Ultra-high resolution compressed sphere beamforming sound source identification method

Abstract

This invention discloses an ultra-high resolution compressed spherical beamforming sound source identification method, comprising the following steps: 1) constructing a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion; 2) providing prior assumptions for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain, and calculating the joint probability density function of the unknown variables; 3) solving for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain according to the joint probability density function of the unknown variables, and estimating the sound source DOA and sound source intensity. This invention overcomes the basis mismatch problem, accurately estimates the off-grid sound source DOA and quantizes the sound source intensity, and achieves ultra-high resolution.

Description

Technical Field

[0001] This invention relates to the field of sound field recognition technology, specifically to a method for identifying sound sources using ultra-high resolution compressed sphere beamforming. Background Technology

[0002] Acoustic holography and beamforming are two noise source identification methods based on acoustic arrays, offering advantages such as fast measurement speed, high acoustic imaging efficiency, and the ability to measure moving sound sources. They can also visualize the sound field, facilitating more intuitive sound source identification and localization.

[0003] Among them, compressed spherical beamforming based on spherical microphone array measurement is an effective way to achieve panoramic sound source identification.

[0004] Traditional compressed beamforming methods mostly rely on discretization of the focusing region and the on-grid assumption to achieve sound source identification. However, this method suffers from a basis mismatch problem, meaning that the sound source identification results deteriorate when the sound source does not fall on the manually divided grid points. This basis mismatch problem limits the widespread application of this technology.

[0005] Therefore, there is an urgent need for a compressed sphere beamforming sound source identification method that can overcome the basis mismatch problem. Summary of the Invention

[0006] The purpose of this invention is to provide an ultra-high resolution compressed sphere beamforming sound source identification method, comprising the following steps:

[0007] 1) Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion;

[0008] 2) Provide prior assumptions for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain, and calculate the joint probability density function of the unknown variables;

[0009] 3) Based on the joint probability density function of the unknown variables, the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain are solved to estimate the source DOA and source intensity.

[0010] The two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain is shown below:

[0011] P=H(Δθ,Δφ)X+N (1)

[0012] In the formula, This is the sound pressure matrix; The source intensity matrix; This is the noise matrix; represents the complex set; Q, L, and G represent the number of microphones, the number of snapshots, and the number of grid points, respectively, with each grid point corresponding to a potential sound source;

[0013] The transfer function matrix H(Δθ,Δφ) is shown below:

[0014] H(Δθ,Δφ)=(A(Γ F )+B θ (Γ F Diag(Δθ)+B φ (Γ F Diag(Δφ)) (2)

[0015] In the formula, Γ F It is the set of directions of each grid point, Γ F ={(θ Fg ,φ Fg |g=1,2,…,G};θ Fg φ Fg represents the elevation and azimuth directions of the g-th grid point; Δθ and Δφ are the DOA offset vectors in the elevation and azimuth directions, respectively; Diag(·) indicates generating a diagonal matrix with the vectors in parentheses as its diagonal.

[0016] Matrix A(Γ) F ), matrix B θ (Γ F ), matrix B φ (Γ F As shown below:

[0017]

[0018]

[0019]

[0020] In the formula, the matrix N is the highest order of the spherical harmonic function; vector matrix vector The superscript H indicates Hermitian transpose; Let m be a spherical harmonic function of order n; n = 0, 1, ..., N, m = -N, ..., 0, ..., N. b is the modal intensity matrix; n (kr F (,ka) represents the intensity of the nth mode; k is the wavenumber; r F Γ is the focusing radius; a is the radius of the sphere array. M It is the set of directions of each microphone, Γ M ={(θ Mq ,φ Mq )|q=1,2,…,Q};θ Fg φFg θ represents the elevation and azimuth directions of the g-th grid point; Mq φ Mq These are the elevation and azimuth directions of the q-th microphone;

[0021] The unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain include the sound source intensity matrix X, the noise matrix N, the DOA offset vector Δθ in the elevation direction, and the DOA offset vector Δφ in the azimuth direction.

[0022] The steps for calculating the joint probability density function of the unknown variables include:

[0023] a) Set the sound source intensity matrix X to follow a two-level prior, and the snapshot data in the sound source intensity matrix X are independent of each other;

[0024] The noise matrix N is set to follow a cyclic symmetric complex Gaussian distribution, and the microphone and snapshot data in the noise matrix N are independent data.

[0025] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction are set to follow a uniform distribution.

[0026] b) Based on the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain and the prior distribution of the noise matrix N, the data likelihood p(P|X) is obtained, i.e.:

[0027]

[0028] In the formula, P .,l The l-th column of the sound pressure matrix P; H = H(Δθ, Δφ); vector X .,l The l-th column of the sound source intensity matrix X; parameter α = σ -2 ;σ 2 Let I be the noise variance; I is the Q×Q dimensional identity matrix.

[0029] c) Calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ), i.e.:

[0030] p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ) (7)

[0031] In the formula, p(X|ξ), p(ξ), p(α), p(Δθ), and p(Δφ) represent probability distributions. ξ is a hyperparameter vector used to control the vector X. .,l The variance of each element;

[0032] In the first-level prior, the sound source intensity matrix X follows a circularly symmetric complex Gaussian distribution, that is:

[0033]

[0034] In the formula, vector X ·,l ξ is the l-th column of the sound source intensity matrix X; ξ is the hyperparameter vector used to control the vector X. ·，l The variance of each element; parameter Λ = Diag(ξ); for any variable parameter u, μ, and Σ respectively refer to X ·,l 、0、Λ;

[0035] In the second-level prior, the hyperparameter vector ξ follows a Gamma distribution, that is:

[0036]

[0037] In the formula, ξ g Let Γ be the g-th element of the hyperparameter vector ξ; for any variable u, Γ(u|a,b)=(Γ(a)) -1 b a u a -1 exp(-bu); Γ(·) is the Gamma function; These are fixed prior values. p(ξ|ρ) is the probability distribution; u, a, and b refer to ξ. g , 1, ρ.

