Off-grid model-based iterative Bayesian focusing sound source localization method

Abstract

The invention relates to the technical field of sound source localization, in particular to an off-grid model-based iterative Bayesian focusing sound source localization method, which comprises the following steps of: acquiring a sound pressure signal acquired by a microphone array; discretizing the sound source plane through a preset step length, and obtaining a discrete grid according to the area of the sound source plane; assuming that the actual sound source position is not on the grid point, constructing an off-grid forward model; modeling a Green function of the off-grid forward model by using first-order Taylor approximation; performing maximum posteriori estimation on the off-grid forward model; and deducing the maximum posteriori estimation of the IBF algorithm under the off-grid forward model through an expectation maximization algorithm to obtain the estimated position of the sound source. According to the method, the problems that in the current sound source target detection process, a sound source is difficult to accurately fall on pre-divided grid points and the existence base is not matched are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of sound source localization, and in particular to a sound source localization method based on iterative Bayesian focusing of an off-grid model. Background Art

[0002] Array signal processing methods based on microphone arrays have been widely used in the fields of sound source target detection and noise control. In complex environments, the sound propagation process is affected by various noise interferences, resulting in unsatisfactory detection performance of the target sound source. The implementation of high-precision sound source target detection methods has become an extremely challenging and difficult task.

[0003] In recent years, the more popular array signal processing method is the sparse reconstruction algorithm (such as the sparse Bayesian method and the penalty function method), which discretizes the target area of ​​interest into multiple grid points and assumes that the sound source falls on the grid points.

[0004] The penalty function method proposed by Wang Ran et al. induces sparsity by introducing a penalty term in the objective function; the sparse Bayesian method proposed by Dai Jisheng et al. introduces sparsity by constructing a heavy-tailed probability density function; the sparse Bayesian method has some advantages over the penalty function method because it can automatically estimate hyperparameters without finding the optimal penalty factor, thereby reducing complexity.

[0005] But in reality, it is difficult for the sound source to fall accurately on the pre-divided grid points, and the off-grid problem has also been widely studied; Zhou Yingmin et al. proposed a computationally efficient root sparse Bayesian method for off-grid DOA estimation, which regards the sampling positions in the coarse grid as adjustable parameters and uses the expectation-maximization algorithm to iteratively refine the coarse grid; Rohan R.Pote et al. proposed an iterative sparse Bayesian procedure that can refine the grid points to improve the resolution near the potential source location while keeping the complexity of each iteration low; but due to the discretization of the region of interest, the sparse Bayesian method faces the basis mismatch problem. Summary of the invention

[0006] In view of the shortcomings of the existing methods, the present invention solves the problems that the sound source is difficult to accurately fall on the pre-divided grid points and there is basis mismatch in the current sound source target detection process.

[0007] The technical solution adopted by the present invention is: a sound source localization method based on iterative Bayesian focusing of an off-grid model comprises the following steps:

[0008] Step 1: Obtain the sound pressure signal collected by the microphone array;

[0009] As a preferred implementation of the present invention, a Hanning window function is used to truncate the sound pressure signal in the time domain.

[0010] As a preferred implementation of the present invention, a sound pressure signal in the time domain is converted into a sound pressure signal in the frequency domain by using a fast Fourier transform.

[0011] Step 2: discretize the sound source plane by a preset step size, and obtain a discrete grid according to the area of ​​the sound source plane;

[0012] Step 3: Assuming that the actual sound source location is not on the grid point, construct an off-grid forward model;

[0013] As a preferred embodiment of the present invention, the formula of the off-grid forward model is:

[0014] p=H OG s+n (1)

[0015] Where p=[p1,...,p m ,...,p M ] T ∈C M represents the sound pressure vector collected by M microphones, p M represents the sound pressure vector collected by the Mth microphone; represents the Green's function of the off-grid forward model, Indicates H OG The qth column of q ,...,s Q ] T ∈C Q represents the source coefficient vector of the off-grid forward model, n=[n1,...,n m ,...,n M ] T ∈C M represents the noise vector.

[0016] Step 4: Model the Green function of the off-grid forward model using the first-order Taylor approximation;

[0017] As a preferred embodiment of the present invention, the formula for modeling using the Green's function is:

[0018]

[0019] in, is the original Green's function; r m represents the mth microphone position, r q represents the position of the qth source in the off-grid model, f represents the frequency, c represents the propagation speed of the sound source, Δr q (x) represents r in the x direction q The change in Δr q (y) represents r in the y direction q The amount of change.

[0020] Step 5: Perform maximum a posteriori estimation on the off-grid forward model;

[0021] As a preferred embodiment of the present invention, the formula for maximum a posteriori estimation is:

[0022]

[0023] in, represents the posterior estimate, [p|s] represents the likelihood function about p given s, and s represents the prior distribution.

