A spectral estimation method for indoor coherent pulse sound source AOA

Abstract

This invention presents a spectral estimation method for the AOA of an indoor coherent pulse sound source—Fourth-Order Cumulant Multiple Matrix Reconstruction (FOC-MMR)—belonging to the field of spatial spectrum estimation. This method performs singular value decomposition (SVD) on the higher-order covariance matrix of the fourth-order cumulant extended virtual array data to obtain higher-order noise feature vectors. These vectors are orthogonally matched with the extended higher-order array manifold vectors to obtain the spatial spectral function, which is then used to reconstruct the three-dimensional sound field of the coherent pulse sound source. The FOC-MMR algorithm of this invention exhibits high ability to distinguish neighboring sound sources and suppress Gaussian noise when applied to a uniform rectangular microphone array. Furthermore, it achieves AOA estimation of wide-angle incident coherent sound sources with high direction-finding accuracy and spatial resolution.

Description

Technical Field

[0001] This invention belongs to the field of indoor acoustics and sound source localization, and particularly relates to a spectral estimation method for an indoor coherent pulse sound source AOA. Background Technology

[0002] The classic Multiple Signal Classification (MUSIC) algorithm, when estimating the Angle of Arrival (AOA) of a coherent sound source, finds that the signal feature matrix and noise feature matrix obtained from the Singular Value Decomposition (SVD) of the underdeterminate microphone array signal covariance matrix are not strictly orthogonal. This leads to aliasing in the sound field reconstructed from the spatial spectrum determined by the array manifold vector and the noise feature matrix, thus failing to effectively estimate the AOA of indoor coherent pulse sound sources.

[0003] The proposed forward and backward spatial smoothing (FBSS) and Toeplitz matrix reconstruction methods can improve the MUSIC algorithm to achieve efficient estimation of the AOA of coherent signals. However, these methods are only applicable to uniform line arrays (ULA), which limits the application of the MUSIC algorithm in multidimensional microphone arrays.

[0004] The MUSIC algorithm, improved based on fourth-order cumulants, can be used for area arrays and other three-dimensional conformal array structures, achieving simultaneous estimation of the azimuth and elevation angles of the AOA. However, the high computational complexity of fourth-order cumulants limits the application of this algorithm under real-time conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a spectral estimation method for indoor coherent pulse sound sources (AOA) to solve the technical problems mentioned in the background section.

[0006] To achieve the above objectives, the specific technical solution of the spectral estimation method for an indoor coherent pulse sound source AOA according to the present invention is as follows:

[0007] A method for estimating the spectrum of an indoor coherent pulse sound source AOA includes the following steps, which are performed sequentially:

[0008] Step S1: Measure the sound pressure signal x(t) of the multi-coherent sound source in the indoor sound field using an area array microphone;

[0009] Step S2: Calculate the covariance matrix Rx of the acoustic array signal after short-time Fourier transform;

[0010] Step S3: Calculate the fourth-order cumulant C of the covariance matrix Rx. 4X And obtain the higher-order noise subspace by its singular value decomposition, wherein it refers to the fourth-order cumulant of the covariance matrix;

[0011] Step S4: Then perform Kronecker product expansion on the array manifold vectors, corresponding to the order of the fourth-order cumulant data;

[0012] Step S5: Calculate the spatial spectrum of the noise feature matrix obtained from singular value decomposition and the transformed array manifold vector to reconstruct the three-dimensional sound field, and finally obtain the AOA estimate.

[0013] Furthermore, the specific content of step S1 is as follows:

[0014] The sound pressure signal x(t) of the multiphase sound source in the indoor sound field is measured by a surface array microphone, and the higher-order Kronecker product transform array manifold vector is derived based on the definition of the linear array manifold vector.

