Acoustic vector and scalar fusion sensor array acoustic imaging method based on wavelet decomposition

Abstract

The invention belongs to the technical field of aircraft acoustic tests, and particularly relates to an acoustic vector and scalar fusion sensor array acoustic imaging method based on wavelet decomposition. The method comprises the following steps: constructing a fused sensor array by using vector microphones and scalar microphones to measure the far-field noise of an aircraft, linearly combining sound pressure signals of each sensor with mass point vibration velocity signals of a sound vector sensor, and establishing a wavelet domain signal receiving model of the sound vector and scalar fused sensor array; and sound source identification and space positioning imaging are carried out by using beam forming methods such as CBF and CLEAN. The method can quickly and accurately identify the sound source with the unsteady state characteristic of the aircraft and carry out spatial positioning imaging, is also suitable for identification and spatial positioning imaging of the sound source with the steady state characteristic, and improves the identification and spatial positioning capabilities of the low and medium frequency sound source. Technical support is provided for aircraft acoustic performance test research, airworthiness evidence obtaining and model identification.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft acoustic test, and in particular relates to an acoustic imaging method of an acoustic vector and scalar fusion sensor array based on wavelet decomposition. Background Art

[0002] Aircraft sound source identification and spatial positioning through experiments are of great significance to the low-noise design, airworthiness certification and model performance identification of aircraft. Aircraft sound source identification and spatial positioning experiments involve a wide range of disciplines, high costs, long cycles and high risks, and therefore face many technical difficulties and limitations. At present, aircraft sound source identification and spatial positioning experiments mostly use spatial acoustic imaging methods based on scalar sensor arrays (i.e., sensor arrays that measure sound pressure signals). Such methods improve the signal-to-noise ratio through frame superposition processing and are generally applicable to steady-state sound emission of aircraft in stable operating conditions and stable environments. Moreover, beamforming methods based on scalar sensor arrays are subject to Rayleigh limits. Refined analysis of the characteristics and spatial positions of low- and medium-frequency sound sources requires a sufficiently large sensor array aperture and a sufficient number of array elements, resulting in large sensor array facilities and site consumption, further increasing the difficulty of experimental implementation. Summary of the invention

[0003] Purpose of the invention: To provide a sensor array acoustic imaging method based on wavelet decomposition and fusion of acoustic vector and scalar.

[0004] Technical solution:

[0005] A sensor array acoustic imaging method based on wavelet decomposition and acoustic vector and scalar fusion, comprising:

[0006] Step 1: Use the acoustic vector and scalar fusion sensor array to measure the aircraft far-field noise signal, linearly combine the sound pressure signal of each sensor with the particle velocity signal of the acoustic vector sensor, and establish the far-field signal model of the acoustic vector and scalar fusion sensor array and the covariance matrix of the far-field signal model;

[0007] Step 2: Perform continuous wavelet transform on any real signal s(t) in the far-field signal model to obtain the array receiving signal model WT=GY+N and the covariance matrix R=E{WT·WT H =GR Y G H +σ 2 I;

[0008] Step 3: Based on the array receiving signal model WT = GY + N, and the covariance matrix of the array receiving signal model R = E{WT · WT H =GR Y G H +σ 2I, uses beamforming methods to perform sound source identification and spatial positioning acoustic imaging.

[0009] Furthermore, in step 1, the far-field signal model is:

[0010] Assume that the acoustic vector and scalar fusion sensor array has a total of M sensor array elements, including r acoustic vector sensor array elements and Mr acoustic scalar sensor array elements, and the sound source is The incident light is incident on the fusion sensor array, θ is the azimuth angle with the x-axis, is the pitch angle with respect to the z-axis, then the far-field signal model of the M-element acoustic vector and scalar fusion sensor array can be expressed as:

[0011]

[0012] In the formula, have

[0013]

[0014] Where X is the received signal vector of the (M+3r)×L dimensional matrix of the M-element acoustic vector and scalar fusion sensor array, N is the (M+3r)×L dimensional noise data vector of the acoustic vector and scalar fusion sensor array that is unrelated to the incident signal, A is the (M+3r)×1 dimensional array flow pattern of the acoustic vector and scalar fusion sensor array, and L is the number of snapshots.