[0024] Step 6: derive the maximum a posteriori estimate of the IBF algorithm under the off-grid forward model through the expectation maximization algorithm (EM) to obtain the estimated position of the sound source;

[0025] As a preferred implementation of the present invention, step six specifically includes:

[0026] Step 61: Give the noise vector n m The distribution has a mean of 0 and a variance of β 2 The complex Gaussian distribution of , then the expression of [p|s] is:

[0027]

[0028] Among them, [p|s] represents the likelihood function of p given s, β 2 Indicates n m The variance of , I represents the identity matrix;

[0029] Step 62: Under the assumption of time stationarity in the IBF algorithm, the prior PDF obeys the following distribution:

[0030]

[0031] Among them, s q represents the qth source coefficient vector of the off-grid forward model, Super prior Expectations, q,i Indicates q The i-th snapshot of 2 Indicates power; represents the initial aperture function;

[0032] Step 63: The iterative process of the IBF algorithm is implemented by the EM algorithm. The iteration formula of the parameters is:

[0033]

[0034] in, represents the posterior estimate of the kth source, α2 represents power, β 2 Indicates n m The variance parameter of ;

[0035] Step 64: The iterative process of the IBF algorithm can be implemented by the EM algorithm, giving the power variance The iteration formula of the parameters is:

[0036]

[0037] Step 65: The iterative process of the IBF algorithm can be implemented by the EM algorithm to give the aperture of the IBF algorithm The iteration formula of the parameters is:

[0038]

[0039] in, represents the initial aperture function, Indicates q,[k] The super prior of

[0040] Step 66: The iterative process of the IBF algorithm can be implemented by the EM algorithm. The iteration formula of the parameters is:

[0041]

[0042] in, are the parameters of the hyper-prior distribution, which can be given before the algorithm runs;

[0043] Step 67, repeat steps 63 to 66 until convergence;

[0044] Step 68: The parameter value given by the a posteriori maximum is used as an estimate of the target signal position.

[0045] Beneficial effects of the present invention:

[0046] 1. By integrating the off-grid model into the IBF algorithm, the iterative formula of the posterior PDF under the IBF algorithm framework is derived; in the forward model, the first-order Taylor approximation is used to estimate the offset of the grid relative to the actual sound source position in the free field; the improved Green's function is combined with the IBF algorithm to solve the basis mismatch problem in the sound source reconstruction process;

[0047] 2. The aperture function and grid offset are jointly estimated in the IBF algorithm to obtain higher spatial resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1It is a flow chart of the sound source localization method based on iterative Bayesian focusing of the off-grid model of the present invention;

[0049] Figure 2 It is a flowchart of the iterative Bayesian focusing algorithm;

[0050] Figure 3 (a)-(c) are the source localization acoustic images of IBF-OG algorithm, IBF algorithm, and off-grid integrated SBL algorithm (SBL-OG) at 1000 Hz, respectively;

[0051] Figure 4 (a)-(c) are the source localization acoustic images of IBF-OG algorithm, IBF algorithm, and off-grid integrated SBL algorithm (SBL-OG) at 2000 Hz, respectively;

[0052] Figure 5 (a)-(c) are the source localization acoustic images of the IBF-OG algorithm, IBF algorithm, and off-grid integrated SBL algorithm (SBL-OG) at 3000 Hz, respectively. DETAILED DESCRIPTION

[0053] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0054] like Figure 1 , 2 As shown, a sound source localization method based on iterative Bayesian focusing of an off-grid model includes the following steps:

[0055] Step 1: Obtain the sound pressure signal collected by the microphone array;

[0056] In order to obtain the signal sound pressure collected by the microphone array, a 56-channel multi-arm spiral microphone array is arranged to collect the signal sound pressure. The signal collected by the microphone array is a time domain signal, which needs to be converted to the frequency domain for calculation in the separation step. The time domain signal is truncated using the Hanning window function, and then the truncated time domain signal is converted into a frequency domain signal through fast Fourier transform. Each segment is a snapshot, thereby obtaining the measurement data p of the microphone, that is, p represents the sound pressure vector collected by M microphones.

[0057] Step 2: discretize the sound source plane by a preset step size, and obtain a discrete grid according to the area of ​​the sound source plane;

[0058] The preset step size is set to 0.05m, resulting in 21×21 grids; for example, in the X-axis direction, the target area where the sound source is located ranges from -0.5m to 0.5m. With a step size of 0.05m, there will be 21 grids in the X-axis direction, and similarly 21 grids in the Y-axis direction, thus obtaining a 21×21 grid.

