Robust super-directional beam forming method and system based on Kronecker product

Abstract

The invention provides a robust super-directional beam forming method and system based on a Kronecker product. Inherent inter-frame correlation between adjacent frames of a voice signal in a short-time Fourier transform domain is introduced into robust super-directional beam forming: firstly, a signal model observed by a microphone array is expressed as a Kronecker product form containing a steering vector and an inter-frame correlation vector, and the steering vector is determined by a geometric structure of the array; the inter-frame correlation vector can be obtained by adopting three methods of time-invariant long-time estimation, time-varying recursive adaptive estimation or data-driven deep learning estimation. And then designing a super-directional beam former into a Kronecker product of a time domain filter and a spatial domain filter, optimizing the time domain filter to realize maximization of white noise gain, and optimizing the spatial domain filter to realize maximization of directional gain. Compared with a traditional scheme, the noise suppression robustness is remarkably improved through combination of time-space domain optimization, and better noise reduction performance is shown in a complex acoustic environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of speech signal processing, and mainly relates to a robust super-directional beamforming method based on a Kronecker product in a short-time Fourier transform domain applied to a microphone array. Background Art

[0002] In the fields of voice communication and human-computer interaction, speech is not only a vehicle for conveying rich information but also a key medium for expressing emotion and intent. However, in practical applications, speech signals are often affected by various factors, such as ambient noise, interference, and room reverberation. These factors significantly reduce speech clarity and intelligibility, thereby affecting communication efficiency. In such situations, microphone arrays, leveraging the synergistic effect of multiple microphones, can effectively extract the desired speech signals from complex acoustic environments. This offers significant advantages in improving the accuracy of speech recognition systems and enhancing the clarity of voice communications.

[0003] Beamforming, a key component of array signal processing, uses directional beamforming to enhance speech signals in the target direction and suppress interference and noise in non-target directions, significantly improving speech signal quality and overall system performance. In many applications, it is desirable for the beamformer to maximize suppression of signals from other directions while preserving the desired signal without distortion. Super-directional beamformers effectively meet this requirement. By maximizing directional gain, they achieve a very narrow beamwidth, enabling the array to precisely focus on sound sources in a specific direction, resulting in higher directional selectivity.

[0004] However, since the super-directional beamformer is very sensitive to the self-noise of the array, the white noise gain at low frequencies is very low, which limits its application in practice. To address the above challenges, a commonly used strategy is to diagonally load the normalized covariance matrix of the noise, namely robust super-directional beamforming. This strategy increases the robustness of the system by sacrificing the high directivity characteristics of the array, but at the same time it will cause the frequency-invariant characteristics of the beam pattern to be lost, which can easily cause distortion of broadband speech signals. Therefore, the present invention will further explore and optimize the robust super-directional microphone array beamforming technology to provide a more effective solution for far-field sound pickup technology in complex acoustic environments. Summary of the Invention

[0005] This paper addresses the drawback of current robust super-directional beamformers, which amplify white noise at low frequencies, by providing a robust super-directional beamforming method based on the Kronecker product in the short-time Fourier transform domain. Compared to traditional super-directional beamformers, this method exploits the time-frequency correlation of the signal between consecutive frames, achieving higher signal-to-noise ratio gains in a variety of noise environments.

[0006] The present invention proposes a robust super-directional beamforming method based on the Kronecker product. By expressing the robust super-directional beamformer as the Kronecker product of a time-domain filter and a spatial-domain filter, this method fully utilizes both the time-domain and spatial-domain information of the signal, thereby significantly improving the performance of the super-directional beamformer. The time-domain filter primarily considers the inter-frame correlation of the signal, while the spatial-domain filter focuses on the inter-channel correlation of the signal. During the filter optimization process, the present invention optimizes the time-domain filter by maximizing the white noise gain, while simultaneously optimizing the spatial-domain filter with the goal of maximizing the directional gain. To address the problem of obtaining the inter-frame correlation vector in the time-domain filter, the present invention innovatively proposes three estimation methods: time-invariant long-time estimation, time-varying recursive adaptive estimation, and data-driven deep learning estimation. These three methods each have their own advantages and can be flexibly selected according to different scenarios and requirements. The inter-frame correlation vectors estimated by the above three methods are applied to the robust super-directional beamforming process. In a variety of complex noise environments, they can achieve better noise reduction performance than traditional methods, providing a more reliable solution for applications in related fields.