[0015] Furthermore, in step 1, the covariance matrix of the far-field signal model is:

[0016] R=XX H =ASS H A H +σ 2 I

[0017] (3) In the formula, the superscript H represents the matrix transpose, I is the identity matrix, and σ is the background noise variance.

[0018] Furthermore, in step 2, a continuous wavelet transform is performed on any real signal s(t) in the far-field signal model to obtain an array receiving signal model, which is specifically:

[0019] The continuous wavelet transform formula for any real signal s(t) is:

[0020]

[0021] In formula (4), WT is the wavelet transform coefficient, a is the wavelet transform scale factor, b is the wavelet transform translation factor, ω 0 is the central angular frequency of the wavelet transform, Represents the Morlet wavelet-based The basis function of the Morlet wavelet transform is represents the Morlet mother wavelet,

[0022]

[0023] Assuming there are K sound sources, the received signal of the mth array element is:

[0024]

[0025] In the formula, τ mk represents the delay of the kth signal reaching the mth array element, e mk Represents the vector coefficient of the kth signal reaching the mth array element, n m (t) is the uncorrelated noise of the mth array element;

[0026] For signal x m (t) is transformed by wavelet to obtain:

[0027]

[0028] Where i is the scale factor i=1,2,…,I, take I scale factors;

[0029] According to Parseval's theorem, we can transform the above formula (7) to get

[0030]

[0031] In the formula, y ai,k (b-τ mk )replace for For b-τ mk The inverse Fourier transform of ai,m (b) Replacement for Inverse Fourier transform of b.

[0032] Wavelet basis functions The center of the frequency window is f i =ω 0 / (2πa i ),i=1,2,…,I,let Δω i / ω i <0.1, then the wavelet coefficient WT m (a i ,b) can be regarded as a narrowband signal, then equation (7) can be written as

[0033]

[0034] At this point, the far-field signal reception model can be expressed as:

[0035]

[0036] In the formula, It is the wavelet coefficient of K×1 dimensional wavelet transform; is the noise wavelet coefficient vector, which represents the frequency domain quantity of the noise signal after wavelet transformation; G(x,y,a i )=[g(x 1 ,y 1 ,a i ),…,g(x K ,y K ,a i )] is an array direction matrix of (M+3r)×K, where:

[0037]

[0038] In the formula, e mk is the vector coefficient of the mth array element, e for scalar array element mk is 1, g(x,y,a i ) is a steering vector of M×1 dimension.

[0039] After simplifying the above model, the array receiving signal model is:

[0040] WT=GY+N (12).

[0041] Furthermore, the covariance matrix of the array receiving signal model is expressed as:

[0042] R=E[WT·WT H ]=GR Y G H +σ 2 I (13).

[0043] Further, step three includes: for the CBF method, using the covariance matrix R=E[WT·WT H ]=GR Y G H +σ 2 I is introduced into the spatial spectrum calculation formula P of the CBF method CBF =W H RW.

[0044] Further, step three includes: for the CLEAN method, using the updated CBF method's spatial spectrum calculation formula P CBF =W H RW, iteratively update the spatial spectrum multiple times to obtain the CLEAN spatial spectrum:

[0045] Further, step three includes: for the CLEAN-SC method, a cross-correlation spectrum is introduced on the basis of the CLEAN method to suppress the mutual interference between sound sources, and the covariance matrix of the received signal vector at the peak position is updated by using the cross-correlation spectrum

[0046] Beneficial effects:

[0047] The method of the present invention uses an acoustic vector and scalar fusion sensor array to measure aircraft acoustic signals, and extends the beamforming method to the processing of acoustic vector and scalar fusion sensor array signals, which can reduce the wave number main lobe width of medium and low frequency signals, improve the resolution of medium and low frequency signals, and realize small-scale array design. Moreover, wavelet transform is suitable for extracting the characteristic sensitive part of transient noise, improving the signal-to-noise ratio of the received signal while retaining the time delay relationship between array elements. Therefore, the acoustic vector and scalar fusion sensor array can realize non-steady-state sound source identification and spatial positioning imaging under small-scale array aperture, and is still suitable for the identification and spatial positioning imaging of sound sources with steady-state characteristics, providing new technical means for aircraft sound source testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0049] Figure 1 A schematic diagram of a technical process provided by an embodiment of the present disclosure;