[0059] Step 3: Assuming that the actual sound source location is not on the grid point, construct an off-grid forward model;

[0060] A grid point refers to the intersection of grid vertices of adjacent grids; the off-grid model includes a forward model and a reverse model. The formula of the off-grid forward model is:

[0061] p=H OG s+n (1)

[0062] Where p=[p1,...,p m ,...,p M ] T ∈C M represents the sound pressure vector collected by M microphones, p M represents the sound pressure vector collected by the Mth microphone; represents the Green's function of the off-grid forward model, Indicates H OG The qth column of q ,...,s Q ] T ∈C Q represents the source coefficient vector of the off-grid forward model, n=[n1,...,n m ,...,n M ] T ∈C M represents the noise vector.

[0063] Step 4: Model the Green function of the off-grid model through the first-order Taylor approximation;

[0064] The formula for modeling Green's function is:

[0065]

[0066] in, is the original Green's function; r m represents the mth microphone position, r q represents the position of the qth source in the off-grid model, f represents the frequency, c represents the propagation speed of the sound source, Δr q (x) represents r in the x direction q The change in Δr q (y) represents r in the y direction qThe change in h'(r m ,r q (x)),h'(r m ,r q (y)) represent the first-order partial differentials of the transfer function in the x-direction and the y-direction respectively; further h'(r m ,r q (x)),h'(r m ,r q (y)) is expressed as:

[0067]

[0068] Since the existing Green's function is a fixed grid, but the actual source position and the grid are offset, and the offset under the off-grid model conforms to the Taylor expansion, the present invention uses the first-order Taylor approximation to model the Green's function of the off-grid model, and the first-order Taylor expansion is the first-order partial differential in the x-direction and the y-direction.

[0069] Step 5: Perform maximum a posteriori (MAP) estimation on the off-grid forward model;

[0070] The formula for maximum a posteriori estimation of the off-grid forward model is:

[0071]

[0072] in, represents the posterior estimate, [p|s] represents the likelihood function about p given s, and s represents the prior distribution.

[0073] Step 6: derive the maximum a posteriori estimate of the IBF algorithm under the off-grid forward model through the expectation maximization algorithm to obtain the estimated position of the sound source;

[0074] Step 6 specifically includes:

[0075] Step 61, initialize the number of iterations K = 0, give the noise vector n m The distribution has a mean of 0 and a variance of β 2 The complex Gaussian distribution of , then the expression of [p|s] is:

[0076]

[0077] Among them, [p|s] represents the likelihood function of p given s, β 2 Indicates n m The variance of , I represents the identity matrix.

[0078] Step 62: Under the assumption of time stationarity in the IBF algorithm, the prior PDF obeys the following distribution:

[0079]

[0080] Among them, s q represents the qth source coefficient vector of the off-grid forward model, Super prior Expectations, q,i Indicates q The i-th snapshot of 2 Indicates power; represents the initial aperture function, which can be considered Random aperture function.

[0081] Step 63: The iterative process of the IBF algorithm is implemented by the EM algorithm. The iteration formula of the parameters is:

[0082]

[0083] in, represents the posterior estimate of the kth source, α 2 represents power, β 2 Indicates n m The variance parameter of .

[0084] Step 64: The iterative process of the IBF algorithm can be implemented by the EM algorithm, giving the power parameter in the IBF algorithm: (maximum a posteriori), variance parameter The iterative formula for (posterior maximization) is:

[0085]

[0086] Step 65: The iterative process of the IBF algorithm can be implemented by the EM algorithm to give the aperture of the IBF algorithm The iteration formula of the parameters is:

[0087]

[0088] in, represents the initial aperture function, Indicates q,[k] The super prior.

[0089] Step 66: The iterative process of the IBF algorithm can be implemented by the EM algorithm. The iterative formula for the parameter (relative strength) is:

[0090]

[0091] in, are the parameters of the hyper-prior distribution, which can be given before the algorithm runs.

[0092] Step 67, repeat steps 63 to 66 until convergence;

[0093] Among them, the convergence criterion is: when the IBF algorithm reaches the iteration termination condition, that is, the minimum mean square error is less than a given threshold or reaches a predefined maximum number of iterations, the IBF algorithm stops iterating.

[0094] Step 68: The parameter value given by the a posteriori maximum is used as an estimate of the target signal position.

[0095] By integrating the off-grid forward model into the IBF algorithm, and deriving the iterative formula of the posterior PDF under the IBF algorithm framework; using the first-order Taylor approximation to estimate the offset of the grid relative to the actual sound source position in the free field; combining the improved Green's function with the IBF algorithm to solve the basis mismatch problem in the sound source reconstruction process; the aperture function and grid offset are jointly estimated in the IBF algorithm to obtain higher spatial resolution.