[0015] M lines and N The array manifold vector of the rectangular planar microphone array is:

[0016] (1)

[0017] (2)

[0018] In equations (1) and (2), ψ xi = 2π / λ dsinθ i cosφ i , ψ zi = 2π / λ dsinθ i sinφ i (i=1…I); where λ is the wavelength of the acoustic signal, and d is the element spacing. θ i : No. i The elevation angle φ of the plane wave emitted by each sound source reaching the array along the main propagation path is... i : No. i The plane waves emitted by each sound source arrive at the array at the corresponding azimuth angles of the main propagation paths. Taking the Kronecker product transform of the array manifold vector in the above equation, the form is:

[0019] (3)

[0020] The array signal data received by the microphone array can be represented in matrix form:

[0021] (4)

[0022] In equation (4), KR(V(ψ))∈C (NM×I) It includes the spatial characteristics of the array and the signal. Include I One signal, It is Gaussian white noise, and the noise is uncorrelated with the signal. : N×M order array manifold vector, then Order AMV (Array manifold vector, AMV), : No. One sound source signal.

[0023] Furthermore, the specific contents of steps S2-S4 are as follows:

[0024] Find the covariance matrix Rx of the acoustic array signal after short-time Fourier transform, and find its fourth-order cumulant C. 4X Furthermore, to correspond to the order of the transformed covariance matrix, the original array manifold vectors need to be reconstructed using the Kronecker product:

[0025] (5)

[0026] In equation (5), M×N microphones with a spacing of d are evenly arranged in a planar rectangular area, i.e., M rows and N columns of array elements, where M is the number of microphone rows and N is the number of microphone columns. Further, the specific content of step S5 is as follows:

[0027] R_C 4X The noise feature matrix C obtained by singular value decomposition 4N The normalized spatial spectrum of the transformed array manifold vector H(ψ) = KR(V(ψ)) is calculated, and finally the AOA estimate is obtained:

[0028] (6)

[0029] In the above formula, ⊙ and These represent the Khatri-Rao product and the Kronecker product of the matrices, respectively. R_C represents the complex conjugate of a matrix, H represents the conjugate of a matrix, and R_C represents the complex conjugate of a matrix. 4X： The fourth-order cumulant matrix C of the array output data 4X The covariance, M, N: uniformly distributed planar rectangular regions with spacing of... d of One microphone; M: number of microphone rows, N: number of microphone columns. C N : Noise subspace.

[0030] Furthermore, the specific content of step S1 is as follows:

[0031] Area array model establishment:

[0032] The spacing is uniformly arranged within the rectangular planar area. d of M × N There are several microphones, assuming the sound field originates from sources at a distance r = [r1, ..., r]. i , ..., r I ]of I Composed of several far-field sound sources, the first i The plane waves emitted by each sound source reach the array at the corresponding elevation angle of the main propagation path. i i and azimuth f i The corresponding AOA is represented as ψ i =( f i , i i ),in f i ∈[180°, 360°] and i i ∈[0, 180°];

[0033] A plane wave propagating in a homogeneous medium is generated by a far-field sound source. P i ( r i , i i , f i Generate and define wavenumber k i for:

[0034] (1)

[0035] In equation (1), u is a unit vector, u = (- sinth i cosφ i , - sinth i sinφ i , - cosθ i ) T λ = c / f, where c is the speed of sound in the medium. f The dominant frequency of the sound source;

[0036] Similar to the definition of an array manifold vector (AMV) for a linear array, the AMV of the m-th (m=1,…,M) row microphone can be defined as follows:

[0037] (2)

[0038] In equation (2), the vector ψ i = [ψ xi , ψ zi ] T , where ψ xi = 2π / λ dsinθ i cosφ i , ψ zi = 2π / λ dsinθ i sinφ i Then the N×M order AMV is: V(ψ) i ) is defined as:

[0039] (3)

[0040] V(ψ) i Rewrite as an NM×1 column vector And rewritten in the form of a Kroneker product, it is expressed as:

[0041] (4)

[0042] In equation (4), A z (ψ zi ) and A x (ψ xi The following represent the AMVs of the microphones in the nth (n=1, ..., N) column and the mth (m=1, ..., M) row, respectively:

[0043]

[0044] The array signal data received by the microphone array can be represented in matrix form:

[0045] (7)

[0046] In formula (7), KR(V(ψ))=[CV(V(ψ1)),…,CV(V(ψ) i )), …,CV(V(ψ I ))]∈C (NM×I) It contains the spatial characteristics of the array and the signal, which are crucial in subsequent data processing because it contains the AOA information of the sound source; Include I One signal, among which They are independent and evenly distributed. and They are the first The amplitude and initial phase of each sound source; The mean is zero and the variance is... Gaussian white noise, and the noise is uncorrelated with the signal;