[0007] The technical solution of the present invention is a robust super-directional beamforming method based on Kronecker product in the short-time Fourier transform domain, comprising the following steps: Step 1: Perform short-time Fourier transform on the multi-channel time-domain noisy signal received by the microphone array and convert it into a frequency-domain signal. The number of microphones in the array is denoted as M , the frequency points are recorded as K , the frame length is recorded as N , then the size of the frequency domain signal is .

[0008] Step 2: Consider the previous time-frequency point related to the current frequency domain observation signal. L time frames, the frequency domain observation signal model of the microphone array is expanded into the form of Kronecker product containing the steering vector and the inter-frame correlation vector. The size of the new model is The length of the steering vector is M , the length of the inter-frame correlation vector is L .

[0009] Step 3: Decompose the beamformer into time and space. The super-directional beamformer is designed as the Kronecker product of the time filter and the spatial filter. The time filter is calculated by maximizing the white noise gain, and the spatial filter is calculated by maximizing the directivity. During the beamforming process, the signal from the desired direction is also guaranteed to pass without distortion. The length of the time filter is L , the length of the spatial filter is M .

[0010] Step 4: Estimate the inter-frame correlation vector. Since the optimal design of the temporal filter is highly dependent on the accuracy of the inter-frame correlation vector, in practical applications, only noisy microphone array observation signals are available, making it impossible to directly calculate the inter-frame correlation of the clean speech signal. To address this technical bottleneck, the present invention proposes three innovative estimation methods to achieve inter-frame correlation vector estimation based on noisy signals: (a) A time-invariant long-term estimation method: This method uses a long-term average to obtain a steady-state estimate of the inter-frame correlation vector based on the first two seconds of the current noisy speech segment and applies this estimate to the entire speech segment. This method is suitable for scenarios with a stable acoustic environment. (b) A time-varying recursive adaptive estimation method: This method calculates the inter-frame correlation vector for each time-frequency point of the noisy signal and updates the inter-frame correlation vector online by introducing a forgetting factor. This method dynamically tracks the time-varying characteristics of the speech signal and is suitable for non-stationary noise environments. (c) A data-driven deep learning estimation method: This method uses a deep learning network to first predict a clean signal from the noisy signal. Time-invariant long-term estimation or time-varying recursive adaptive estimation is then performed based on the predicted clean signal.

[0011] Step 5: Beamform the multi-channel noisy signal. The Kronecker product-based robust super-directional beamformer constructed in step 3 is used to perform spatiotemporal filtering on the noisy signal observed by the extended microphone array constructed in step 2 to obtain a frequency domain output signal, including: Traverse each frame of the frequency domain signal of the microphone array, for each frame of the frequency domain signal, traverse each frequency point, intercept the frequency point of the current frame and the frequency point of the forward frame. L The frequency points corresponding to the time frames constitute the target signal; the robust super-directional beamformer is used to perform weighted filtering on the target signal to obtain the corresponding frequency domain output signal.

[0012] Step 6: inversely transforming the frequency domain output signal into a time domain output signal, including: converting the frequency domain output signal into a time domain output signal by using an inverse short-time Fourier transform technology.

[0013] Based on the same inventive concept, the present invention also provides an electronic device, comprising: one or more processors; a storage device for storing one or more programs; When one or more programs are executed by the one or more processors, the one or more processors are caused to implement the Kronecker product-based robust super-directive beamforming method.

[0014] Based on the same inventive concept, the present invention further designs a computer-readable medium having a computer program stored thereon, and when the program is executed by a processor, the robust super-directional beamforming method based on the Kronecker product is implemented.