[0096] The spatial resolution of the sound source localization results of the method of the present invention (IBF-OG) and the IBF algorithm and SBL-OG at different frequencies is compared; Figure 3-Figure 5 As shown, it can be seen that the spatial resolution of the positioning results of the three algorithms is very high because they are all sparse algorithms; from the source positioning results, the positioning accuracy of the present invention is the highest, while the IBF algorithm has a basis mismatch problem, resulting in pseudo sources, and the SBL-OG algorithm also has a basis mismatch problem, and the number of pseudo sources is relatively small, and the positioning accuracy is lower than that of the present invention; Figure 3 In the analysis, due to the low analysis frequency, the positioning accuracy of the IBF algorithm and the SBL-OG algorithm is very poor; with the increase of frequency, the positioning accuracy of the IBF algorithm and the SBL-OG algorithm is improved; the method of the present invention always maintains a high positioning accuracy. In terms of the sound power quantization level, the method of the present invention and the IBF algorithm always maintain the best sound power quantization level due to the introduction of the aperture function information in the prior PDF, and the SBL-OG algorithm does not have an advantage in the quantization of the sound power level.

[0097] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A sound source localization method based on iterative Bayesian focusing of an off-grid model, characterized in that: The following steps are involved: Step 1: Obtain the sound pressure signal collected by the microphone array; Step 2: discretize the sound source plane by a preset step size, and obtain a discrete grid according to the area of ​​the sound source plane; Step 3: Assuming that the actual sound source location is not on the grid point, construct an off-grid forward model; Step 4: Model the Green function of the off-grid forward model using the first-order Taylor approximation; Step 5: Perform maximum a posteriori estimation on the off-grid forward model; Step 6: Use the expectation maximization algorithm to derive the maximum a posteriori estimate of the IBF algorithm under the off-grid forward model to obtain the estimated position of the sound source.

2. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 1, characterized in that: The formula for the off-grid forward model is: p=H OG s+n (1) Where p=[p1,...,p m ,...,p M ] T ∈C M represents the sound pressure vector collected by M microphones, p M represents the sound pressure vector collected by the Mth microphone; represents the Green's function of the off-grid forward model, Indicates H OG The qth column of q ,...,s Q ] T ∈C Q represents the source coefficient vector of the off-grid forward model, n=[n1,...,n m ,...,n M ] T ∈C M represents the noise vector.

3. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 2, characterized in that: The formula for modeling Green's function is: in, is the original Green's function; r m represents the mth microphone position, r q represents the position of the qth source in the off-grid model, f represents the frequency, c represents the propagation speed of the sound source, Δr q (x) represents r in the x direction q The change in Δr q (y) represents r in the y direction q The amount of change.

4. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 3, characterized in that: The formula for maximum a posteriori estimation is: in, represents the posterior estimate, [p|s] represents the likelihood function about p given s, and s represents the prior distribution.

5. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 4, characterized in that: Step 6 specifically includes: Step 61: Give the noise vector n m The distribution has a mean of 0 and a variance of β 2 The complex Gaussian distribution of , then the expression of [p|s] is: Among them, [p|s] represents the likelihood function of p given s, β 2 Indicates n m The variance of , I represents the identity matrix; Step 62: Under the assumption of time stationarity in the IBF algorithm, the prior PDF obeys the following distribution: Among them, s q represents the qth source coefficient vector of the off-grid forward model, Super prior Expectations, q,i Indicates q The i-th snapshot of 2 Indicates power; represents the initial aperture function; Step 63: The iterative process of the IBF algorithm is implemented by the EM algorithm. The iteration formula of the parameters is: in, represents the posterior estimate of the kth source, α 2 represents power, β 2 Indicates n m The variance parameter of ; Step 64: The iterative process of the IBF algorithm can be implemented by the EM algorithm, giving the power variance The iteration formula of the parameters is: Step 65: The iterative process of the IBF algorithm can be implemented by the EM algorithm to give the aperture of the IBF algorithm The iteration formula of the parameters is: in, represents the initial aperture function, Indicates q,[k] The super prior of Step 66: The iterative process of the IBF algorithm can be implemented by the EM algorithm. The iteration formula of the parameters is: in, are the parameters of the hyper-prior distribution, which can be given before the algorithm runs; Step 67, repeat steps 63 to 66 until convergence; Step 68: The parameter value given by the a posteriori maximum is used as an estimate of the target signal position.

6. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 1, characterized in that: The Hanning window function is used to truncate the sound pressure signal in the time domain.

7. The sound source localization method based on iterative Bayesian focusing of the off-grid model according to claim 1, characterized in that: Fast Fourier transform is used to convert the sound pressure signal in the time domain into the sound pressure signal in the frequency domain.

8. An iterative Bayesian focused sound source localization system based on an off-grid model, characterized in that: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement the off-grid model-based iterative Bayesian focused sound source localization method as described in any one of claims 1 to 7.

9. A computer readable medium storing a computer program code, characterized in that: When the computer program code is executed by a processor, the method for sound source localization based on iterative Bayesian focusing of an off-grid model as described in any one of claims 1 to 7 is implemented.

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