[0050] Figure 2 A comparison diagram of implementation effects provided for an embodiment of the present disclosure shows a comparison between the spatial spectrum of the CLEAN method based on wavelet decomposition of the present disclosure and the spatial spectrum of the traditional CLEAN method based on Fourier analysis. DETAILED DESCRIPTION

[0051] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0052] The noise radiated by an aircraft during flight includes engine noise, body noise, landing gear noise and other types, and their generation mechanisms and radiation characteristics are different. Traditional array signal processing-based methods use scalar microphone arrays for noise source identification and spatial positioning imaging. It generally assumes that the sound source is a steady-state sound source, so it captures data within a period of time, such as 0.5s, and converts it to the frequency domain and divides it into multiple narrow bands for processing. For some non-steady-state noises such as sporadic noise, it usually appears as a transient signal with a short duration and time-varying characteristics. If traditional frequency domain processing is used, only capturing signals within sporadic time periods will result in insufficient frequency resolution. If the capture time is too long, it is easy to introduce noise influences from other time periods, that is, the problem of balancing the time window and frequency window in time-frequency analysis occurs.

[0053] In this regard, the present disclosure proposes an acoustic imaging method for an acoustic vector and scalar fusion sensor array based on wavelet decomposition. In view of the problem of non-steady-state noise in aircraft, wavelet analysis with complete orthogonal basis functions with transient characteristics is used for decomposition, and the signal-to-noise ratio of transient signals is improved on the basis of better extraction of transient characteristics, which is beneficial to subsequent array signal processing. At the same time, an acoustic vector and scalar fusion sensor array is used to measure aircraft far-field noise signals, and a sensor array signal model of acoustic vector and scalar fusion in the Morlet wavelet domain is constructed, and then beamforming methods such as CBF and CLEAN are used for spatial spectrum estimation to improve the resolution of medium and low frequency signals, realize the identification and spatial positioning imaging of medium and low frequency transient sound sources in aircraft, and at the same time, it is still suitable for sound source identification and spatial positioning imaging with steady-state characteristics.

[0054] For example, Figure 1 This is the implementation process of this method. First, a signal model of the sensor array that fuses the acoustic vector and scalar is constructed, and it is converted into the Morlet wavelet domain using wavelet transform. According to the wavelet coefficients of the narrowband signal corresponding to the wavelet frequency window, the wavelet domain covariance matrix is ​​calculated, and then the spatial spectrum is estimated using beamforming methods such as CBF and CLEAN. By superimposing the spatial spectrum results of the main energy frequency bands, the identification and spatial positioning of non-steady-state sound sources or steady-state sound sources can be achieved.

[0055] The present invention provides a sensor array acoustic imaging method based on wavelet decomposition and acoustic vector and scalar fusion, comprising:

[0056] Step 1: Linearly combine the acoustic pressure signal of each sensor with the particle velocity signal of the acoustic vector sensor to establish the far-field signal model of the acoustic vector and scalar fusion sensor array;

[0057] Step 2: Perform continuous wavelet transform on any real signal s(t) in the far-field signal model to obtain the array receiving signal model WT=GY+N and the covariance matrix R=E{WT·WT H =GRY G H +σ 2 I;

[0058] Step 3: Based on the array receiving signal model WT = GY + N, and the covariance matrix of the array receiving signal model R = E{WT · WT H =GR Y G H +σ 2 I, uses beamforming methods to perform sound source identification and spatial positioning acoustic imaging.

[0059] Step 1, specifically:

[0060] Assume that the acoustic vector and scalar fusion sensor array has a total of M sensor array elements, including r acoustic vector sensor array elements and Mr acoustic scalar sensor array elements, and the sound source is The incident light is incident on the fusion sensor array, θ is the azimuth angle with the x-axis, is the pitch angle with respect to the z-axis, then the far-field signal model of the M-element acoustic vector and scalar fusion sensor array can be expressed as:

[0061]

[0062] In the formula, have

[0063]

[0064] Where X is the received signal vector of the (M+3r)×L dimensional matrix of the M-element acoustic vector and scalar fusion sensor array, N is the (M+3r)×L dimensional noise data vector of the acoustic vector and scalar fusion sensor array that is unrelated to the incident signal, A is the (M+3r)×1 dimensional array flow pattern of the acoustic vector and scalar fusion sensor array, and L is the number of snapshots;

