A time-frequency domain underdetermined blind source separation method and system based on double sensors

Abstract

The application discloses a time-frequency domain underdetermined blind source separation method and system based on double sensors, which comprises two stages: in the first stage, a single source point with high clustering characteristics is detected by using a clustering and matching tracking algorithm, and a mixing matrix is estimated, so that high-precision mixing matrix estimation is realized; in the second stage, a time-frequency domain signal recovery problem is converted into a sparse recovery model with a relaxed sparse condition, the constraint of the number of sources on the self-source point in the traditional blind source separation algorithm is broken, and good separation effect is realized. The application is suitable for the double-sensor underdetermined blind source separation scene with more source numbers, low mixing signal-to-noise ratio and serious aliasing, and has strong applicability and practicability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing, and particularly relates to a time-frequency domain underdetermined blind source separation method and system based on double sensors. BACKGROUND

[0002] Blind source separation technology refers to reconstructing original signals from observation signals or mixed signals without any prior knowledge or specific statistical information of signal sources. Underdetermined blind source separation has a wide range of applications, such as wireless communication, biomedical signal processing, speech processing, image processing and pattern recognition. Underdetermined blind source separation lacks sufficient observation information, and is therefore still a very challenging problem.

[0003] Since many signals in nature are sparse in the time-frequency domain, blind source separation algorithms usually convert mixed signals to the time-frequency domain for processing based on the time-frequency sparsity of source signals. Existing underdetermined blind source separation algorithms can generally be divided into two steps: first, a clustering algorithm such as K-means clustering or a potential function-based clustering algorithm is used to estimate the mixing matrix, and then a subspace decomposition or a tracking algorithm-based algorithm is used to recover the source signals. However, most underdetermined blind source separation algorithms usually limit the number of sensors to more than two and assume that the number of source points in the time-frequency domain does not exceed the number of sensors, which obviously limits the application of double-sensor blind source separation algorithms. In addition, the performance of most underdetermined blind source separation algorithms depends on the number of sensors, i.e. when the number of sensors is small and the number of sources is large, the mixing matrix estimation and source separation of the blind source separation algorithm will be significantly affected. SUMMARY

[0004] In view of the problems that the existing blind source separation method is prone to low mixing matrix estimation accuracy and poor source recovery effect in the case of a large number of sources, high time-frequency overlap and a small number of sensors, the present application provides a time-frequency domain underdetermined blind source separation method and system based on double sensors, which can overcome the limitations of the existing blind source separation method under double-sensor settings.

[0005] To achieve the above purpose, the technical solution provided by the present application is a time-frequency domain underdetermined blind source separation method based on double sensors, comprising the following steps:

[0006] Step 1: converting the double-channel observation signal to the time-frequency domain through short-time Fourier transform;

[0007] Step 2: selecting strong energy self-source points from the observation signal time-frequency points obtained in step 1;

[0008] Step 3: clustering the strong energy self-source points, taking the cluster centers of each class as the initial estimated direction vectors, and splicing the initial estimated direction vectors to obtain an initial spatial vector dictionary.

[0009] Step 4, using the orthogonal matching pursuit algorithm to select high clustering characteristic single source points from strong energy self-source points;

[0010] Step 5, clustering the high clustering characteristic single source points, and taking the clustering center as an estimated column vector of a mixing matrix ;

[0011] Step 6, selecting self-source points from the observation signal time-frequency points obtained in step 1, and taking the self-source point set as Ω asp ;

[0012] Step 7, vectorizing the self-source point set Ω asp and the estimated mixing matrix to construct a sparse recovery model of source separation;

[0013] Step 8, using a spectral projection gradient descent algorithm based on L1 norm to solve the sparse recovery model;

[0014] Step 9, performing inverse short-time Fourier transform on the time-frequency domain source signals separated in step 8 to obtain separated source signals.

[0015] Moreover, in step 1, based on the linear instantaneous model assumption, it is assumed that there are N sources and two sensors in the environment, and the signal received by the sensor array can be represented as:

[0016] x(t) = As(t) + n(t) (1)

[0017] In the formula, x(t) represents a double-channel observation signal, s(t) represents a source signal to be estimated, n(t) represents a noise signal, A represents a mixing matrix, and t represents time.