[0047] (8)

[0048] In formula (7) KR ( V ( ψ ))∈ C (NM×I) For matrix A z ( ψ z ) and □( A x ( ψ x The Khatri-Rao product of ) is expressed as:

[0049] (9)

[0050] in z j and x j Representing matrices respectively A z ( ψ z )and A x ( ψ x ) j The column, Equation (9) contains the signal source AOA data vector. ψ And can be defined as:

[0051] (10)

[0052] In equation (9) M lines and N Array element pairs I AMV of a single source, i.e. A z ( ψ z )∈C (M×I) and A x ( ψ x )∈C (N×I They are represented as follows:

[0053] (11)

[0054] (12)

[0055] Furthermore, the specific contents of steps S2-S4 are as follows:

[0056] Perform higher-order matrix transformations on it

[0057] In order to obtain sound source information from the signal data received from the array, MN × I The STFT obtained by applying a Kaiser window to a 3D signal matrix is ​​expressed as follows: X Then perform singular value decomposition, and equation (7) can be written as:

[0058] (13)

[0059] Where, U∈C (MN×MN) and V∈C (I×I) The column vectors are respectively XX H and X H X eigenvectors, D∈R (MN×I) It is a diagonal matrix composed of singular values ​​arranged in descending order; from the above definition, it can be seen that the column vectors of U and V are respectively the signal data covariance matrix R. u =E{ XX H} and R v =E{ X H X The eigenvectors of}, the singular values ​​in D are related to the number and energy of the received signals, V(ψ): AMV, S(k) of a step microphone: Include There are three coherent signals, N(t): The mean is zero and the variance is... Gaussian white noise, and the noise is independent of the signal;

[0060] The fourth-order cumulant matrix of X in equation (13) can be expressed as:

[0061] (14)

[0062] Based on the properties of the Kronecker product, the fourth-order cumulant of the signal and noise is expressed as:

[0063] (15)

[0064] From equations (13), (14), and (15), to simplify the formula, let H(ψ) = KR(V(ψ)). X The fourth-order cumulant C 4x Represented in matrix form:

[0065] (16)

[0066] In the formula Indicates conjugate; for the fourth-order cumulant matrix C of the array output data 4X The covariance is expressed as:

[0067] (17)

[0068] For R_C 4X Eigenvalue decomposition is performed to obtain the signal subspace C. S ∈C (NM)^2×I^2 ) and noise subspace C N ∈C (NM)^2×((NM)^2-I^2 ) ;

[0069] Furthermore, the specific content of step S5 is as follows:

[0070] Based on the spatial spectrum formula defined by the Multiple Signal Classification (MUSIC) algorithm, the normalized spatial spectrum (NSS) of the higher-order matrix transformation method—the fourth-order cumulant multiple matrix reconstruction (FOC-MMR) method—defined by the sound pressure data X transformed by the fourth-order cumulant and Kroneker product and the array manifold vector H(ψ) can be expressed as:

[0071] (18)

[0072] In equation (18), the spatial spectrum P ( ψ )∈C I2×I2 The AOA information contains I sound sources, with P(ψ) as the objective function, where ψ = [ψ1, ..., ψ2]. i ,…,ψ I ] is the independent variable of the function. The problem of finding the maximum value P(ψ) in equation (18) is defined as equation (19). By dividing the space θ∈[0, 180°] and φ∈[180°, 360°] with a resolution of 1°, we can find the ψ(θ, φ) that maximizes P(ψ). This numerical solution is the AOA estimate.

[0073] (19)

[0074] In equation (18) ⊙ and These represent the Khatri-Rao product and the Kronecker product of the matrices, respectively. H represents the complex conjugate of a matrix, and M and N represent uniformly arranged planar rectangular regions with spacing of . d of There are 1 microphone, M: number of microphone rows, and N: number of microphone columns.