[0015] Compared with the prior art, the present invention has the following beneficial effects: By decomposing the robust super-directional beamformer into a time-domain filter and a spatial-domain filter, the two sub-filters achieve maximum suppression of white noise and diffuse noise, respectively. The proposed filter achieves better signal-to-noise ratio gain than traditional methods in various noise environments. In addition, the present invention innovatively proposes three inter-frame correlation vector estimation methods based on noisy signals, including time-invariant long-term estimation, time-varying recursive adaptive estimation, and data-driven deep learning estimation. These methods improve the adaptability and robustness of the beamformer for different noise scenarios. In addition, the present invention systematically compares the proposed robust super-directional beamforming method based on the Kronecker product with traditional super-directional beamforming methods. Experimental results show that the proposed method exhibits superior performance in key indicators such as signal-to-noise ratio gain and speech quality perception evaluation. In particular, the beamformer corresponding to the time-varying recursive adaptive estimation performs better than the beamformer corresponding to the time-invariant long-term estimation, but the computational complexity is relatively high. In summary, the present invention has significant advantages in noise suppression and signal-to-noise ratio improvement, and provides new ideas and methods for the development of robust super-directional beamforming technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention provides a flow chart of a robust super-directional beamforming method based on Kronecker product.

[0017] Figure 2 Schematic diagram of a uniform linear microphone array provided in an embodiment of the present invention.

[0018] Figure 3 This is an error analysis when the inter-frame correlation vector is estimated in a time-invariant manner using a noisy signal and a clean signal respectively in an embodiment of the present invention.

[0019] Figure 4 The performance of four fixed robust super-directional beamformers (the estimation of their inter-frame correlation vectors corresponds to a time-invariant method) in the embodiments of the present invention under diffuse noise, white noise, and interference noise environments.

[0020] Figure 5 This is an error analysis when adaptively estimating an inter-frame correlation vector using a noisy signal and a clean signal respectively in an embodiment of the present invention.

[0021] Figure 6 The performance of two adaptive beamformers and two fixed beamformers in the embodiment of the present invention under diffuse noise and white noise environments.

[0022] Figure 7 This is the FullSubNet network architecture used in the embodiment of the present invention to predict the complex ideal ratio mask using a data-driven deep learning method.

[0023] Figure 8 This is a performance comparison of the data-driven deep learning method used in the embodiment of the present invention to predict the inter-frame correlation vector with the time-invariant and time-varying methods. DETAILED DESCRIPTION

[0024] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0025] Example 1 The flowchart of the robust super-directional beamforming method proposed in the present invention is as follows: Figure 1 shown.

[0026] First, the signal is collected and STFT transformed. As shown in Figure 2, there is a space composed of M The uniform linear array (ULA) is composed of omnidirectional microphone sensors. The end-fire direction of the microphone array is 0°. According to the ideal propagation model, the incoming wave direction is θ The steering vector is denoted as , Indicates the frequency index. Taking the first microphone as the reference microphone, the m The time delay of the sound source signal observed by each microphone relative to the reference microphone is: (1) in is the time delay between the signal incident from the end-fire direction of the array to the adjacent microphone array elements, represents the distance between adjacent microphones, represents the speed of sound. At this time, the steering vector Written as: (2) in, is the sampling frequency, j is the imaginary unit, , K is the total number of frequency points of Fourier transform. Beamforming is the process of weighting and summing the signals received by each microphone as the output. The size of the weight is related to the direction of the wave of the desired signal, so that the array has different gains for signals from different directions in space, thereby performing spatial filtering. Beamforming usually constrains the signal to be in the desired direction. The above is passed without distortion, that is: (3) in is the beamformer, Equivalent to exist The value of when.

[0027] Microphone receiving signal It can be expressed in the short-time Fourier transform domain as: (4) in, represents the timeframe index, Indicates the The observation signal of the microphone. and represent the clean signal vector and noise signal vector received by the microphone array, respectively, and and Not relevant.