[0018] The double-channel observation signal is converted from the time domain to the time-frequency domain using a short-time Fourier transform algorithm, and the specific calculation method is as follows:

[0019]

[0020] In the formula, S x (t,f) is the time-frequency representation of the observation signal after short-time Fourier transform, x(τ) represents the τth sampling point of the observation signal, h(τ-t) represents a Hamming window, e represents a natural constant, j represents a complex number, π represents a circular constant, and t and f represent time and frequency.

[0021] Moreover, in step 2, the points with a relative amplitude greater than a threshold T0 in the time-frequency domain of the observation signal are defined as strong energy self-source points, and the strong energy self-source point set Ω sep is represented as follows:

[0022]

[0023] where S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, ||S x (t,f) || represents the amplitude of the time-frequency point of the observed signal, represents the time-frequency point with the largest amplitude in the time-frequency point of the observed signal, and T0 is the strong energy time-frequency point selection threshold.

[0024] Moreover, the number of clusters N0 is set according to the properties of the mixing matrix in step 3, and N0 is greater than the number of sources N. The cluster center after clustering is defined as the initial estimated direction vector, and the mathematical representation of clustering the strong energy self-source point is as follows:

[0025]

[0026] wherein, represents the cluster center of the nth class, which is also the direction vector corresponding to the time-frequency point of the nth class, represents the time-frequency point of the nth cluster in the strong energy self-source point, represents the number of time-frequency points in the cluster, t and f represent time and frequency, represents the direction vector corresponding to the (t,f)th time-frequency point, and the union of all elements of each sub-class is Ω sep , i.e.

[0027] The is spliced to obtain the initial spatial vector dictionary

[0028] Moreover, the orthogonal matching pursuit algorithm is used to perform the first decomposition on the strong energy self-source point in step 4, and the specific calculation method is as follows:

[0029]

[0030] wherein, represents the value of that makes the expression take the minimum value, and ||·|| represents amplitude calculation, x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, represents the cluster center of the nth class, represents the Moore-Penrose pseudo-inverse, and the direction vector solved corresponds to the nth1 source existing in the strong energy time-frequency point.

[0031] The residual vector obtained by decomposing formula (5) is decomposed again to calculate the residual vector r (1) (t,f) of the strong energy time-frequency point after removing the nth1 source, i.e.:

[0032]

[0033] where S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the cluster center of the nth class, denotes Moore-Penrose pseudo-inverse of

[0034] The residual vector r (1) (t,f) is decomposed, i.e.,

[0035]

[0036] where S denotes the direction vector solved, denotes the value of that makes the expression take the minimum value, ||·|| denotes the amplitude calculation, denotes the cluster center of the nth class, denotes Moore-Penrose pseudo-inverse of

[0037] The direction vector solved by the secondary decomposition There is the nth2source corresponding to the strong energy time-frequency point, so S x The secondary decomposition of (t,f) can be expressed as follows:

[0038]

[0039]

[0040]

[0041] where S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, C1denotes the contribution of the nth1source to the strong energy time-frequency point, denotes the direction vector solved by the first decomposition, C2denotes the contribution of the nth2source to the strong energy time-frequency point, denotes the direction vector solved by the second decomposition, r (2) (t,f) denotes the residual vector of the strong energy time-frequency point after removing the source n1and the source n2, <·,·> denotes the inner product operation, denotes Moore-Penrose pseudo-inverse of

[0042] The ratio of C1and C2is used to determine the high clustering characteristic single source point, i.e.,

[0043]

[0044] where T hcp denotes the self-source clustering property, C1 denotes the contribution of the n1th source to the strong energy time-frequency point, C2 denotes the contribution of the n2th source to the strong energy time-frequency point, S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the direction vector solved by the first decomposition, <·,·> denotes the inner product operation, denotes the Moore-Penrose pseudo-inverse of denotes the direction vector solved by the second decomposition, β hcp is a set threshold.

[0045] The time-frequency point satisfying formula (11) is a high clustering single source point, and the high clustering property single source point set is defined as Ω hcp .

