization model for the covariance matrix is ​​as follows:

[0034]

[0035] Among them ||·|| * The nuclear norm of a matrix is ​​denoted as . It is defined as the eigenvalue λ i The sum, minimizing the objective function It is to find the one with the smallest nuclear norm.

[0036] A(·) represents the sampling operator that retrieves elements from the diagonal block of a matrix;

[0037] S03.7: A: Based on the specific construction and algorithmic filling of the spectral matrix, the multi-signal classification algorithm imaging process of asynchronous cylindrical measurements can be represented as:

[0038]

[0039] in, for The vector form of U is calculated from the measured sound pressure, which is derived from the actual position of the microphone array at each asynchronous measurement location on the cylinder. ss The subspace spanned by the eigenvectors corresponding to the eigenvalues ​​in the equation.

[0040] B: Based on the specific construction and algorithmic filling of the spectral matrix, the beamforming algorithm imaging process can be represented as follows:

[0041]

[0042] Where, p BF for The vector form of the sound pressure is calculated from the measured sound pressure level, which is derived from the actual position of the microphone array at each location. Used to compensate for the time delay and amplitude attenuation during forward propagation.

[0043] S03.8: Calculate the imaging error of the low-frequency sound source by comparing the inner and outer orbits using the 2-norm:

[0044]

[0045]

[0046] In the above technical solution, the asynchronous measurement technology provided by the present invention for 3D imaging of multi-point heterogeneous low-frequency sound sources has the following beneficial effects:

[0047] This multi-point, non-planar low-frequency sound source 3D imaging method utilizes a 3D spherical array with a 3D spiral orbital trajectory at its center, combined with the array's rotational movement. For multi-point, non-planar sound sources, it employs a 3D spiral parallel upward orbital-rotation-asynchronous measurement technique. This technique can approximate the measurement results of microphone arrays with larger apertures and higher density to a certain extent, achieving a complementary effect and further improving longitudinal resolution. Finally, through beamforming algorithms or multi-signal classification algorithms for cylindrical asynchronous measurements, it achieves rapid imaging at multiple non-planar points at low frequencies (below 500Hz). This successfully improves upon the current limitation of imaging only at high frequencies in three-dimensional space, truly achieving high resolution for point sound sources. This method is beneficial for large-scale, long-distance measurements and allows for intelligent automated measurements using mechanical devices. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0049] Figure 1 A flowchart illustrating the application of asynchronous measurement technology based on the 3D spiral orbit trajectory of two spherical array centers and the rotation of the spherical array in 3D imaging of multi-point heterogeneous low-frequency sound sources, provided in an embodiment of the present invention.

[0050] Figure 2 A distribution diagram of a 600mm diameter 3D spherical array microphone provided for an embodiment of the present invention;

[0051] Figure 3 Distribution diagram of center point coordinates O(0,0,0) of a 600mm diameter 3D spherical array provided in an embodiment of the present invention;

[0052] Figure 4 This invention provides a 3D trajectory diagram of a sphere array center exhibiting parallel upward and clockwise rotation in a 3D double helix pattern, as shown in the embodiment of the invention.

[0053] Figure 5 The projection of the sphere array center in a 3D double helix parallel upward revolution (clockwise rotation) onto the xy plane is provided in the embodiment of the present invention;

[0054] Figure 6 The distribution diagram of the center of the sphere array according to the spiral trajectory (2 spiral lines, 20 points in each line, of which 10 points are one cycle of rotation, and the angle of each point is 36°, which is evenly divided into the revolution angle and the rotation angle, rotating clockwise) is provided for the embodiments of the present invention.

[0055] Note: Figure 6To demonstrate the location of the moving point, the 3D model was converted into a 2D diagram. Point 10 coincides with the sound source. For details on point 10, please refer to the 3D diagram.