[0038] The noise matrix N satisfies the following equation:

[0039]

[0040] In the formula, N ·,l The l-th column of the noise matrix N; parameter α = σ -2 ;σ 2 Let be the noise variance; I be the Q×Q dimensional identity matrix; p(N|α) be the probability distribution;

[0041] Wherein, the parameter α follows a Gamma distribution, that is:

[0042] p(α|c,d)=Gamma(α|c,d), (11)

[0043] In the formula, All are fixed prior values. p(α|c,d) is the probability distribution;

[0044] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction satisfy the following equation:

[0045] Δθ g ~U(-d θ / 2,d θ / 2) (12)

[0046] Δφ g ~U(-d φ / 2,d φ / 2) (13)

[0047] In the formula, d θ With d φ These represent the grid spacing along the latitude (θ) and longitude (φ) directions, respectively. U(-d θ / 2,d θ / 2), U(-d φ / 2,d φ / 2) represents a set.

[0048] The steps for solving the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain to obtain the direction of sound arrival and the sound source intensity include:

[0049] I) Constructing the Expectation-Maximization Algorithm Model Right now:

[0050]

[0051] In the formula, This indicates taking the expectation of the posterior distribution of X;

[0052] II) Use the expectation-maximization algorithm model to solve for the DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction, that is:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, Indicates taking the real part; "*" is the conjugate symbol; " is the Hadamard product operator; v θ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; Wθ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix B θ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ g This represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots. Matrix A refers to matrix A(Γ). F ); As a parameter;

[0060] parameter μ ·,l The parameter Σ is shown below:

[0061] μ ·,l =αΣH H P ·,l (twenty one)

[0062] Σ=(αH H H+Λ -1 ) -1 (twenty two)

[0063] In the formula, Indicates taking the real part; "*" is the conjugate symbol; " is the Hadamard product operator; v θ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix B θ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ gThis represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots. Matrix A refers to matrix A(Γ). F );

[0064] III) Calculate the estimated values ​​of the sound source DOA and the sound source intensity.

[0065] The sound source DOA As shown below:

[0066]

[0067] In the formula, P max Δθ represents the maximum energy in all grid point directions; ε represents the preset energy threshold; Δθ Fg , Δφ Fg This represents the DOA offset of the g-th grid point in the direction of elevation and azimuth.

[0068] Wherein, the energy P of the g-th grid point g As shown below:

[0069]

[0070] In the formula, u g,· Σ is the g-th row vector of matrix u. gg X is the vector in the g-th row and g-th column of matrix Σ. L is the total number of snapshots. g,· It is the g-th column of the sound source intensity matrix X.

[0071] Sound source intensity estimate As shown below:

[0072]

[0073] In the formula, (·) + Represents the Moore-Penrose pseudoinverse; matrix

[0074] The technical advantages of this invention are undeniable. The method provided by this invention represents the DOA (Direction of Arrival) of a sound source at any location in space as the sum of the grid point DOA and the off-grid offset. Then, a two-dimensional off-grid compressed spherical beamforming off-grid model is constructed using Taylor series expansion in the spherical harmonic domain. Finally, the off-grid offset of the DOA is solved using sparse Bayesian inference theory and the expectation-maximization algorithm, thereby realizing the estimation of the sound source DOA and the quantized sound source intensity, effectively alleviating the basis mismatch problem. Furthermore, since the off-grid offset estimation of the DOA is provided for all potential sound sources located at (or near) all grid points, the method provided by this invention has ultra-high resolution. Attached Figure Description

[0075] Figure 1 This is the microphone array measurement layout of the present invention;

[0076] Figure 2 This is an image of the sound source in this embodiment; Figure 2 (a) is an image of the sound source at 2000 Hz; Figure 2 (b) is an image of the sound source at 4000Hz; Figure 2 (c) is an image of the sound source at 6000Hz. Detailed Implementation

[0077] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0078] Example 1:

[0079] See Figures 1 to 2 A method for identifying sound sources using ultra-high resolution compressed sphere beamforming includes the following steps:

[0080] 1) Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion;

[0081] The two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain is shown below:

[0082] P=H(Δθ,Δφ)X+N (1)

[0083] In the formula, This is the sound pressure matrix; The source intensity matrix; This is the noise matrix; represents the complex set; Q, L, and G represent the number of microphones, the number of snapshots, and the number of grid points, respectively, with each grid point corresponding to a potential sound source;

[0084] The transfer function matrix H(Δθ,Δφ) is shown below:

[0085] H(Δθ,Δφ)=(A(Γ F )+B θ (Γ F Diag(Δθ)+B φ (Γ F Diag(Δφ)) (2)

[0086] In the formula, Γ F It is the set of directions of each grid point, Γ F ={(θ Fg ,φFg |g=1,2,…,G};Γ M It is the set of directions of each microphone, Γ M ={(θ Mq ,φ Mq )|q=1,2,…,Q};θ Fg φ Fg θ represents the elevation and azimuth directions of the g-th grid point; Mq φ Mq represents the elevation and azimuth directions of the q-th microphone; Δθ and Δφ are the DOA offset vectors in the elevation and azimuth directions, respectively; Diag(·) indicates generating a diagonal matrix with the vectors in parentheses as its diagonal;

[0087] Matrix A(Γ) F ), matrix B θ (Γ F ), matrix B φ (Γ F As shown below:

[0088]

[0089]

[0090]

[0091] In the formula, the matrix N is the highest order of the spherical harmonic function; vector matrix vector The superscript H indicates Hermitian transpose; Let m be a spherical harmonic function of order n; n = 0, 1, ..., N, m = -N, ..., 0, ..., N. b is the modal intensity matrix; n (kr F (,ka) represents the intensity of the nth mode; k is the wavenumber; r F is the focusing radius; a is the radius of the sphere array.