[0028] Without loss of generality, the present invention assumes that the incident direction of the desired sound source signal is , and its corresponding steering vector is simply written as The signal model is: (5) in, Represents the desired sound source signal received by the reference microphone.

[0029] In the short-time Fourier transform domain, the present invention attempts to use the correlation information of adjacent time frames to better estimate the clean signal. L time frames, formula (5) is expanded to: (6) in, represents the Kronecker product, (7) Formula (7) is the length of L vector, and Is the length of The vector of The definitions are similar. The present invention assumes that: (8) in, Is the length of L The inter-frame correlation vector of is independent of frequency. Therefore, equation (6) can be written as: (9) That is, the observation signal of the microphone array can be expressed as the Kronecker product of the steering vector and the inter-frame correlation vector.

[0030] Based on the signal model constructed by Equation (9), a robust super-directional beamformer based on Kronecker product is designed. , which is represented as a time domain filter and spatial filters The Kronecker product: (10) in, Is the length of L The time domain filter, Is the length of M The enhanced signal Expressed as: (11) Based on the above derivation, various beamformers can be designed in theory. In order to achieve a trade-off between white noise gain and directivity factor, the present invention obtains a time domain filter by maximizing the white noise gain. , the spatial filter is obtained by maximizing the directivity factor Based on this, the super-pointing beamformer It can be expressed as: (12) in, (13) in, is the normalized covariance matrix under isotropic noise environment: (14) The Kronecker product-based robust super-directional beamformer constructed by equation (12) is used to perform spatiotemporal filtering on the noisy signal observed by the extended microphone array constructed in equation (6) to obtain a frequency domain output signal; then, an inverse short-time Fourier transform (iSTFT) is performed to obtain the final enhanced time domain signal.

[0031] In the above process, the inter-frame correlation vector The estimation of is crucial to the performance of the beamformer. This invention innovatively proposes three estimation methods for the inter-frame correlation vector and introduces them into equation (12).

[0032] First, considering the wide-band stationary characteristics of speech signals, we assume that the inter-frame correlation vector is time-invariant, which is also the simplest approach. Previous methods usually directly obtain the inter-frame correlation vector from the clean signal: (15) in, is the expected signal vector received by the reference microphone, as shown in equation (7), is the conjugate representation of the desired sound source signal received by the reference microphone. Mathematical expectation Approximated by short-time averaging, T Indicates the total number of frames involved in the average calculation.

[0033] However, in real-world scenarios, clean speech signals are often difficult to obtain directly. One feasible approach is to use pre-recorded clean speech signals to estimate the inter-frame correlation vector and apply it to other signals. However, the inter-frame correlation vector estimated in this way may not be compatible with other speech signals, thereby affecting the performance of the final beamformer. The present invention proposes to estimate the inter-frame correlation vector directly based on the noisy signal. For each speech, the inter-frame correlation vector is calculated by taking the first two seconds of the noisy signal received by the reference microphone: (16) in, is the noisy signal vector received by the reference microphone, and The definition is similar to It means that the reference microphone receives the conjugate noisy signal, and it is easy to get: (17) Is the length of L The error vector is very difficult to estimate in real scenes. The present invention simplifies the estimation to a certain extent: Assuming that the background noise only contains Gaussian white noise, then (18) in, and are the energies of the clean signal and noise, respectively, is a unit vector whose first element is 1 and the rest are all 0. is the SNR estimate received by the reference microphone. According to formula (18): (19) Thus we get: (20) Analyzing formula (20), as the input signal-to-noise ratio As the error vector Gradually decreases. When it is very large, it can be considered = The present invention also performs and The mean-squared error (MSE) between (twenty one) in, represents the Euclidean norm, The MSE of 20 speech signals is averaged. The simulation results are as follows: Figure 3 As shown, L = 4. Similarly, MSE decreases as the input signal-to-noise ratio increases.