[0056] Figure 7 The image distribution diagram of one sound source on the inner track and four sound sources on the outer track in the front-to-right face beamforming algorithm with a transparency of 0.1 provided in the embodiment of the present invention;

[0057] Figure 8 The image distribution diagram of one sound source on the inner track and four sound sources on the outer track in the beamforming algorithm on the reverse-left side with a transparency of 0.1, provided in an embodiment of the present invention;

[0058] Figure 9 The distribution map of one sound source in the inner track and four sound sources in the outer track in the NCSM-MUSIC algorithm imaging on the front-right side with a transparency of 0.1 provided in the embodiment of the present invention;

[0059] Figure 10 The distribution map of one sound source on the inner track and four sound sources on the outer track in the NCSM-MUSIC algorithm imaging on the reverse-left side with a transparency of 0.1 provided in the embodiment of the present invention. Detailed Implementation

[0060] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0061] like Figure 1-10 As shown, a asynchronous measurement technique for 3D imaging of multi-point, non-planar low-frequency sound sources includes the following steps:

[0062] S01: The 3D double helix orbit trajectory of the center movement of the 3D spherical microphone array is constructed using the double helix formula. Then, combined with the characteristics of the rotation of the 3D spherical microphone array, 3D double helix orbit-rotation-3D asynchronous measurement is performed.

[0063] S02: Conventional asynchronous measurement achieves a larger and denser aperture array by moving a single planar array. 3D double helix revolution-rotation-3D asynchronous measurement is designed for the special double helix revolution trajectory with evenly distributed polar angles (3D double helix arc trajectory). Based on the center of the 3D spherical array, the 3D spherical microphone array is moved, and the 3D spherical microphone is further rotated with equal polar angles, so that different positions correspond to different microphone distributions. The advantage is that it exceeds the constraints defined by the measurement using a single fixed planar array. At the same time, the parallel upward revolution of the 3D double cylindrical helix achieves a complementary effect and improves the longitudinal sound source resolution imaging in a certain spatial domain.

[0064] S03: Imaging of multi-point heterogeneous sound sources can be achieved by using beamforming algorithms and multi-signal classification algorithms for 3D cylinder non-synchronous measurement (NCSM-MUSIC-3D algorithm). First, two 3D spherical arrays are used to collect signals at each point by rotating on their own axes and moving along a 3D double helix orbital trajectory, and the signals are preprocessed. Then, a cross-spectral matrix is ​​constructed and filled using a fast iterative threshold shrinkage algorithm. Finally, imaging is performed using beamforming algorithms or the NCSM-MUSIC-3D algorithm.

[0065] This multi-point, non-planar low-frequency sound source 3D imaging method utilizes a 3D spherical array with a 3D spiral orbital trajectory at its center, combined with the array's rotation. For multi-point, non-planar sound sources, it employs a 3D spiral parallel upward orbital-rotation-asynchronous measurement technique, which to some extent approximates the measurement results of microphone arrays with larger apertures and higher density, achieving a complementary effect and further improving longitudinal resolution. Finally, through beamforming algorithms or multi-signal classification algorithms for cylindrical asynchronous measurements, it achieves rapid imaging at multiple non-planar points at low frequencies (below 500Hz), successfully improving upon the current limitation of imaging only at high frequencies in 3D space. This method truly achieves high resolution for point sound sources, facilitating large-scale, long-distance measurements and enabling intelligent automated measurements using mechanical devices.

[0066] In step S01, the 3D imaging method for the sound source utilizes a non-synchronous measurement method that combines a 3D double helix revolution of points with the rotation of a spherical array. This is an improvement on the non-synchronous measurement method in real-world scenarios. The 3D double helix revolution is used to make the array larger and denser, while for a single fixed array, the rotation is used to transform the originally sparse array into a dense array, while retaining the pattern of a 3D spherical array. The formulas for the 3D double helix revolution trajectory of the center of the spherical array and the rotation of the spherical array are as follows:

[0067]

[0068] z1=θ1

[0069]

[0070]

[0071]

[0072] θ1=θ1+ω1*t

[0073] θ2=θ2+ω2*t

[0074]