[0092] 2) Provide prior assumptions for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain, and calculate the joint probability density function of the unknown variables;

[0093] The unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain include the sound source intensity matrix X, the noise matrix N, the DOA offset vector Δθ in the elevation direction, and the DOA offset vector Δφ in the azimuth direction.

[0094] The steps for calculating the joint probability density function of the unknown variables include:

[0095] 2.1) Set the sound source intensity matrix X to follow a two-level prior, and the snapshot data in the sound source intensity matrix X are independent of each other;

[0096] The noise matrix N is set to follow a cyclic symmetric complex Gaussian distribution, and the microphone and snapshot data in the noise matrix N are independent data.

[0097] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction are set to follow a uniform distribution.

[0098] 2.2) Based on the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain and the prior distribution of the noise matrix N, the data likelihood is obtained, i.e.:

[0099]

[0100] In the formula, P ·,l Let H be the l-th column of the sound pressure matrix P; H = H(Δθ, Δφ);

[0101] 2.3) Calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ), i.e.:

[0102] p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ) (7)

[0103] In the formula, p(X|ξ), p(ξ), p(α), p(Δθ), and p(Δφ) represent probability distributions.

[0104] In the first-level prior, the sound source intensity matrix X follows a circularly symmetric complex Gaussian distribution, that is:

[0105]

[0106] In the formula, vector X ·,l ξ is the l-th column of the sound source intensity matrix X; ξ is the hyperparameter vector used to control the vector X. ·l The variance of each element; parameter Λ = Diag(ξ); for any variable parameter

[0107] In the second-level prior, the hyperparameter vector ξ follows a Gamma distribution, that is:

[0108]

[0109] In the formula, ξ g Let Γ be the g-th element of the hyperparameter vector ξ; for any variable u, Γ(u|a,b)=(Γ(a)) -1 ba u a -1 exp(-bu); Γ(·) is the Gamma function; It is a fixed prior value.

[0110] The noise matrix N satisfies the following equation:

[0111]

[0112] In the formula, N ·,l The l-th column of the noise matrix N; parameter α = σ -2 ;σ 2 Let I be the noise variance; I is the Q×Q dimensional identity matrix.

[0113] Wherein, the parameter α follows a Gamma distribution, that is:

[0114] p(α|c,d)=Gamma(α|c,d), (11)

[0115] In the formula, All of them are fixed prior values.

[0116] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction satisfy the following equation:

[0117] Δθ g ~U(-d θ / 2,d θ / 2) (12)

[0118] Δφ g ~U(-d φ / 2,d φ / 2) (13)

[0119] In the formula, d θ With d φ These represent the grid spacing in the latitude (θ) and longitude (φ) directions, respectively.

[0120] 3) Based on the joint probability density function of the unknown variables, the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain are solved to estimate the source DOA and source intensity.

[0121] The steps for solving the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain to obtain the direction of sound arrival and the sound source intensity include:

[0122] 3.1) Construct the expectation-maximization algorithm model, namely:

[0123]

[0124] In the formula, It indicates the expectation of the posterior distribution of X; the superscript ∧ indicates the estimator;

[0125] 3.2) Use the expectation-maximization algorithm model to solve for the DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction, that is:

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] μ ·,l =αΣH H P ·,l (twenty one)

[0133] Σ=(αH H H+Λ -1 ) -1 (twenty two)

[0134] In the formula, Indicates taking the real part; "*" is the conjugate symbol; " is the Hadamard product operator; v θ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates that the g-th element of the vector within the parentheses will be removed.

[0135] 3.3) Calculate the estimated values ​​of the sound source DOA and the sound source intensity.

[0136] The sound source DOA is shown below:

[0137]

[0138] In the formula, P maxRepresents the maximum energy in all grid point directions; ε represents the preset energy threshold.

[0139] The energy of the g-th grid point is shown below:

[0140]

[0141] In the formula, u g,· Σ is the g-th row vector of u. gg Let Σ be the vector in the g-th row and g-th column. L is the total number of snapshots.

[0142] Sound source intensity estimate As shown below:

[0143]

[0144] In the formula, (·) + Represents the Moore-Penrose pseudoinverse; matrix Example 2:

[0145] A method for identifying sound sources using ultra-high resolution compressed sphere beamforming includes the following steps:

[0146] Step 1: Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion.

[0147] P=H(Δθ,Δφ)X+N

[0148] in, For sound pressure matrix, The source intensity matrix, Here, Q, L, and G represent the number of microphones, the number of snapshots, and the number of potential sound sources (grid points), respectively.

[0149] H(Δθ,Δφ)=(A(Γ F )+B θ (Γ F Diag(Δθ)+B φ (Γ F )Diag(Δφ))

[0150]

[0151]

[0152]

[0153] Γ F It is the set of directions of each grid point, Γ F ={(θ Fg ,φ Fg )|g=1,2,…,G},ΓM It is the set of directions of each microphone, Γ M ={(θ Mq ,φ Mq )|q=1,2,…,Q}, Δθ and Δφ are the DOA offset vectors in the elevation and azimuth directions, respectively, and Diag(·) represents generating a diagonal matrix with the vectors inside the brackets as the diagonal. N is the highest order of the spherical harmonic function. It is an nth-order m-th spherical harmonic function. "H" represents the Hermitian transpose.