[0046] Moreover, in step 5, the clustering number N0 is equal to the source number N, and the mathematical representation of clustering the high clustering property single source point is as follows:

[0047]

[0048] wherein, denotes the clustering center of the nth class, which is also the direction vector corresponding to the time-frequency point of the nth class, denotes the time-frequency point of the nth clustering in the high clustering property single source point, denotes the Moore-Penrose pseudo-inverse of , t and f denote time and frequency, denotes the direction vector corresponding to the (t,f)th time-frequency point, and the union of all elements of each subclass is Ω hcp , that is are spliced to obtain the estimated mixing matrix

[0049] Moreover, in step 6, the point with a relative amplitude greater than the threshold T1 in the time-frequency domain of the observed signal is defined as a self-source point, and the specific calculation method is as follows:

[0050]

[0051] wherein, Ω asp denotes the self-source set, S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, and ||S x (t,f)|| denotes the amplitude of the time-frequency point of the observed signal, ​​T1 is a threshold value selected from a source point.

[0052] Moreover, all time-frequency points in the source point set Ω asp are combined into a vector z of MN asp ×1 in step 7.

[0053]

[0054] In the formula, z is a vectorized representation of the source point set, M represents the number of sensors, N asp represents the number of source points, represents the Mth channel of the mixed signal, and N asp represents the Nth time-frequency point.

[0055] The Kronecker product is calculated from the estimated mixing matrix and the unit matrix , and is mathematically represented as follows:

[0056]

[0057] In the formula, Ψ is a sparse observation matrix, represents the Kronecker product, represents a unit matrix of the shape N asp × N asp , and Δ MN represents a diagonal matrix of the shape N asp × N asp , whose diagonal elements are equal to the elements in the estimated mixing matrix

[0058] Based on the vectorized representation z of the source point set and the sparse observation matrix Ψ, a sparse recovery model is constructed as follows:

[0059]

[0060]

[0061] In the formula, λ≥0 is a regularization parameter for ensuring the sparsity of the solution; y represents the vectorized representation of the source signal, represents the L2 norm, and |||1 represents the L1 norm.

[0062] The application also provides a time-frequency domain underdetermined blind source separation system based on a double sensor, which is used for implementing the time-frequency domain underdetermined blind source separation method based on a double sensor.

[0063] Furthermore, it includes a processor and a memory, the memory being used to store program instructions, and the processor being used to call the program instructions in the memory to execute the time-frequency domain underdetermined blind source separation method based on dual sensors as described above.

[0064] Compared with the prior art, the present invention has the following advantages:

[0065] 1) It can be applied to both real and complex matrix estimation;

[0066] 2) Based on high-cluster single-source point estimation of the mixture matrix, it still achieves high-precision mixture matrix estimation even when there are many sources, severe time-frequency aliasing, and low signal-to-noise ratio of the observed signal;

[0067] 3) Source recovery based on the sparsity of self-source points can effectively handle the situation where the number of sources on self-source points is greater than the number of sensors, breaking the limitation of the number of self-source points on the traditional blind source separation algorithm and improving the source recovery effect of the dual-sensor underdetermined blind source separation algorithm. Attached Figure Description

[0068] Figure 1 This is a flowchart of an embodiment of the present invention.

[0069] Figure 2 shows the results of selecting the source points for the high clustering characteristics of the present invention. Figure 2(a) shows the selection of source points for the high clustering characteristics of the real number mixture matrix, and Figure 2(b) shows the selection of source points for the high clustering characteristics of the complex number mixture matrix. Detailed Implementation

[0070] This invention provides a time-frequency domain underdetermined blind source separation method and system based on dual sensors. It overcomes the problems of low accuracy in mixing matrix estimation and poor source recovery in existing blind source separation methods when the number of sources is large, the time-frequency overlap is high, and the number of sensors is small. The technical solution of this invention will be further described below using wireless communication signals as an example, in conjunction with the accompanying drawings and embodiments.

[0071] Example 1

[0072] like Figure 1 As shown, this invention provides a time-frequency domain underdetermined blind source separation method based on dual sensors, comprising the following steps:

[0073] Step 1: Convert the dual-channel observation signal to the time-frequency domain using a short-time Fourier transform.

[0074] This invention is based on the assumption of a linear instantaneous model. Assuming there are N sources and two sensors in the environment, the signal received by the sensor array can be expressed as:

[0075] x(t)=As(t)+n(t) (1)

[0076] In the formula, x(t) represents a double-channel observation signal, s(t) represents a source signal to be estimated, n(t) represents a noise signal, A represents a mixing matrix, and t represents time.