[0065] According to the far-field signal model, A is a linear combination of the sound pressure channels of each sensor of the acoustic vector and scalar fusion sensor array and the measurement signals of the particle velocity channel of the acoustic vector sensor. The particle velocity channel fully meets the traditional acoustic scalar array signal processing requirements. From a mathematical point of view, the information processing received by the acoustic vector sensor array is incorporated into the acoustic scalar sensor array signal processing framework. Compared with the acoustic scalar sensor array signal analysis, there are only three more dimensions of equation constraints. The sampling covariance matrix in the acoustic scalar sensor array signal processing framework is:

[0066] R=XX H =ASS H A H +σ 2 I (3)

[0067] Where the superscript H represents the matrix transpose, I is the unit matrix, and σ is the background noise variance.

[0068] Step 2:

[0069] The continuous wavelet transform formula for any real signal s(t) is

[0070]

[0071] In formula (4), WT is the wavelet transform coefficient, a is the wavelet transform scale factor, b is the wavelet transform translation factor, ω 0 is the central angular frequency of the wavelet transform, Represents the Morlet wavelet-based The basis function of the Morlet wavelet transform is represents the Morlet mother wavelet,

[0072]

[0073] Assuming there are K sound sources, the received signal of the mth array element is

[0074]

[0075] In the formula, τ mk represents the delay of the kth signal reaching the mth array element, e mk Represents the vector coefficient of the kth signal reaching the mth array element, n m (t) is the uncorrelated noise of the mth array element.

[0076] Signal x m (t) is transformed by wavelet to obtain:

[0077]

[0078] Where i is the scale factor i = 1, 2,…, I, and I scale factors are taken.

[0079] According to Parseval's theorem, we can transform the above formula (7) to get

[0080]

[0081] In the formula, y ai,k (b-τ mk )replace for For b-τ mk The inverse Fourier transform of replace for Inverse Fourier transform of b.

[0082] Wavelet basis functions The center of the frequency window is f i =ω 0 / (2πa i ),i=1,2,…,I,let Δω i / ω i <0.1, then the wavelet coefficient WT m (a i ,b) can be regarded as a narrowband signal, then equation (7) can be written as

[0083]

[0084] At this point, the far-field signal reception model can be expressed as:

[0085]

[0086] In the formula, It is the wavelet coefficient of K×1 dimensional wavelet transform; is the noise wavelet coefficient vector, which represents the frequency domain quantity of the noise signal after wavelet transformation; G(x,y,a i )=[g(x 1 ,y 1 ,a i ),…,g(x K ,y K ,a i )] is an array direction matrix of (M+3r)×K, where:

[0087]

[0088] In the formula, e mk is the vector coefficient of the mth array element, e for scalar array element mk is 1, g(x,y,a i ) is a steering vector of M×1 dimension.

[0089] After simplifying the above model, the array receiving signal model is:

[0090] WT=GY+N (12)

[0091] The sampling covariance matrix can be expressed as

[0092] R=E[WT·WT H ]=GR Y G H +σ 2 I (13)

[0093] Step 3: Use conventional beamforming methods, such as the CBF method and the CLEAN method, to perform sound source identification and spatial positioning imaging. Specifically:

[0094] Conventional beamforming methods are essentially to perform certain phase compensation on the signals received by each array element and then superimpose them, scanning the superposition results of different spatial grid points as spatial spectrum estimation imaging images. For the CBF method, there are:

[0095] P CBF =W H RW (14)

[0096] Where W is the weight vector, P CBF is the spatial spectrum amplitude.

[0097] The angular resolution of the CBF method is relatively low. Therefore, based on the results of the CBF method, the CLEAN method uses the CBF method for multiple iterations to weaken the influence of the side lobes of the strongest target source on the imaging results. In this way, the spatial spectrum of the weaker sound source that is not affected by the strong target source can be obtained.

[0098] The key to the CLEAN method involves the point spread function. Assuming that there is a point sound source of unit intensity at a certain grid point, the CBF method spatial spectrum function of the sensor array used for the point sound source is the point spread function. For a given sensor array formation, the point spread function of each grid point is different. The CLEAN method uses the point spread function to remove the sidelobe effect in the CBF method results to improve the angular resolution of the CBF method.