[0154] Let b be the modal intensity matrix. n (kr F ,ka) represents the intensity of the nth mode, and k is the wave number. Let g be a constant matrix, and as κ changes from -n to n, g n,m The ((N+κ)(2N+1)+N-m+1)th element is A n,m β n,m,κ The remaining elements are 0. β n,m,κ It is all those with the same κ value The sum of, Its corresponding κ is κ = 2u + vmw. o, u, v, and w are all positive integers, o increases from m to n, u increases from 0 to m, v increases from 0 to om, and w increases from 0 to omv. It is an exponential function. For imaginary units, " is the Kronecker product.

[0155] Step 2: Provide prior hypotheses for all unknown variables (X, N, Δθ, and Δφ) and calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ).

[0156] We assume that X follows a two-level prior and that each snapshot is independent. In the first level, X follows a circularly symmetric complex Gaussian distribution, i.e.

[0157]

[0158] Among them, X ·,l Let ξ be the l-th column of X, and let ξ be the hyperparameter vector that controls X. ·,l The variance of each element, Λ = Diag(ξ), for any variable In the second level, let ξ follow a Gamma distribution.

[0159]

[0160] ξ g Let Γ be the g-th element of ξ. For any variable u, Γ(u|a,b)=(Γ(a)). -1 b a u a-1 exp(-bu), Γ(·) are the Gamma function. It is a fixed prior value.

[0161] We assume that N follows a cyclically symmetric complex Gaussian distribution, and that the data from each microphone and each snapshot are independent of each other.

[0162]

[0163] Where, N ·,l For the l-th column of N, α = σ -2 , σ 2 Let I be the noise variance, and I be a Q×Q dimensional identity matrix. Typically, α is unknown, therefore we assume α follows a Gamma distribution.

[0164] p(α|c,d)=Gamma(α|c,d),

[0165] in, All are fixed prior values. Combining the off-grid model of compressed spherical beamforming and the prior distribution of N, according to Bayes' theorem, the data likelihood can be obtained as follows:

[0166]

[0167] Among them, P ·,l Let H be the l-th column of P, and H be the abbreviation of H(Δθ,Δφ).

[0168] Let Δθ and Δφ follow a uniform distribution, that is, their g-th element satisfies

[0169] Δθ g ~U(-d θ / 2,d θ / 2)

[0170] Δφ g ~U(-d φ / 2,d φ / 2)

[0171] Where, d θ With d φ These represent the grid spacing in the latitude (θ) and longitude (φ) directions, respectively.

[0172] The joint probability density function p(X,P,α,ξ,Δθ,Δφ) is

[0173] p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ)

[0174] Step 3: Solve for Δθ and Δφ using the expectation-maximization algorithm.

[0175] The mathematical model for solving Δθ and Δφ is as follows:

[0176]

[0177] in, This represents the expectation of the posterior distribution of X.

[0178] Solving the above model using the expectation-maximization algorithm yields the following results:

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] in,

[0186] μ ·,l =αΣH H P ·,l

[0187] Σ=(αH H H+Λ -1 ) -1

[0188] The symbol indicates taking the real part, and "*" is the conjugate symbol. " is the Hadamard product operator. θ|g and v φ|g It is v θ and v φ The g-th element, W θ|g,g and W φ|g,g It is W θ and W φ The g-th row and g-th column vector, W θ|·,g and W φ|·,g It is W θ and W φThe g-th column vector, (·) -g This indicates that the g-th element of the vector within the parentheses will be removed.

[0189] Step 4: Estimate the DOA of the sound source

[0190] Step 5: Estimate the intensity of the sound source.

[0191] Example 3:

[0192] See Figures 1 to 2 A method for identifying sound sources using ultra-high resolution compressed sphere beamforming includes the following steps:

[0193] Step 1: Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion;

[0194] The compressed sphere beamforming sound source identification method provided by this invention utilizes a microphone array to measure sound signals. Figure 1 Array measurement model. A spherical coordinate system is established with the origin at the center of the microphone array. The DOA of the i-th (i = 1, 2, ..., I) sound source in space is represented as (θ...). Si ,φ Si The focusing region is discretized into G (G >> I) fixed grid points, and the direction of the grid point closest to the i-th sound source is marked as... According to the Taylor expansion formula, the transfer function vector a(θ) corresponding to the i-th sound source Si ,φ Si It can be approximated as

[0195]

[0196] definition It is stipulated that for any i∈{1,2,…,I}, if If it is established, then X g,· =S i,· , where X g,· With S i,· Let g represent the g-th row of X and the i-th row of S, respectively. Otherwise, Δθ g =0, Δφ g =0,X g,· =0. Combining equations (1) and (2), we obtain the two-dimensional off-grid compressed spherical beamforming model.

[0197] P=H(Δθ,Δφ)X+N (3)

[0198] in,

[0199] H(Δθ,Δφ)=(A(Γ F )+Bθ (Γ F Diag(Δθ)+B φ (Γ F Diag(Δφ)) (4)

[0200] Step 2: Provide prior hypotheses for all unknown variables (X, N, Δθ, and Δφ) and calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ).

[0201] Assume that X follows a two-level prior with each snapshot data being independent: In the first level, X follows a circularly symmetric complex Gaussian distribution, i.e.

[0202]

[0203] Among them, X ·,l Let ξ be the l-th column of X, and let ξ be the hyperparameter vector that controls X. ·,l The variance of each element, Λ = Diag(ξ), for any variable In the second level, let ξ follow a Gamma distribution.

[0204]

[0205] ξ g Let Γ be the g-th element of ξ. For any variable u, Γ(u|a,b)=(Γ(a)). -1 b a u a-1 exp(-bu), Γ(·) are the Gamma function. It is a fixed prior value. The prior distribution defined by equations (5) and (6) implies that X ·,l Both the real and imaginary parts of X follow a Laplace distribution and have the same probability density function that peaks at the origin. Therefore, this two-layer prior hypothesis is a sparse prior hypothesis, which causes most row vectors in X to be zero vectors.