[0077] The double-channel observation signal is converted from the time domain to the time-frequency domain using a short-time Fourier transform algorithm, and the specific calculation is as follows:

[0078]

[0079] In the formula, S x (t,f) is a time-frequency representation of the observation signal after the short-time Fourier transform, e is a natural constant, π represents a circular constant, j represents a complex number, t and f represent time and frequency, x(τ) represents the τth sampling point of the observation signal, and h(τ-t) represents a Hamming window, the window length is set to 1024 sampling points, and the window shift is 256 sampling points in this embodiment.

[0080] Step 2: Selecting strong energy self-source points from the observation signal time-frequency points obtained in step 1.

[0081] A threshold T0 is set, and the points with a relative amplitude greater than the threshold T0 in the observation signal time-frequency domain are defined as strong energy self-source points, and the set of strong energy self-source points Ω sep which can be represented as follows:

[0082]

[0083] In the formula, S x (t,f) is a time-frequency representation of the observation signal after the short-time Fourier transform, ||S x (t,f)|| represents the amplitude of the observation signal time-frequency point, represents the time-frequency point with the largest amplitude in the observation signal time-frequency point, and T0 is the strong energy time-frequency point selection threshold, which is set to 0.2 in this embodiment.

[0084] The selection of the self-source points not only improves the robustness of the noise, but also reduces the computational complexity.

[0085] Step 3: Clustering the strong energy self-source points, taking the clustering centers of each class as the initial estimated direction vectors, and splicing the initial estimated direction vectors to obtain an initial spatial vector dictionary.

[0086] In this embodiment, the K-means clustering algorithm is used, and the number of clusters is set according to the simulation experiment results and the properties of the mixing matrix. If the mixing matrix is a real matrix, the number of clusters N0 is set to 16, and if the mixing matrix is a complex matrix, the number of clusters N0 is set to 6. The clustering centers after clustering are defined as the initial estimated direction vectors, and the mathematical representation of clustering the strong energy self-source points is as follows:

[0087]

[0088] wherein, denotes the cluster center of the nth class, which is also the direction vector corresponding to the time-frequency point of the nth class, denotes the time-frequency point of the nth cluster from the source point of strong energy, denotes the number of time-frequency points in denotes the direction vector corresponding to the (t,f)th time-frequency point, t and f denote time and frequency, and the union of all elements of each sub-class is Ω sep i.e.

[0089] Splicing to obtain the initial spatial vector dictionary Set the number of clusters to be greater than the number of sources, i.e. N0>N, as shown in FIG. 2, so as to ensure that the direction vectors of all sources are contained in the initial estimated mixing matrix, and at the same time, the multi-source point or low-cluster characteristic single-source point is gathered near the remaining classes, so as to improve the estimation accuracy of the direction vector of the single-source point.

[0090] Step 4: using the orthogonal matching pursuit algorithm to select the high-cluster characteristic single-source point from the source point of strong energy.

[0091] The orthogonal matching pursuit algorithm is used to perform the first decomposition on the source point of strong energy, and the specific calculation method is as follows:

[0092]

[0093] wherein, S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the cluster center of the nth class, denotes Moore-Penrose pseudo-inverse of corresponding to the nth1 source, denotes the value of that makes the expression take the minimum value, ||·|| denotes amplitude calculation.

[0094] The residual vector obtained by decomposing formula (5) is decomposed again to calculate the residual vector r (1) (t,f) after removing the nth1 source from the time-frequency point of strong energy, i.e.

[0095]

[0096] wherein, S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the cluster center of the nth class, denotes the Moore-Penrose pseudo-inverse of

[0097] decomposes the residual vector r (1) (t,f), i.e.,

[0098]

[0099] wherein, denotes the direction vector solved, denotes the clustering center of the nth class, denotes the Moore-Penrose pseudo-inverse of denotes the value of which makes the expression take the minimum value, and ||·|| denotes the amplitude calculation.