[0099] If g is defined as the steering vector corresponding to a sound source, we have

[0100] P PSF =|W H g| 2 (15)

[0101] Where W is the weight vector, P PSF It is the point spread function, which is related to the formation and the position of the sound source. Its waveform is similar to the spatial spectrum of the CBF method. This feature causes the beamforming method based on the CBF method to be affected by the Rayleigh limit and sidelobes.

[0102] The calculation steps of the CLEAN method are as follows:

[0103] (1) Using the CBF method to obtain the conventional beamforming spatial spectrum, we have

[0104]

[0105] Wherein, j represents the jth search point, superscript i represents the ith iteration, and i=0 at this time.

[0106] (2) Calculate the spectrum peak and position of the current conventional beamforming spatial spectrum;

[0107] (3) Calculate the point spread function at the spectral peak position;

[0108] (4) Subtract the point spread function obtained in step (3) from the currently known spatial spectrum, and we have

[0109]

[0110] In the formula, is the covariance matrix of the received signal vector at the spectral peak position, and are the spatial spectrum peak after the i-th iteration and the steering vector of the peak position. (i) To replace the existing P (i-1) The maximum peak of the spectrum is

[0111]

[0112] In the formula, λ is a constant that controls the sharpness of the spectrum peak, ε j is the coordinate value of the jth search point, ε max for The corresponding coordinate values.

[0113] (5) Repeat steps (2) to (4) until the termination condition "the covariance matrix at this time is greater than the 1 norm of the previous covariance matrix" is met, that is,

[0114] |R (V+1) |≥|R (V) | (19)

[0115] Where V is the number of final iterations.

[0116] Finally, the CLEAN spatial spectrum is estimated as:

[0117]

[0118] The computational performance of the CLEAN method is heavily dependent on the accuracy of the point spread function. The CLEAN method can improve the performance of the CBF method when the incident source is correlated and coherent, but for non-correlated sources that are far apart and dual sources that are close together, its performance is not much improved compared to the CBF method. Therefore, the CLEAN-SC method of the deallocation source is used, so that the obtained point spread function still has good acoustic imaging performance when there is a large error.

[0119] The CLEAN method assumes that the point sound sources at each grid point are uncorrelated. In practice, this condition is usually not met, so CLEAN-SC introduces the concept of cross-correlation spectrum, that is,

[0120]

[0121] The above cross-spectral effect caused by signal correlation is not considered in step (4) of the CLEAN method. CLEAN-SC requires that when W k =W max When, for any W j Needs to be satisfied

[0122]

[0123] That is, there is

[0124]

[0125] In the formula

[0126]

[0127] Set its diagonal elements to zero to suppress the influence of background noise, and we get

[0128]

[0129] in

[0130]

[0131] In the formula, H (i) h (i) (h (i) ) H The CLEAN-SC method uses formula (23) to replace G in formula (17) (i) , suppressing mutual interference between sound sources, thus achieving better acoustic imaging performance.

[0132] For example, Figure 2 A comparison diagram of implementation effects provided for an embodiment of the present disclosure shows a comparison of the spatial spectrum of the CLEAN method based on wavelet decomposition of the present disclosure and the spatial spectrum of the traditional CLEAN method based on Fourier analysis. It can be seen that the beam obtained by the method of the present disclosure based on wavelet decomposition is narrower.

Claims

1. A sensor array acoustic imaging method based on wavelet decomposition and acoustic vector and scalar fusion, characterized in that: include: Step 1: Use the acoustic vector and scalar fusion sensor array to measure the aircraft far-field noise signal, linearly combine the sound pressure signal of each sensor with the particle velocity signal of the acoustic vector sensor, and establish the far-field signal model of the acoustic vector and scalar fusion sensor array and the covariance matrix of the far-field signal model; Step 2: Perform continuous wavelet transform on any real signal s(t) in the far-field signal model to obtain the array receiving signal model WT=GY+N and the covariance matrix R=E{WT·WT H =GR Y G H +σ 2 I; Step 3: Based on the array receiving signal model WT = GY + N, and the covariance matrix of the array receiving signal model R = E{WT · WT H =GR Y G H +σ 2 I, uses beamforming methods to perform sound source identification and spatial positioning acoustic imaging.