[0206] We assume that N follows a cyclically symmetric complex Gaussian distribution, and that the data from each microphone and each snapshot are independent of each other.

[0207]

[0208] Where, N ·,l For the l-th column of N, α = σ -2 , σ 2 Let I be the noise variance, and I be a Q×Q dimensional identity matrix. Typically, α is unknown, therefore it is assumed that α follows a Gamma distribution.

[0209] p(α|c,d)=Gamma(α|c,d) (8)

[0210] in, All are fixed prior values. Combining the off-grid model of compressed spherical beamforming and the prior distribution of N, according to Bayes' theorem, the data likelihood can be obtained as follows:

[0211]

[0212] Among them, P ·,l Let H be the l-th column of P, and H be the abbreviation of H(Δθ,Δφ).

[0213] Let Δθ and Δφ follow a uniform distribution, that is, their g-th element satisfies

[0214] Δθ g ~U(-d θ / 2,d θ / 2) (10)

[0215] Δφ g ~U(-d φ / 2,d φ / 2) (11)

[0216] Where, d θ With d φ These represent the grid spacing in the latitude (θ) and longitude (φ) directions, respectively.

[0217] Calculate p(X,P,α,ξ,Δθ,Δφ) based on equations (9), (5), (6), (8), (10), and (11).

[0218] p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ) (12)

[0219] Step 3: Solve for Δθ and Δφ using the expectation-maximization algorithm.

[0220] Step 301: Establish a mathematical model

[0221] The mathematical model for solving Δθ and Δφ is as follows:

[0222]

[0223] in, This represents the expectation of the posterior distribution of X.

[0224] Omit the distributions unrelated to Δθ in equation (13) and maximize Equivalent to maximizing because

[0225]

[0226] maximize Equivalent to minimizing

[0227]

[0228] Where C is a constant,

[0229]

[0230]

[0231] μ ·,l =αΣH H P ·,l (18)

[0232] Σ=(αH H H+Λ -1 ) -1 (19)

[0233] The symbol indicates taking the real part, and "*" is the conjugate symbol. " is the Hadamard product operator.

[0234] Ultimately, Δθ should satisfy

[0235] Δθ=argmin(Δθ T W θ Δθ-2(v θ ) T Δθ) (20)

[0236] Similarly, when updating Δφ, Δφ should satisfy...

[0237] Δφ=argmin(Δφ T W φ Δφ-2(v φ ) T Δφ) (21)

[0238] in,

[0239]

[0240]

[0241] Step 302: Solve equations (20) and (21) to obtain Δθ and Δφ.

[0242] Find the partial derivatives of equation (20) with respect to Δθ and equation (21) with respect to Δφ, and obtain the following results.

[0243]

[0244]

[0245] Setting equations (24) and (25) to 0, we get

[0246]

[0247]

[0248] v θ|g and v φ|g It is v θ and v φ The g-th element, W θ|g,g and W φ|g,g It is W θ and W φ The g-th row and g-th column vector, W θ|·,g and W φ|·,g It is W θ and W φ The g-th column vector, (·) -g This indicates that the g-th element of the vector within the parentheses will be removed.

[0249] Apply constraints to the elements in Δθ and Δφ, and let Δθ g ∈[-d θ / 2,d θ / 2],Δφ g ∈[-d φ / 2,d φ / 2], obtained

[0250]

[0251]

[0252] Step 4: Estimate the two-dimensional direction of arrival (DOA) of the sound source.

[0253] Calculate the energy at each grid point; the energy at the g-th grid point is...

[0254]

[0255] u g,· Σ is the g-th row vector of u. gg It is the vector in the g-th row and g-th column of Σ.

[0256] If the energy in a direction at a certain grid point is not less than 20 dB below the maximum energy, a sound source is generally considered to exist in that direction (near) the grid point. Therefore, the estimated DOA of the sound source is...

[0257]

[0258] Among them, P max This represents the maximum energy in all grid point directions.

[0259] Step 5: Estimate the sound source intensity

[0260] Estimating the sound source intensity using the least squares method

[0261]

[0262] in,(·) + This indicates the Moore-Penrose pseudo-inverse.

[0263] Example 4:

[0264] Simulation experiments of the ultra-high resolution compressed sphere beamforming sound source identification method described in Examples 1-3 include the following:

[0265] 1. Determine the array to be used, and assume a point source at a specified location that radiates sound waves of a specific frequency with a specific intensity, and calculate the sound pressure signal received by the microphone.

[0266] 2. Establish an off-grid compressed sphere beamforming model based on equations (3) and (4);

[0267] 3. According to equations (26)-(29) in step 302, we obtain Δθ and Δφ;

[0268] 4. Estimate the DOA of the sound source based on step 4;

[0269] 5. Estimate the sound source intensity based on step 5.

[0270] The simulation settings are as follows: At 2000Hz, the positions of the five sound sources are (1m, 98°, 201°), (1m, 98°, 221°), (1m, 47°, 32°), (1m, 122°, 309°), and (1m, 68°, 133°). At 4000Hz and 6000Hz, the coordinates of the first two sound sources are compressed to (1m, 98°, 192°) and (1m, 98°, 204°) and (1m, 98°, 198°) and (1m, 98°, 208°), respectively, while the coordinates of the remaining sound sources remain unchanged. The sound source intensities are 100dB, 100dB, 97.5dB, 95dB, and 92dB, respectively. (Reference 2.0×10) -5 Pa). SNR was set to 40dB, and the number of snapshots was set to 40. The simulation used a rigid ball array from Bruel & Kjarr containing 36 Model 4958 microphones (e.g., Pa). Figure 1 (As shown) The sound signal was measured with a radius of 0.0975m.