[0075] Where, x 11 The x-axis displacement of the spiral 1 is represented by its revolution around the sun, and the y-axis displacement is represented by its revolution around the sun. 11 The x-axis represents the displacement of the spiral 1 around the y-axis. 12 The x-axis displacement of the spiral 2 revolutions, y-axis displacement 12 Let θ1 represent the y-axis displacement of the spiral 2's revolution, z1 represent the z-axis displacement, r1 represent the distance from the center of the sphere array's trajectory, θ1 represent the 3D spiral's revolution angle range, x2 represent the x-axis displacement of rotation, y2 represent the y-axis displacement of rotation, z2 represent the z-axis displacement of rotation, and r2 represent the distance from the center of the sphere array to the microphone. θ1 represents the rotation elevation angle, θ2 represents the rotation plane angle range, ω1 represents the angular velocity of the 3D spiral revolution of the sphere array, ω2 represents the angular velocity of the sphere array rotation, and t represents time.

[0076] In step S02, for low-frequency multi-point skewed sound sources, assuming the sound sources are steady-state, the sound sources are distributed in various corners, while the 3D spherical array (with M microphones) moves at equal angles γ, combining 3D spiral revolution with equal angle γ rotation. It identifies several locations and collects signals from each location.

[0077] In step S03, for low-frequency multi-point heterogeneous sound sources, the imaging method using beamforming algorithm and NCSM-MUSIC-3D algorithm is as follows;

[0078] S03.1: Assuming the sound source is a steady-state sound source, the sound source is distributed in various corners, while the 3D spherical array (with M microphones) moves along a 3D double helix orbital trajectory with equal angle γ, combined with equal angle γ rotation. Each location is identified, and signals are collected from each location.

[0079] S03.2: Assuming a Q-uncorrelated far-field narrowband signal exists on the source plane, therefore, in the cylindrical non-synchronous measurement (NCSM) {l} th The data vector received at positions (l = 1, ..., L) can be represented in the frequency domain as:

[0080] P {l} =G {l} S+E {l}

[0081] Where S = [s1, ..., s Q ] T ∈C Qx1P represents the far-field narrowband uncorrelated signal in the frequency domain; P is the received signal vector; E represents the uncertainty of the model, including noise interference and model approximation.

[0082] S03.3: Assume that the noise is an independent and identically distributed (iid) random variable following a complex Gaussian distribution; This is the guide vector for the spatial array;

[0083]

[0084] in, t and t′ represent the position vector of the sound source and the signal emission time, respectively. t and t represent the position vector of the receiver and the signal reception time, respectively; |·| represents the magnitude of the vector; and δ(.) represents the Dirac function.

[0085] S03.4: Filling the spectral matrix according to its specific construction and algorithm can be represented as follows: The second step of NCSM is covariance matrix completion. Using NCSM, the small covariance matrix of each measurement position in the orbital trajectory can be obtained. The received signal data vector P {l} The covariance matrix is ​​expressed as:

[0086]

[0087] in, It is the covariance matrix of uncorrelated sources. q th The power of the source;

[0088] S03.5: A block diagonal matrix can be obtained directly. The composite covariance matrix representing missing terms has its off-diagonal blocks empty, replaced by zeros due to the lack of phase relationships between consecutive positions. Then, a complete composite covariance matrix is ​​obtained. The matrix can be obtained. Finally, the covariance matrix needs to be analyzed. The goal of continuing with fast eigenvalue decomposition of sparse symmetric matrices is to enable the algorithm to perform fast and accurate imaging.

[0089] S03.6: The covariance matrix completion problem can be formulated as a constrained optimization problem. The fast iterative shrinkage threshold analysis algorithm is used to solve the constrained optimization problem. Compared with simultaneous measurement, the algorithm inevitably leads to matrix completion errors. A complete optimization model for the covariance matrix is ​​as follows:

[0090]

[0091] Among them ||·|| * The nuclear norm of a matrix is ​​denoted as . It is defined as the eigenvalue λ i The sum, minimizing the objective function It is to find the one with the smallest nuclear norm.

[0092] A(·) represents the sampling operator that retrieves elements from the diagonal block of a matrix;

[0093] S03.7: A: Based on the specific construction and algorithm for filling the spectral matrix, the NCSM-MUSIC-3D imaging process can be represented as:

[0094]

[0095] in, for The vector form of U is calculated from the measured sound pressure level, which is derived from the actual position of the microphone array at each NCSM location. ss The subspace spanned by the eigenvectors corresponding to the eigenvalues ​​in the equation.