[0034] The inter-frame correlation vector obtained by the time-invariant long-time estimation method is applied to the designed super-pointing beamformer, and its performance is as follows: Figure 4 As shown in Figure 2. Where MDF represents the traditional robust super-directional beamformer , as shown in formula (13); KP-RMDF-AI represents the first robust super-directional beamformer based on Kronecker product proposed in this paper , a pre-recorded 10 s clean speech signal is used to estimate the inter-frame correlation vector, which is uniformly applied to all other signals; KP-RMDF-A-II represents the second Kronecker product-based robust super-directional beamformer proposed in this paper , whose inter-frame correlation vector is calculated by the clean signal of the first 2 seconds of each speech, and then applied to the entire speech itself, corresponding to formula (15), which represents an ideal situation; KP-RMDF-A-III represents the third Kronecker product-based robust super-directional beamformer proposed in this invention , whose inter-frame correlation vector is calculated from the noisy signal 2 seconds before each speech, and then applied to the entire speech itself, corresponding to Equation (16). Sub-figures (a), (b), and (c) respectively show the signal-to-noise ratio gains of the four beamformers in diffuse noise, interference noise, and white noise environments. The experimental settings are: M = 6, = 0.01m, = 0.32 s, the input SNR is [10, 15] dB in the diffuse noise and interference noise environments, and the input SNR is [20, 25] dB in the white noise environment.

[0035] However, the above time-invariant method cannot fully capture the time-varying characteristics of the signal. A more effective method is to estimate the inter-frame correlation vector in an adaptive manner, ideally recursively from the clean signal: (twenty two) Among them, 0< <1 indicates a forgetting factor. is a vector The first element of =

[0036] It is worth noting that since the inter-frame correlation vector is time-varying, the obtained robust super-directional beamformer is also time-varying, that is, an adaptive beamformer.

[0037] Similarly, the inter-frame correlation vector can be recursively calculated from the noisy signal observed by the microphone: (twenty three) in, = In the description of the time-invariant part, the ideal inter-frame correlation vector estimated by the clean signal is modeled as the sum of the inter-frame correlation vector estimated by the noisy signal and the error vector. Similarly, in the Gaussian white noise environment, it is easy to obtain: (twenty four) in, Indicates the signal at the time-frequency point ( k ,t ) at the input signal-to-noise ratio, when When it is larger, it can be seen as: . Similar to formula (21), the present invention also calculates and The MSE between Figure 5 Shows the mean of the MSE of 20 voices over time frames t The three broken lines correspond to different input signal-to-noise ratios. It can be seen that the higher the input signal-to-noise ratio, and The smaller the MSE between them.

[0038] Substituting the inter-frame correlation vector obtained by time-varying adaptive recursive estimation into equation (12), we get the adaptive beamformer. Its performance is compared with the fixed beamformer obtained by the time-invariant method, as shown in Figure 6 As shown. KP-RMDF-BI represents the first adaptive beamformer based on Kronecker product. , whose inter-frame correlation vector is related to the time frame and is obtained recursively from the clean speech, corresponding to formula (22), which represents an ideal situation; KP-RMDF-B-II represents the second adaptive beamformer based on Kronecker product , whose inter-frame correlation vector is recursively obtained from the noisy signal, corresponding to Equation (23). Sub-figures (a) and (b) show the signal-to-noise ratio gains of the four beamformers in diffuse noise and white noise environments, respectively. The experimental settings are: M = 6, = 0.01m, = 0.32 s, =0.2. The input SNR is [10, 15] dB in a diffuse noise environment and [20, 25] dB in a white noise environment. As can be seen, the adaptive beamformer achieves significantly higher SNR gains than the fixed beamformer, but at the expense of higher computational complexity.