[0271] Simulation results:

[0272] Figure 2These are sound source imaging images at three different frequencies. In each image, "*" and "" are used to indicate the sound source. "The DOA of the reconstructed sound source and the actual sound source are indicated respectively. It can be seen that the DOA of all sound sources is accurately identified, and the estimated sound source intensity is also close to the true value; even if the distance between the sound sources is small, the method provided by this invention can still successfully separate and accurately identify them."

[0273] The ultra-high resolution compressed sphere beamforming sound source identification method provided by this invention can effectively overcome the basis mismatch problem. Simulation results show that this method can accurately estimate the DOA of off-grid sound sources and quantize the sound source intensity, while achieving ultra-high resolution.

[0274] Example 5:

[0275] A method for identifying sound sources using ultra-high resolution compressed sphere beamforming includes the following steps:

[0276] 1) Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion;

[0277] 2) Provide prior assumptions for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain, and calculate the joint probability density function of the unknown variables;

[0278] 3) Based on the joint probability density function of the unknown variables, the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain are solved to estimate the source DOA and source intensity.

[0279] Example 6:

[0280] The ultra-high resolution compressed spherical beamforming sound source identification method is described in Example 5. The two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain is shown below:

[0281] P=H(Δθ,Δφ)X+N (1)

[0282] In the formula, This is the sound pressure matrix; The source intensity matrix; This is the noise matrix; represents the complex set; Q, L, and G represent the number of microphones, the number of snapshots, and the number of grid points, respectively, with each grid point corresponding to a potential sound source;

[0283] The transfer function matrix H(Δθ,Δφ) is shown below:

[0284] H(Δθ,Δφ)=(A(Γ F )+B θ (Γ F Diag(Δθ)+B φ (ΓF Diag(Δφ)) (2)

[0285] In the formula, Γ F It is the set of directions of each grid point, Γ F ={(θ Fg ,φ Fg |g=1,2,…,G};θ Fg φ Fg represents the elevation and azimuth directions of the g-th grid point; Δθ and Δφ are the DOA offset vectors in the elevation and azimuth directions, respectively; Diag(·) indicates generating a diagonal matrix with the vectors in parentheses as its diagonal.

[0286] Matrix A(Γ) F ), matrix B θ (Γ F ), matrix B φ (Γ F As shown below:

[0287]

[0288]

[0289]

[0290] In the formula, the matrix N is the highest order of the spherical harmonic function; vector matrix vector The superscript H indicates Hermitian transpose; Let m be a spherical harmonic function of order n; n = 0, 1, ..., N, m = -N, ..., 0, ..., N. b is the modal intensity matrix; n (kr F (,ka) represents the intensity of the nth mode; k is the wavenumber; r F Γ is the focusing radius; a is the radius of the sphere array. M It is the set of directions of each microphone, Γ M ={(θ Mq ,φ Mq )|q=1,2,…,Q};θ Fg φ Fg θ represents the elevation and azimuth directions of the g-th grid point; Mq φ Mq It represents the elevation and azimuth directions of the q-th microphone;

[0291] Example 7:

[0292] The method for identifying sound sources using ultra-high resolution compressed spherical beamforming is described in Example 5. The unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain include the sound source intensity matrix X, the noise matrix N, the DOA offset vector Δθ in the elevation direction, and the DOA offset vector Δφ in the azimuth direction.

[0293] Example 8:

[0294] The ultra-high resolution compressed spherical beamforming sound source identification method, the main content of which is described in Example 5, includes the following steps for calculating the joint probability density function of unknown variables:

[0295] a) Set the sound source intensity matrix X to follow a two-level prior, and the snapshot data in the sound source intensity matrix X are independent of each other;

[0296] The noise matrix N is set to follow a cyclic symmetric complex Gaussian distribution, and the microphone and snapshot data in the noise matrix N are independent data.

[0297] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction are set to follow a uniform distribution.

[0298] b) Based on the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain and the prior distribution of the noise matrix N, the data likelihood p(P|X) is obtained, i.e.:

[0299]

[0300] In the formula, P ·,l The l-th column of the sound pressure matrix P; H = H(Δθ, Δφ); vector X ·,l The l-th column of the sound source intensity matrix X; parameter α = σ -2 ;σ 2 Let I be the noise variance; I is the Q×Q dimensional identity matrix.

[0301] c) Calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ), i.e.:

[0302] p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ) (7)

[0303] In the formula, p(X|ξ), p(ξ), p(α), p(Δθ), and p(Δφ) represent probability distributions. ξ is a hyperparameter vector used to control the vector X. ·,l The variance of each element;

[0304] Example 9:

[0305] The ultra-high resolution compressed spherical beamforming sound source identification method is described in Example 5. In the first-level prior, the sound source intensity matrix X follows a circularly symmetric complex Gaussian distribution, i.e.:

[0306]

[0307] In the formula, vector X ·,l ξ is the l-th column of the sound source intensity matrix X; ξ is the hyperparameter vector used to control the vector X. ·,l The variance of each element; parameter Λ = Diag(ξ); for any variable parameter u, μ, and Σ respectively refer to X ·,l 、0、Λ;

[0308] In the second-level prior, the hyperparameter vector ξ follows a Gamma distribution, that is:

[0309]

[0310] In the formula, ξ g Let Γ be the g-th element of the hyperparameter vector ξ; for any variable u, Γ(u|a,b)=(Γ(a)) -1 b a u a -1 exp(-bu); Γ(·) is the Gamma function; These are fixed prior values. p(ξ|ρ) is the probability distribution; u, a, and b refer to ξ. g , 1, ρ.