[0100] The direction vector solved by the secondary decomposition corresponds to the nth2 source existing in the strong energy time-frequency point, so S x The secondary decomposition of r(t,f) can be expressed as follows:

[0101]

[0102]

[0103]

[0104] wherein, S x (t,f) is the time-frequency representation of the observed signal after the short-time Fourier transform, C1 denotes the contribution of the nth1 source to the strong energy time-frequency point, denotes the direction vector solved by the first decomposition, C2 denotes the contribution of the nth2 source to the strong energy time-frequency point, denotes the direction vector solved by the second decomposition, r (2) (t,f) denotes the residual vector after the strong energy time-frequency point removes the source n1 and the source n2, and <·,·> denotes the inner product operation, denotes the Moore-Penrose pseudo-inverse of

[0105] For a single source point, theoretically C2≈0, but in the actual environment, due to noise interference, most time-frequency points are difficult to meet this condition, so the ratio of C1 to C2 is used for high clustering characteristic single source point determination, i.e.,

[0106]

[0107] wherein, T hcp ​​C1 and C2 represent the contribution of the n1th and n2th source to the strong energy time-frequency point respectively, S x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, C1 and C2 represent the contribution of the n1th and n2th source to the strong energy time-frequency point respectively, S C1 and C2 represent the contribution of the n1th and n2th source to the strong energy time-frequency point respectively, S Moore-Penrose pseudo-inverse of C1 and C2 represent the contribution of the n1th and n2th source to the strong energy time-frequency point respectively, S hcp is a set threshold.

[0108] The time-frequency point satisfying formula (11) is a high clustering single source point, and the high clustering characteristic single source point set is defined as Ω hcp The present application filters out most of the interference time-frequency points from the observed signal time-frequency domain through high clustering characteristic single source point detection, and realizes high-precision mixed matrix estimation.

[0109] Step 5, clustering the high clustering characteristic single source points, and taking the clustering center as the column vector of the estimated mixed matrix .

[0110] In this embodiment, K-means clustering algorithm is adopted, and the number of clusters is equal to the number of sources, that is, N0=N, and this embodiment takes the number of sources N=4 as an example, which is mathematically expressed as follows:

[0111]

[0112] In the formula, is the clustering center of the nth class, and is also the direction vector corresponding to the time-frequency point of the nth class, is the direction vector corresponding to the (t,f) time-frequency point, t and f represent time and frequency, is the time-frequency point of the nth cluster in the high clustering characteristic single source point, is the clustering center of the nth class, is the number of time-frequency points in hcp , that is, is spliced to obtain the estimated mixed matrix

[0113] Step 6, selecting self-source points from the observed signal time-frequency points obtained in step 1, and the self-source point set is denoted as Ω asp .

[0114] A threshold T1 is set, and the point with a relative amplitude greater than the threshold T1 in the observed signal time-frequency domain is defined as a self-source point, that is, a time-frequency point of at least one source, and the specific calculation method is as follows:

[0115] ​

[0116] Ω asp represents the set of self-source points, x (t,f) is the time-frequency representation of the observed signal after short-time Fourier transform, ||S x (t,f)|| represents the amplitude of the time-frequency point of the observed signal, represents the time-frequency point with the largest amplitude in the time-frequency points of the observed signal, T1 is the self-source point selection threshold, and T1 is set to 0.03 in the embodiment.

[0117] The self-source point detection step can filter out noise points in the time-frequency domain and reduce the computational complexity.

[0118] Step 7, vectorize the set of self-source points Ω asp and the estimated mixing matrix to construct a sparse recovery model for source separation.

[0119] Step 7, vectorize the set of self-source points Ω asp to form an MN asp ×1 vector z, which is mathematically represented as follows:

[0120]

[0121] In the formula, z is the vectorized representation of the set of self-source points, M represents the number of sensors, M=2 in the embodiment, N asp represents the number of self-source points, represents the Mth channel of the mixed signal. asp

[0122] The estimated mixing matrix and the identity matrix are used to calculate the Kronecker product, which is mathematically represented as follows:

[0123]

[0124] In the formula, Ψ is a sparse observation matrix, represents the Kronecker product, represents an identity matrix with a shape of N asp ×N asp , Δ mn (m=1,...,M,n=1,...,N) represents a diagonal matrix with a shape of N asp ×N asp , and the diagonal elements are equal to the elements in

[0125] Based on the vectorized representation z of the set of self-source points and the sparse observation matrix Ψ, the sparse recovery model is constructed as follows:​​

[0126]

[0127]

[0128] where λ≥0 is a regularization parameter to guarantee the sparsity of the solution; y represents the source signal in vectorized representation, denotes the L2 norm, and |||1 denotes the L1 norm.

[0129] Step 8, the sparse recovery model is solved by using a spectral projected gradient descent algorithm based on the L1 norm.