[0096] B: Based on the specific construction and algorithmic filling of the spectral matrix, the beamforming algorithm imaging process can be represented as follows:

[0097]

[0098] Among them, P BF for The vector form of the sound pressure is calculated from the measured sound pressure level, which is derived from the actual position of the microphone array at each location. Used to compensate for the time delay and amplitude attenuation during forward propagation;

[0099] S03.8: Calculate the imaging error of the low-frequency sound source by comparing the inner and outer orbits using the 2-norm:

[0100]

[0101]

[0102] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for 3D imaging of multi-point, non-planar low-frequency sound sources using asynchronous measurement technology, characterized in that, Includes the following steps: S01: The 3D double helix orbit trajectory of the center movement of the 3D spherical microphone array is constructed using the double helix formula. Then, combined with the characteristics of the rotation of the 3D spherical microphone array, 3D double helix orbit-rotation-3D asynchronous measurement is performed. S02: Conventional asynchronous measurement achieves a larger and denser aperture array by moving a single planar array. 3D double helix revolution-rotation-3D asynchronous measurement is designed for the special double helix revolution trajectory with evenly distributed polar angles. Based on the center of the 3D spherical array, the 3D spherical microphone array is moved, and the 3D spherical microphone is further rotated with equal polar angles, so that different positions correspond to different microphone distributions. The advantage is that it exceeds the constraints defined by the measurement using a single fixed planar array. At the same time, the parallel upward revolution of the 3D double cylindrical helix achieves a complementary effect and improves the longitudinal sound source resolution imaging in a certain spatial domain. S03: Imaging of multi-point heterogeneous sound sources can be achieved by using beamforming algorithms and multi-signal classification algorithms for asynchronous cylindrical measurements. First, two 3D spherical arrays are used to rotate and move along a 3D double helix orbital trajectory to collect signals at each point and preprocess the signals. Then, a cross-spectral matrix is ​​constructed and filled using a fast iterative threshold shrinkage algorithm. Finally, imaging is performed using either beamforming algorithms or multi-signal classification algorithms for asynchronous cylindrical measurements.

2. The asynchronous measurement technique for 3D imaging of multi-point, non-planar low-frequency sound sources according to claim 1, characterized in that: In step S01, the 3D imaging method for the sound source utilizes a non-synchronous measurement method that combines a 3D double-helix revolution of points with the rotation of a spherical array. This is an improvement on the non-synchronous measurement method in real-world scenarios. The 3D double-helix revolution is used to make the array larger and denser, while for a single fixed array, the rotation is used to transform the originally sparse array into a dense array, while retaining the pattern of a 3D spherical array. The formulas for the 3D double-helix revolution trajectory of the center of the spherical array and the rotation of the spherical array are as follows: z1=θ1 θ1=θ1+ω1*t θ2=θ2+ω2*t θ1∈[-4π, 4π], θ2∈[0, 2π], Where, x 11 The x-axis displacement of the spiral 1 is represented by its revolution around the sun, and the y-axis displacement is represented by its revolution around the sun. 11 The x-axis represents the displacement of the spiral 1 around the y-axis. 12 The x-axis displacement of the spiral 2 revolutions, y-axis displacement 12 Let represent the y-axis displacement of the spiral 2, z1 represent the z-axis displacement, r1 represent the distance from the center of the sphere array, θ1 represent the 3D spiral's revolution angle range, and x2 represent the x-axis displacement of the rotation. y2 represents the displacement along the y-axis, z2 represents the displacement along the z-axis, and r2 represents the distance from the center of the sphere array to the microphone. θ1 represents the rotation elevation angle, θ2 represents the rotation plane angle range, ω1 represents the angular velocity of the 3D spiral revolution of the sphere array, ω2 represents the angular velocity of the sphere array rotation, and t represents time.