[0311] The noise matrix N satisfies the following equation:

[0312]

[0313] In the formula, N ·,l The l-th column of the noise matrix N; parameter α = σ -2 ;σ 2 Let be the noise variance; I be the Q×Q dimensional identity matrix; p(N|α) be the probability distribution;

[0314] Wherein, the parameter α follows a Gamma distribution, that is:

[0315] p(α|c,d)=Gamma(α|c,d), (11)

[0316] In the formula, All are fixed prior values. p(α|c,d) is the probability distribution;

[0317] The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction satisfy the following equation:

[0318] Δθ g ~U(-d θ / 2,d θ / 2) (12)

[0319] Δφ g ~U(-d φ / 2,d φ / 2) (13)

[0320] In the formula, d θ With d φ These represent the grid spacing along the latitude (θ) and longitude (φ) directions, respectively. U(-d θ / 2,d θ / 2), U(-d φ / 2,d φ / 2) represents a set.

[0321] Example 10:

[0322] The ultra-high resolution compressed spherical beamforming sound source identification method, the main contents of which are described in Example 5, includes the following steps: solving for the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain to obtain the direction of arrival and the intensity of the sound source.

[0323] I) Constructing the Expectation-Maximization Algorithm Model Right now:

[0324]

[0325] In the formula, This indicates taking the expectation of the posterior distribution of X;

[0326] II) Use the expectation-maximization algorithm model to solve for the DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction, that is:

[0327]

[0328]

[0329]

[0330]

[0331]

[0332]

[0333] In the formula, Indicates taking the real part; "*" is the conjugate symbol; " is the Hadamard product operator; vθ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix B θ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ g This represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots. Matrix A refers to matrix A(Γ). F ); As a parameter;

[0334] parameter μ ·,l The parameter Σ is shown below:

[0335] μ ·,l =αΣH H P ·,l (twenty one)

[0336] Σ=(αH H H+Λ -1 ) -1 (twenty two)

[0337] In the formula, Indicates taking the real part; "*" is the conjugate symbol; " is the Hadamard product operator; v θ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix Bθ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ g This represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots. Matrix A refers to matrix A(Γ). F );

[0338] III) Calculate the estimated values ​​of the sound source DOA and the sound source intensity.

[0339] Example 11:

[0340] The ultra-high resolution compressed sphere beamforming sound source identification method is described in Example 5, wherein the sound source DOA... As shown below:

[0341]

[0342] In the formula, P max Δθ represents the maximum energy in all grid point directions; ε represents the preset energy threshold; Δθ Fg , Δφ Fg This represents the DOA offset of the g-th grid point in the direction of elevation and azimuth.

[0343] Wherein, the energy P of the g-th grid point g As shown below:

[0344]

[0345] In the formula, u g,· Σ is the g-th row vector of matrix u. gg X is the vector in the g-th row and g-th column of matrix Σ. L is the total number of snapshots. g,· It is the g-th column of the sound source intensity matrix X.

[0346] Example 12:

[0347] The ultra-high resolution compressed sphere beamforming sound source identification method, the main contents of which are described in Example 5, includes the sound source intensity estimation value. As shown below:

[0348]

[0349] In the formula, (·) + Represents the Moore-Penrose pseudoinverse; matrix

Claims

1. A method for identifying sound sources using ultra-high resolution compressed spherical beamforming, characterized in that, Includes the following steps: 1) Construct a two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain based on Taylor expansion; 2) Provide prior assumptions for the unknown variables in the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain, and calculate the joint probability density function of the unknown variables; 3) Based on the joint probability density function of the unknown variables, the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain are solved to estimate the source DOA and source intensity. The two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain is shown below: P=H(Δθ,Δφ)X+N (1) In the formula, This is the sound pressure matrix; The source intensity matrix; This is the noise matrix; represents the complex set; Q, L, and G represent the number of microphones, the number of snapshots, and the number of grid points, respectively, with each grid point corresponding to a potential sound source; The transfer function matrix H(Δθ,Δφ) is shown below: H(Δθ,Δφ)=(A(Γ F )+B θ (C F )Diag(Δθ)+B φ (C F )Diag(Δφ) (2) In the formula, Γ F It is the set of directions of each grid point, Γ F ={(θ Fg ,φ Fg |g=1,2,…,G};θ Fg φ Fg represents the elevation and azimuth directions of the g-th grid point; Δθ and Δφ are the DOA offset vectors in the elevation and azimuth directions, respectively; Diag(·) indicates generating a diagonal matrix with the vectors in parentheses as its diagonal. Matrix A(Γ) F ), matrix B θ (Γ F ), matrix B φ (Γ F As shown below: In the formula, the matrix N is the highest order of the spherical harmonic function; vector matrix vector The superscript H indicates Hermitian transpose; Let m be a spherical harmonic function of order n; n = 0, 1, ..., N, m = -N, ..., 0, ..., N. b is the modal intensity matrix; n (kr F (,ka) represents the intensity of the nth mode; k is the wavenumber; r F Γ is the focusing radius; a is the radius of the sphere array; Γ M It is the set of directions of each microphone, Γ M ={(θ Mq ,φ Mq )|q=1,2,…,Q};θ Fg φ Fg θ represents the elevation and azimuth directions of the g-th grid point; Mq φ Mq These are the elevation and azimuth directions of the q-th microphone; The unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain include the sound source intensity matrix X, the noise matrix N, the DOA offset vector Δθ in the elevation direction, and the DOA offset vector Δφ in the azimuth direction. The steps for calculating the joint probability density function of the unknown variables include: 2.1) Set the sound source intensity matrix X to follow a two-level prior, and the snapshot data in the sound source intensity matrix X are independent of each other; The noise matrix N is set to follow a cyclic symmetric complex Gaussian distribution, and the microphone and snapshot data in the noise matrix N are independent data. The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction are set to follow a uniform distribution. 2.2) Based on the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain and the prior distribution of the noise matrix N, the data likelihood p(P|X) is obtained, i.e.: In the formula, P ·,l The l-th column of the sound pressure matrix P; H = H(Δθ, Δφ); vector X ·,l The l-th column of the sound source intensity matrix X; parameter α = σ -2 ;σ 2 Let I be the noise variance; I is the Q×Q dimensional identity matrix. 2.3) Calculate the joint probability density function p(X,P,α,ξ,Δθ,Δφ), i.e.: p(X,P,α,ξ,Δθ,Δφ)=p(P|X)p(X|ξ)p(ξ)p(α)p(Δθ)p(Δφ) (7) In the formula, p(X|ξ), p(ξ), p(α), p(Δθ), and p(Δφ) represent probability distributions; ξ is a hyperparameter vector used to control the vector X. .,l The variance of each element.