2. The method according to claim 1, characterized in that In step 1, the far-field signal model is: Assume that the acoustic vector and scalar fusion sensor array has a total of M sensor array elements, including r acoustic vector sensor array elements and Mr acoustic scalar sensor array elements, and the sound source is The incident light is incident on the fusion sensor array, θ is the azimuth angle with the x-axis, is the pitch angle with respect to the z-axis, then the far-field signal model of the M-element acoustic vector and scalar fusion sensor array can be expressed as: In the formula, have Where X is the received signal vector of the (M+3r)×L dimensional matrix of the M-element acoustic vector and scalar fusion sensor array, N is the (M+3r)×L dimensional noise data vector of the acoustic vector and scalar fusion sensor array that is unrelated to the incident signal, A is the (M+3r)×1 dimensional array flow pattern of the acoustic vector and scalar fusion sensor array, and L is the number of snapshots.

3. The method according to claim 2, characterized in that In step 1, the covariance matrix of the far-field signal model is: R=XX H =ASS H A H +σ 2 I (3) Where the superscript H represents the matrix transpose, I is the unit matrix, and σ is the background noise variance.

4. The method according to claim 1, characterized in that: In step 2, any real signal s(t) in the far-field signal model is subjected to continuous wavelet transform to obtain the array receiving signal model, which is specifically: The continuous wavelet transform formula for any real signal s(t) is: In formula (4), WT is the wavelet transform coefficient, a is the wavelet transform scale factor, b is the wavelet transform translation factor, ω0 is the central angular frequency of the wavelet transform, Represents the Morlet wavelet-based The basis function of the Morlet wavelet transform is represents the Morlet mother wavelet, Assuming there are K sound sources, the received signal of the mth array element is: In the formula, τ mk represents the delay of the kth signal reaching the mth array element, e mk Represents the vector coefficient of the kth signal reaching the mth array element, n m (t) is the uncorrelated noise of the mth array element; For signal x m (t) is transformed by wavelet to obtain: Where i is the scale factor i=1,2,…,I, take I scale factors; According to Parseval's theorem, we can transform the above formula (7) to obtain: In the formula, use replace for For b-τ mk The inverse Fourier transform of replace for Inverse Fourier transform of b; Wavelet basis functions The center of the frequency window is f i =ω0 / (2πa i ),i=1,2,…,I,let Δω i / ω i <0.1, then the wavelet coefficient WT m (a i ,b) can be regarded as a narrowband signal, then equation (7) can be written as At this point, the far-field signal reception model can be expressed as: In the formula, It is the wavelet coefficient of K×1 dimensional wavelet transform; is the noise wavelet coefficient vector, which represents the frequency domain quantity of the noise signal after wavelet transformation; G(x,y,a i )=[g(x1,y1,a i ),...,g(x K ,y K ,a i )] is an array direction matrix of (M+3r)×K, where: In the formula, e mk is the vector coefficient of the mth array element, e for scalar array element mk is 1, g(x,y,a i ) is a steering vector of M×1 dimension; After simplifying the above model, the array receiving signal model is: WT=GY+N (12).

5. The method according to claim 1, characterized in that In step 2, the covariance matrix of the array receiving signal model is expressed as: R=E[WT·WT H ]=GR Y G H +σ 2 I (13)。 6. The method according to claim 1, characterized in that In step 3, for the CBF method, the covariance matrix of the array receiving signal model is used, R = E[WT · WT H ]=GR Y G H +σ 2 I is introduced into the spatial spectrum calculation formula P of the CBF method CBF =W H RW.

7. The method according to claim 6, characterized in that Step 3 includes: for the CLEAN method, using the updated CBF method's spatial spectrum calculation formula P CBF =W H RW, iteratively update the spatial spectrum multiple times to obtain the CLEAN spatial spectrum:

8. The method according to claim 7, characterized in that Step 3 includes: for the CLEAN-SC method, introducing the cross-correlation spectrum on the basis of the CLEAN method to suppress the mutual interference between sound sources, and using the cross-correlation spectrum to update the covariance matrix of the received signal vector at the peak position of the spectrum

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