[0075] The spectral estimation method for an indoor coherent pulse sound source AOA of the present invention has the following advantages:

[0076] (1) Due to the suppression effect of higher-order cumulants on Gaussian noise, the FOC-MMR method can still have high spatial resolution and direction finding accuracy when the SNR is low (SNR<0dB); (2) The array scalability of fourth-order cumulants allows the algorithm to supplement the features of coherent sound sources, thereby greatly increasing the decoherence capability of the signal; (3) Using short-time Fourier transform to process sound pressure data in frames can reduce the computational complexity of traditional fourth-order cumulants and improve the computational speed, thus making it possible to achieve real-time sound source tracking and localization. Attached Figure Description

[0077] Figure 1 It is a uniform rectangular matrix model.

[0078] Figure 2 shows Experiment I of Example 1 ( ψ 1 = (225°, 120°) ψ AOA estimation results for 2 = (315°, 60°) (a) Based on FS-MLE (SNR=5) dB (b) Based on FOC-MMR (SNR=5) dB (c) Based on FS-MLE (SNR=10) dB (d) Based on FOC-MMR (SNR=10) dB ).

[0079] Figure 3 shows the indoor area array pulse sound source acquisition in Example 1: (a) schematic diagram of the sound source AOA, and (b) experimental site diagram. Detailed Implementation

[0080] To better understand the purpose, structure, and function of this invention, the following detailed description of the spectral estimation method for an indoor coherent pulse sound source AOA, in conjunction with the accompanying drawings, is provided.

[0081] To address the problem of energy diffusion in the subspace of coherent sound sources and the difficulty in effectively estimating the angle of arrival (AOA) due to the underranked covariance matrix, a new indoor coherent pulse sound source estimation method—Fourth-Order Cumulant Multiple Matrix Reconstruction (FOC-MMR)—is proposed. This method obtains high-order noise eigenvectors by performing singular value decomposition (SVD) on the high-order covariance matrix of the expanded virtual array data using fourth-order cumulant matrix. These eigenvectors are orthogonally matched with the expanded high-order array manifold vectors, falling within the field of spatial spectrum estimation. By reconstructing the virtual sound pressure array data to obtain a full-rank high-order covariance matrix, this method not only solves the problem of energy diffusion between noise and signal eigenvectors caused by signal coherence but also achieves AOA estimation for multiple coherent sound sources with wide-angle incidence with high direction-finding accuracy and spatial resolution.

[0082] As shown in Figures 2 and 3, experiments were conducted on a coherent pulse source under a uniform rectangular array with M=8 array elements. The proposed FOC-MMR method was compared with the Frequency Smoothing Maximum Likelihood Estimation (FS-MLE) algorithm. When performing AOA estimation on the coherent pulse signal within the room, the FOC-MMR method exhibited higher grating lobe suppression and direction-finding accuracy. Furthermore, it maintained high robustness even when Gaussian white noise with an SNR of 5dB was added to the array sound pressure data.

[0083] Example 1: 1. Experimental results of a coherent pulse sound source based on an area array

[0084] Step 1: Measure the sound pressure signal of the coherent sound source in the room using a microphone array. The sampling frequency of the microphone array is 8kHz, and the frequency of the sound source is... f =1kHz. A schematic diagram of indoor coherent pulse sound source acquisition is shown below. Figure 3a and Figure 3b As shown.

[0085] Step 2: For coherent pulse sound sources located at (225°, 120°) and (315°, 60°), Gaussian white noise with SNR=5dB and 10dB is added to the collected sound pressure data. Then, the spatial spectrum of the sound field is reconstructed using the FOC-MMR method, thereby estimating the AOA of the coherent sound source. Figure 2b and Figure 2d As shown.

[0086] Step 3: To fully demonstrate the superiority of this invention in reconstructing the covariance matrix of sound pressure data based on fourth-order cumulants, the coherent pulse sound source signal in Example 1 is compared using the Frequency Smoothing Maximum Likelihood Estimation (FS-MLE) method. The AOA estimation result obtained using FS-MLE is as follows: Figure 2a and Figure 2c As shown. From Figure 2a and Figure 2c As can be seen, due to noise interference, the FS-MLE algorithm cannot effectively remove the influence of Gaussian noise, resulting in low estimation accuracy and low grating lobe suppression capability. The method designed in this invention, however, can obtain more accurate results in AOA estimation of coherent pulse sources with added Gaussian noise, making it suitable for widespread application.