2. The ultra-high resolution compressed sphere beamforming sound source identification method according to claim 1, characterized in that, In the first-level prior, the sound source intensity matrix X follows a circularly symmetric complex Gaussian distribution, that is: In the formula, vector X .,l ξ is the l-th column of the sound source intensity matrix X; ξ is the hyperparameter vector used to control the vector X. ·,l The variance of each element; parameter Λ = Diag(ξ); for any variable parameter u, μ, and Σ respectively refer to X ·,l 、0、Λ; In the second-level prior, the hyperparameter vector ξ follows a Gamma distribution, that is: In the formula, ξ g Let Γ be the g-th element of the hyperparameter vector ξ; for any variable u, Γ(u|a,b)=(Γ(a)) -1 b a u a-1 exp(-bu); Γ(·) is the Gamma function; It is a fixed prior value; p(ξ|ρ) is the probability distribution; u, a, and b represent ξ. g , 1, ρ.

3. The ultra-high resolution compressed sphere beamforming sound source identification method according to claim 1, characterized in that, The noise matrix N satisfies the following equation: In the formula, N ·,l The l-th column of the noise matrix N; parameter α = σ -2 ;σ 2 Let be the noise variance; I be the Q×Q dimensional identity matrix; p(N|α) be the probability distribution; Wherein, the parameter α follows a Gamma distribution, that is: p(α|c,d)=Gamma(α|c,d), (11) In the formula, All are fixed prior values; p(α|c,d) is a probability distribution.

4. The ultra-high resolution compressed sphere beamforming sound source identification method according to claim 1, characterized in that, The DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction satisfy the following equation: Δθ g ~U(-d θ / 2,d θ / 2) (12) Δφ g ~U(-d φ / 2,d φ / 2) (13) In the formula, d θ With d φ These represent the grid spacing along the latitude (θ) and longitude (φ) directions, respectively; U(-d θ / 2,d θ / 2), U(-d φ / 2,d φ / 2) represents a set.

5. The ultra-high resolution compressed sphere beamforming sound source identification method according to claim 1, characterized in that, The steps for solving the unknown variables of the two-dimensional off-grid compressed spherical beamforming model in the spherical harmonic domain to obtain the direction of sound arrival and the sound source intensity include: 1) Construct the Expectation-Maximization Algorithm Model Right now: In the formula, This indicates taking the expectation of the posterior distribution of X; 2) Use the expectation-maximization algorithm model to solve for the DOA offset vector Δθ in the elevation direction and the DOA offset vector Δφ in the azimuth direction, that is: In the formula, The symbol "*" indicates taking the real part; "*" is the conjugate symbol. The Hadamard product operator; v θ|g and v φ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W φ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|.,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix B θ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ g This represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots; matrix A refers to matrix A(Γ). F ); As a parameter; parameter μ .,l The parameter Σ is shown below: m ·,l =aΣH H P ·,l (21) Σ=(αH H H+L -1 ) -1 (22) In the formula, The symbol "*" indicates taking the real part; "*" is the conjugate symbol. The Hadamard product operator; v θ|g and v θ|g It is a vector v θ sum vector v φ The g-th element; W θ|g,g and W θ|g,g It is matrix W θ Sum matrix W φ The g-th row and g-th column vector; W θ|·,g and W φ|·,g It is matrix W θ Sum matrix W φ The g-th column vector; (·) -g This indicates removing the g-th element of the vector within the parentheses; matrix B θ Matrix B φ Referential matrix B θ (Γ F ), matrix B φ (Γ F );Δθ g , Δφ g This represents the DOA offset in the elevation direction and the DOA offset in the azimuth direction of the g-th grid point; L is the total number of snapshots; matrix A refers to matrix A(Γ). F ); 3) Calculate the estimated values ​​of the sound source DOA and the sound source intensity.

6. The ultra-high resolution compressed spherical beamforming sound source identification method according to claim 5, characterized in that, The sound source DOA As shown below: In the formula, P max Δθ represents the maximum energy in all grid point directions; ε represents the preset energy threshold; Δθ Fg , Δφ Fg This represents the DOA offset of the g-th grid point in the direction of elevation and azimuth. Wherein, the energy P of the g-th grid point g As shown below: In the formula, u g,. Σ is the g-th row vector of matrix u. gg X is the vector in the g-th row and g-th column of matrix Σ; L is the total number of snapshots; X g,· It is the g-th column of the sound source intensity matrix X.

7. The ultra-high resolution compressed sphere beamforming sound source identification method according to claim 5, characterized in that, Sound source intensity estimate As shown below: In the formula, (·) + Represents the Moore-Penrose pseudoinverse; matrix

Images