3. The asynchronous measurement technique for 3D imaging of multi-point, non-planar low-frequency sound sources according to claim 1, characterized in that: In step S02, for low-frequency multi-point skewed sound sources, assuming the sound source is a steady-state sound source, the sound source is distributed in various corners, and the 3D spherical array moves at equal angles γ, combining 3D spiral revolution with equal angle γ rotation. It identifies several locations and collects signals from each location.

4. The asynchronous measurement technique for 3D imaging of multi-point, non-planar low-frequency sound sources according to claim 1, characterized in that: In step S03, for low-frequency multi-point heterogeneous sound sources, the imaging method using beamforming algorithm and cylindrical asynchronous measurement multi-signal classification algorithm is as follows; S03.1: Assuming the sound source is a steady-state sound source, the sound source is distributed in various corners, while the 3D spherical array (with M microphones) moves along a 3D double helix orbital trajectory with equal angle γ, combined with equal angle γ rotation. Each location is identified, and signals are collected from each location. S03.2: Assuming a Q-uncorrelated far-field narrowband signal exists on the source plane, therefore, in the asynchronous cylindrical measurement, the {l}th... th The data vector received at positions (l = 1, ..., L) can be represented in the frequency domain as: P {l} =G {l} S+E {l} Where S = [s1, ..., s Q ] T ∈C Qx1 P represents the far-field narrowband uncorrelated signal in the frequency domain; P is the received signal vector; E represents the uncertainty of the model, including noise interference and model approximation. S03.3: Assume that the noise is an independent and identically distributed (iid) random variable following a complex Gaussian distribution; This is the guide vector for the spatial array; in, t and t′ represent the position vector of the sound source and the signal emission time, respectively. t and t represent the position vector of the receiver and the signal reception time, respectively; |·| represents the magnitude of the vector; and δ(.) represents the Dirac function. S03.4: Filling the spectral matrix according to its specific construction and algorithm can be represented as follows: The second step of the asynchronous cylindrical measurement is covariance matrix completion. Using the asynchronous cylindrical measurement, the small covariance matrix of each measurement position in the orbital trajectory can be obtained. The received signal data vector P {l} The covariance matrix is ​​expressed as: in, It is the covariance matrix of uncorrelated sources. q th The power of the source; S03.5: A block diagonal matrix can be obtained directly. The composite covariance matrix representing missing terms has its off-diagonal blocks empty, replaced by zeros due to the lack of phase relationships between consecutive positions. Then, a complete composite covariance matrix is ​​obtained. The matrix can be obtained. Finally, the covariance matrix needs to be analyzed. The goal of continuing with fast eigenvalue decomposition of sparse symmetric matrices is to enable the algorithm to perform fast and accurate imaging. S03.6: The covariance matrix completion problem can be formulated as a constrained optimization problem. The fast iterative shrinkage threshold analysis algorithm is used to solve the constrained optimization problem. Compared with simultaneous measurement, the algorithm inevitably leads to matrix completion errors. A complete optimization model for the covariance matrix is ​​as follows: Among them ||·|| * The nuclear norm of a matrix is ​​denoted as . It is defined as the eigenvalue λ i The sum, minimizing the objective function It is to find the one with the smallest nuclear norm. A(·) represents the sampling operator that retrieves elements from the diagonal block of a matrix; S03.7: A: Based on the specific construction and algorithmic filling of the spectral matrix, the multi-signal classification algorithm imaging process of asynchronous cylindrical measurements can be represented as: in, for The vector form of U is calculated from the measured sound pressure, which is derived from the actual position of the microphone array at each asynchronous measurement location on the cylinder. ss The subspace spanned by the eigenvectors corresponding to the eigenvalues ​​in the equation; B: Based on the specific construction and algorithmic filling of the spectral matrix, the beamforming algorithm imaging process can be represented as follows: Among them, P BF for The vector form of the sound pressure is calculated from the measured sound pressure level, which is derived from the actual position of the microphone array at each location. Used to compensate for the time delay and amplitude attenuation during forward propagation; S03.8: Calculate the imaging error of the low-frequency sound source by comparing the inner and outer orbits using the 2-norm:

Images