[0130] The present application adopts a spectral projected gradient descent algorithm based on the L1 norm (SPGL1) to solve the sparse recovery model in step 7.3 (formula (16)), and calculates the source signal y in vectorized representation, that is, the large-scale underdetermined problem can be effectively solved, and the algorithm is suitable for real number and complex number operations.

[0131] Step 9, the time-frequency domain source signal separated in step 8 is subjected to inverse short-time Fourier transform to obtain the separated source signal.

[0132] Embodiment Two

[0133] Based on the same inventive concept, the present application further provides a time-frequency domain underdetermined blind source separation system based on double sensors, which comprises a processor and a memory, the memory is used for storing program instructions, and the processor is used for calling the program instructions in the memory to execute the time-frequency domain underdetermined blind source separation method based on double sensors as described above.

[0134] The specific embodiments described herein are merely illustrative of the spirit of the present application. Those skilled in the art of the present application can make various modifications or supplements to the described specific embodiments or replace them with similar ways, without departing from the spirit of the present application or exceeding the scope defined by the appended claims.

Claims

1. A double-sensor based time-frequency domain underdetermined blind source separation method, characterized in that, The method comprises the following steps: Step 1, converting the double-channel observation signal to time-frequency domain by short-time Fourier transform; Step 2, selecting strong energy self-source points from the time-frequency points of the observation signal obtained in step 1; Step 3, clustering the strong energy self-source points, taking the clustering centers of each class as the initial estimated direction vectors, and splicing the initial estimated direction vectors to obtain an initial spatial vector dictionary; Setting the number of clusters according to the properties of the mixing matrix and let be greater than the number of sources N , define the cluster centers after clustering as the initial estimated direction vectors, and the mathematical representation of clustering from the source point with strong energy is as follows: （4） In the formula, represents the cluster center of the th class, and also represents the direction vector corresponding to the time-frequency point of the th class, represents the time-frequency point of the n th cluster from the source point of strong energy, represents the number of time-frequency points in , and represents time and frequency, represents the direction vector corresponding to the th time-frequency point, and the union of all elements of each sub-class is , that is, ; The initial spatial vector dictionary is obtained by splicing ;​ Step 4, selecting high clustering characteristic single-source points from the strong energy self-source points by using an orthogonal matching pursuit algorithm; Step 5. Cluster the high-clustered single-source points, using the cluster centers as the estimated mixing matrix column vectors. Let the number of clusters be equal to the number of sources N The mathematical representation of clustering a single-source point with high clustering characteristics is as follows: （12） In the formula, denotes the cluster center of the th class, and also the direction vector corresponding to the time-frequency point of the th class, denotes the time-frequency point of the th cluster in the high clustering characteristic single source point, denotes the number of time-frequency points in , and denotes time and frequency, denotes the direction vector corresponding to the th time-frequency point, and the union of all elements of each sub-class is , that is , and the splicing of obtains the estimated mixing matrix Step 6: Selecting self-source points from the time-frequency points of the observation signal obtained in Step 1, and the set of self-source points is denoted as ; Step 7, collect the source points from the source set and estimate the mixing matrix perform a vectorized representation, construct a sparse recovery model for source separation; Step 8, solving the sparse recovery model by using an L1 norm-based spectral projection gradient descent algorithm; Step 9, performing inverse short-time Fourier transform on the time-frequency domain source signals separated in step 8 to obtain separated source signals.

2. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 1, characterized in that: Based on the linear instantaneous model assumption in Step 1, assuming there are N two sensors in the environment, the signal received by the sensor array can be represented as: （1） wherein denotes the two-channel observation signal, denotes the source signal to be estimated, denotes the noise signal, denotes the mixing matrix, t denotes time; The double-channel observation signal is converted from time domain to time-frequency domain by using a short-time Fourier transform algorithm, and the specific calculation manner is as follows: （2） wherein is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the k-th sample point of the observed signal, denotes the Hamming window, denotes the natural constant, e denotes the complex number, denotes the natural constant, denotes the circular constant, and denotes time and frequency.

3. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 2, characterized in that: In step 2, the relative amplitude of the observed signal in the time-frequency domain is defined to be greater than a threshold. The point is a strong energy self-source point, and the set of strong energy self-source points. It is expressed as follows: （3） wherein is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the amplitude of the time-frequency point of the observed signal, denotes the time-frequency point with the largest amplitude in the time-frequency point of the observed signal, is the threshold for the selection of the strong energy time-frequency point.

4. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 1, wherein: In step 4, the strong energy self-source points are decomposed for the first time by using an orthogonal matching pursuit algorithm, and the specific calculation manner is as follows: （5） wherein, denotes the value of the expression that minimizes denotes the magnitude calculation, is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the cluster center of the th class, denotes the Moore-Penrose pseudo-inverse of the direction vector corresponding to the strong energy time-frequency point exists theth source; The residual vector obtained by decomposing equation (5) is decomposed again to calculate the strong energy time-frequency point to remove the residual vector after the source That is:​ （6） wherein is a time-frequency representation of the observed signal after short-time Fourier transform, denotes the cluster center of the th class, denotes the Moore-Penrose pseudo-inverse; to the residual vector decomposition, i.e.: （7） wherein denotes the solved direction vector, denotes the value of the expression which is minimized denotes the magnitude calculation, denotes the cluster center of the denotes the Moore-Penrose pseudo inverse;​​ The direction vector obtained by quadratic decomposition The existence of the first high-energy time-frequency point. One source, therefore The quadratic decomposition of can be expressed as follows: （8） （9） （10） In the formula, This is the time-frequency representation of the observed signal after short-time Fourier transform. Indicates the first The contribution of each source to this high-energy time-frequency point. This represents the direction vector obtained from the first decomposition. Indicates the first The contribution of each source to this high-energy time-frequency point. This represents the direction vector obtained from the second decomposition. This indicates that the source is removed from the high-energy time-frequency point. Heyuan The residual vector after This represents the inner product operation. express Moore-Penrose pseudo-reverse.

5. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 4, characterized in that: The high clustering characteristic single-source point determination in step 4 is performed by using the ratio of and , that is: （11） wherein, denotes the clustering characteristic from the source point, denotes the contribution of the th source to the strong energy time-frequency point, denotes the contribution of the th source to the strong energy time-frequency point, is the time-frequency representation of the observed signal after short-time Fourier transform, denotes the direction vector solved by the first decomposition, denotes the inner product operation, denotes the Moore-Penrose pseudo-inverse of denotes the direction vector solved by the second decomposition, is a set threshold value;​ The time-frequency point satisfying formula (11) is a high clustering single-source point, and a high clustering characteristic single-source point set is defined as .

6. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 2, characterized in that: Step 6 defines the relative amplitude of the observed signal in the time-frequency domain that is greater than a threshold. The point is the source point, and the specific calculation method is as follows: （13） wherein, denotes a set of source points, is a time-frequency representation of the observed signal after a short-time Fourier transform, denotes the amplitudes of the time-frequency points of the observed signal, denotes the time-frequency point with the largest amplitude among the time-frequency points of the observed signal, is a threshold for selecting source points.

7. The double-sensor based time-frequency domain underdetermined blind source separation method according to claim 6, characterized in that: Step 7 combines all time-frequency points from the source point set into one vector z, mathematically represented as follows: （14） where z is a vector representation of the source point set, M represents the number of sensors, represents the number of source points, represents the i-th time-frequency point of the j-th channel of the mixed signal, M represents the i-th time-frequency point of the j-th channel of the mixed signal, represents the i-th time-frequency point of the j-th channel of the mixed signal, from the estimated mixing matrix with the identity matrix the Kronecker product is calculated, mathematically represented as follows: （15） In the formula, For sparse observation matrices, Indicates the Kronecker product. Indicates shape as The identity matrix, Indicates shape as The diagonal matrix whose diagonal elements are equal to the estimated mixture matrix. elements in ; Vectoring representation based on a set of self-source points and a sparse observation matrix , a sparse recovery model is constructed as follows: （16） （17） wherein is a regularization parameter for ensuring sparsity of the solution; denotes the source signal in vectorized representation, denotes the L2 norm, denotes the L1 norm.

8. A two-sensor based time-frequency domain underdetermined blind source separation system, characterized in that, The method comprises a processor and a memory, the memory is used for storing program instructions, and the processor is used for calling the program instructions in the memory to execute the double-sensor-based time-frequency domain underdetermined blind source separation method according to any one of claims 1-7.

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