[0087] In the experiment, coherent pulse sound sources S1 and S2 were both located 1m directly in front of the array, i.e., in the y=-1m plane. Three measurements were performed to eliminate the randomness of the experimental results. To verify the robustness and accuracy of the algorithm under low signal-to-noise ratio, Gaussian white noise with SNR=5dB and SNR=10dB was added to the array sound pressure data, respectively. AOA estimation was performed using the Frequency Smoothing Maximum Likelihood Estimation (FS-MLE) and FOC-MMR methods. Spectral estimation was performed on the spatial regions θ∈[0, 180°] and φ∈[180°, 360°] with a spatial resolution of 1°. The robustness and direction-finding accuracy of the algorithm were compared based on the sound field imaging results and the mean root mean square error e.

[0088] The root mean square error e, which measures the accuracy of AOA estimation, is defined by the following formula:

[0089] (20)

[0090] in, This indicates the number of measurements in each experimental group. , and , , which are the actual value of the sound source AOA and the estimated value of the spatial spectrum, respectively.

[0091] Gaussian white noise with different signal-to-noise ratios (SNR=5dB, 10dB) was added to the data acquired by the array. AOA was estimated using Frequency Smoothing Maximum Likelihood Estimation (FS-MLE) and FOC-MMR methods, with a spatial resolution of 1°. and Spectral estimation was performed on the spatial region, and the robustness and direction-finding accuracy of the algorithm were compared based on the acoustic field imaging results and the mean root mean square error e. The experimental results are shown in Table 1.

[0092] Table 1. Different signal-to-noise ratios (SNR=5) dB 10 dB AOA estimation results and mean root mean square error e for FS-MLE and FOC-MMR

[0093]

[0094] 2. Reconstructing the sound field from the spatial spectrum of a coherent pulse sound source

[0095] Figure 2 shows the sound field reconstruction of the coherent pulse sound source based on URA in Experiment I, which includes different signal-to-noise ratios (SNR=5). dB 10 dB The acoustic imaging image below is based on the FS-MLE algorithm and FOC-MMR method. 'o' and the numbers represent the actual AOA of the sound source. The numerical representation of the sound source estimation AOA.

[0096] By reconstructing the sound pressure data of each window in the frequency domain using fourth-order cumulants to expand the virtual array metadata, a high-order covariance matrix is ​​obtained. The high-order full-rank covariance matrix (SVD), containing all coherent signal features, effectively separates the high-order signal eigenvectors and high-order noise eigenvectors (HO-NFV) of the coherent pulse sound source. This not only suppresses Gaussian white noise mixed in with low signal-to-noise ratio sound signals in the air but also achieves effective estimation of the AOA of the coherent pulse sound source. The high-order array manifold vector (HO-AMV), which is orthogonally matched to HO-NFV, is determined by the signal frequency and array structure, and solved using equations (18) and (19). Let the spatial spectrum function Take the maximum value, that is, The estimated value.

[0097] The spatial grid of the sound source is plotted at a resolution of 1°. and The algorithm can only effectively estimate the DOA of sound sources located at grid points. If the actual DOA of the sound source is not located at a grid node (i.e., far from the grid point), a smaller resolution grid needs to be created, which greatly increases the computational load. Experiments have shown that, under the same computational environment, the FS-MLE method is approximately 2.5 times faster than the FOC-MMR method.

[0098] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for estimating the spectrum of an indoor coherent pulse sound source (AOA), characterized in that, Includes the following steps, And the following steps are performed in sequence: Step S1: Measure the sound pressure signal x(t) of the multi-coherent sound source in the indoor sound field using an area array microphone; Step S2: Calculate the covariance matrix Rx of the acoustic array signal after short-time Fourier transform; Step S3: Calculate the fourth-order cumulant C of the covariance matrix Rx. 4X And obtain the higher-order noise subspace by its singular value decomposition, wherein it refers to the fourth-order cumulant of the covariance matrix; Step S4: Then perform Kronecker product expansion on the array manifold vectors, corresponding to the order of the fourth-order cumulant data; Step S5: Calculate the spatial spectrum of the noise feature matrix obtained from singular value decomposition and the transformed array manifold vector to reconstruct the three-dimensional sound field, and finally obtain the AOA estimate.

2. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 1, characterized in that, The specific details of step S1 are as follows: The sound pressure signal x(t) of the multiphase sound source in the indoor sound field is measured by a surface array microphone, and the higher-order Kronecker product transform array manifold vector is derived based on the definition of the linear array manifold vector. M lines and N The array manifold vector of the rectangular planar microphone array is: （1） （2） In equations (1) and (2), ψ xi = 2π / λ dsinθ i cosφ i , ψ zi = 2π / λ dsinθ i sinφ i (i=1…I); where λ is the wavelength of the acoustic signal, and d is the element spacing. θ i : No. i The elevation angle φ of the plane wave emitted by each sound source reaching the array along the main propagation path is... i : No. i The plane waves emitted by each sound source arrive at the array at the corresponding azimuth angles of the main propagation paths. Taking the Kronecker product transform of the array manifold vector in the above equation, the form is: （3） The array signal data received by the microphone array can be represented in matrix form: (4) In equation (4), KR(V(ψ))∈C (NM×I) It includes the spatial characteristics of the array and the signal. Include I One signal, It is Gaussian white noise, and the noise is uncorrelated with the signal. : N×M order array manifold vector, then Order AMV (Array manifold vector, AMV), : No. One sound source signal.

3. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 1, characterized in that, The specific contents of steps S2-S4 are as follows: Find the covariance matrix Rx of the acoustic array signal after short-time Fourier transform, and find its fourth-order cumulant C. 4X Furthermore, to correspond to the order of the transformed covariance matrix, the original array manifold vectors need to be reconstructed using the Kronecker product: （5） In equation (5), M×N microphones with a spacing of d are evenly arranged in a rectangular area, i.e., M rows and N columns of array elements, where M is the number of microphone rows and N is the number of microphone columns.

4. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 1, characterized in that, The specific details of step S5 are as follows: R_C 4X The noise feature matrix C obtained by singular value decomposition 4N The normalized spatial spectrum of the transformed array manifold vector H(ψ) = KR(V(ψ)) is calculated, and finally the AOA estimate is obtained: （6） In the above formula, ⊙ and These represent the Khatri-Rao product and the Kronecker product of the matrices, respectively. R_C represents the complex conjugate of a matrix, H represents the conjugate of a matrix, and R_C represents the complex conjugate of a matrix. 4X： The fourth-order cumulant matrix C of the array output data 4X The covariance, M, N: uniformly distributed planar rectangular regions with spacing of... d of One microphone; M: Number of microphone rows, N: Number of microphone columns C N : Noise subspace.

5. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 2, characterized in that, The specific content of step S1 is as follows: Array model establishment: The spacing is uniformly arranged within the rectangular area of ​​the plane. d of M × N There are several microphones, assuming the sound field originates from sources at a distance r = [r1, ..., r2]. i , ..., r I ]of I Composed of several far-field sound sources, the first i The plane waves emitted by each sound source reach the array at the corresponding elevation angle of the main propagation path. θ i and azimuth φ i The corresponding AOA is represented as ψ i =( φ i , θ i ),in φ i ∈[180°, 360°] and θ i ∈[0, 180°]; A plane wave propagating in a homogeneous medium is generated by a far-field sound source. P i ( r i , θ i , φ i Generate and define wavenumber k i for: （1） In equation (1), u is a unit vector, u = (- sinθ i cosφ i , - sinθ i sinφ i , - cosθ i ) T λ = c / f, where c is the speed of sound in the medium. f The dominant frequency of the sound source; Similar to the definition of the array manifold vector for a linear array, the array manifold vector of the microphones in rows m = 1, ..., M can be defined as: （2） In equation (2), the vector ψ i = [ψ xi , ψ zi ] T , where ψ xi = 2π / λ dsinθ i cosφ i , ψ zi = 2π / λ dsinθ i sinφ i Then the N×M order array manifold vector is: V(ψ) i ) is defined as: （3） V(ψ) i Rewrite as an NM×1 column vector And rewritten in the form of a Kroneker product, it is expressed as: （4） In equation (4), A z (ψ zi ) and A x (ψ xi ) represent the array manifold vectors of the microphones in columns n=1, ..., N and rows m=1, ..., M, respectively: The array signal data received by the microphone array can be represented in matrix form: (7) In formula (7), KR(V(ψ))=[CV(V(ψ1)),…,CV(V(ψ) i )), …,CV(V(ψ I ))]∈C (NM×I) It contains the spatial characteristics of the array and the signal, which are crucial in subsequent data processing because it contains the AOA information of the sound source; Include I One signal, among which They are independent and evenly distributed. and They are the first The amplitude and initial phase of each sound source; The mean is zero and the variance is... Gaussian white noise, and the noise is uncorrelated with the signal; （8） In formula (7) KR ( V ( ψ ))∈ C (NM×I) For matrix A z ( ψ z ) and □( A x ( ψ x The Khatri-Rao product of ) is expressed as: （9） in z j and x j Representing matrices respectively A z ( ψ z )and A x ( ψ x ) j The column, Equation (9) contains the signal source AOA data vector. ψ And can be defined as: （10） In equation (9) M lines and N Array element pairs I AMV of a single source, i.e. A z ( ψ z )∈C (M×I) and A x ( ψ x )∈C (N×I They are represented as follows: （11） （12）。 6. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 3, characterized in that, The specific contents of steps S2-S4 are as follows: Perform higher-order matrix transformations on it In order to obtain sound source information from the signal data received by the array, MN × I The STFT representation of a 3D signal matrix with a Kaiser window is as follows: X Then perform singular value decomposition, and equation (7) can be written as: （13） Where, U∈C (MN×MN) and V∈C (I×I) The column vectors are respectively XX H and X H X eigenvectors, D∈R (MN×I) It is a diagonal matrix composed of singular values ​​arranged in descending order; from the above definition, it can be seen that the column vectors of U and V are respectively the signal data covariance matrix R. u =E{ XX H } and R v =E{ X H X The eigenvectors of}, the singular values ​​in D are related to the number and energy of the received signals, V(ψ): AMV, S(k) of a step microphone: Include There are three coherent signals, N(t): The mean is zero and the variance is... Gaussian white noise, and the noise is independent of the signal; The fourth-order cumulant matrix of X in equation (13) can be expressed as: （14） Based on the properties of the Kronecker product, the fourth-order cumulant of the signal and noise is expressed as: （15） From equations (13), (14), and (15), to simplify the formula, let H(ψ) = KR(V(ψ)). X The fourth-order cumulant C 4x Represented in matrix form: （16） In the formula Indicates conjugate; for the fourth-order cumulant matrix C of the array output data 4X The covariance is expressed as: （17） For R_C 4X Eigenvalue decomposition is performed to obtain the signal subspace C. S ∈C (NM)^2×I^2 ) and noise subspace C N ∈C (NM )^2×((NM)^2-I^2 ) .

7. The spectral estimation method for an indoor coherent pulse sound source AOA according to claim 4, characterized in that, The specific details of step S5 are as follows: Based on the spatial spectrum formula defined by the multiple signal classification algorithm, the normalized spatial spectrum of the high-order matrix transformation method—the fourth-order cumulant multiple matrix reconstruction method—defined by the sound pressure data X transformed by the fourth-order cumulant and Kroneker product and the array manifold vector H(ψ) can be expressed as: （18） In equation (18), the spatial spectrum P ( ψ )∈C I2×I2 The AOA information contains I sound sources, with P(ψ) as the objective function, where ψ = [ψ1, ..., ψ2]. i ,…,ψ I ] is the independent variable of the function. The problem of finding the maximum value P(ψ) in equation (18) is defined as equation (19). By dividing the space θ∈[0, 180°] and φ∈[180°, 360°] with a resolution of 1°, we can find the ψ(θ, φ) that maximizes P(ψ). This numerical solution is the AOA estimate. (19) In equation (18) ⊙ and These represent the Khatri-Rao product and the Kronecker product of the matrices, respectively. H represents the complex conjugate of a matrix, and M and N represent uniformly arranged planar rectangular regions with spacing of . d of There are 1 microphone, M: number of microphone rows, and N: number of microphone columns.

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