[0039] In addition to time-invariant long-term estimation and time-varying recursive adaptive estimation, the present invention also proposes to use a data-driven deep learning method to estimate the inter-frame correlation vector. Specifically, the present invention adopts the FullSubNet network structure, such as Figure 7 As shown in Figure 2. The architecture consists of a fullband block for capturing global cross-band dependencies and a subband block for extracting time-varying features. The network is trained to predict the complex ideal ratio mask (cIRM) from the reference microphone observation signal. Its input is defined as follows: (25) (26) in, Indicates that the noisy signal received by the first microphone (i.e., the reference microphone) is k Frequency point, t The magnitude of the STFT coefficients for each time frame, is a hyperparameter that controls the number of adjacent time-frequency units considered in sub-band modeling. The output of the network is the predicted value of cIRM, The clean signal estimated by the network is expressed as follows: (27) in, represents the Hadamard product.

[0040] Clean signal estimated based on the network Calculate the inter-frame correlation vector, including the time-invariant long-time estimate in Equation (15) (using the first two seconds of clean speech estimation The two methods are KP-RMDF-CI and KP-RMDF-C-II, respectively. Figure 8 (a) and (b) represent the signal-to-noise ratio gains of the fixed beamformer and the adaptive beamformer in a diffuse noise environment, respectively. The experimental settings are: M = 6, = 0.01m, = 0.32 s, = 0.2, and the input SNR in a diffuse noise environment is [10, 15] dB. As can be seen, the performance of KP-RMDF-CI is between KP-RMDF-A-II and KP-RMDF-A-III, and the performance of KP-RMDF-C-II is between KP-RMDF-BI and KP-RMDF-B-II, which is in line with expectations.

[0041] The three estimation methods can be used in different scenarios and can be selected based on specific needs. The time-invariant method is suitable for scenarios with stable acoustic environments and high real-time processing requirements. The time-varying method dynamically tracks the time-varying characteristics of the speech signal and is suitable for non-stationary noise environments. The third deep learning method has the highest computational complexity, but it is more accurate than the first two methods because it uses the noisy signal y to estimate the inter-frame correlation vector.

[0042] In general, the present invention utilizes the correlation between adjacent frames in the STFT domain and proposes an innovative robust super-directional beamforming method, which fuses the time domain filter and the spatial domain filter through the Kronecker product, optimizes the time domain filter by maximizing the white noise gain, and optimizes the spatial domain filter by maximizing the directivity factor. Among them, this method faces a key challenge, namely the estimation of the inter-frame correlation vector. The present invention proposes three correlation vector estimation methods: time-invariant long-time estimation method, time-varying adaptive recursive estimation method and data-driven deep learning method. The simulation experimental results verify the advantages of the proposed method. The method provides a new idea for achieving robust and high-performance beamforming and has good practical application potential.

[0043] Example 2 Based on the same inventive concept, the present invention also provides an electronic device, comprising one or more processors; a storage device for storing one or more programs; when one or more programs are executed by the one or more processors, the one or more processors implement the method described in Example 1.

[0044] Since the device described in the second embodiment of the present invention is an electronic device used to implement the robust super-directional beamforming method based on the Kronecker product in the first embodiment of the present invention, those skilled in the art will be able to understand the specific structure and variations of the electronic device based on the method described in the first embodiment of the present invention, and therefore will not be described in detail here. All electronic devices used in any of the methods in the embodiments of the present invention fall within the scope of protection of the present invention.

[0045] Example 3 Based on the same inventive concept, the present invention further provides a computer-readable medium having a computer program stored thereon, which implements the method described in the first embodiment when the program is executed by a processor.

[0046] Since the device described in Example 3 of the present invention is a computer-readable medium used to implement the robust super-directional beamforming method based on the Kronecker product in Example 1 of the present invention, those skilled in the art will be able to understand the specific structure and variations of the electronic device based on the method described in Example 1 of the present invention, and therefore will not be described in detail here. All electronic devices used in a method of an embodiment of the present invention fall within the scope of protection of the present invention.

[0047] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A robust super-directional beamforming method based on Kronecker product, characterized by: Perform short-time Fourier transform on the multi-channel time-domain noisy signal received by the microphone array and convert it into a frequency-domain signal; The frequency domain observation signal model is expanded into a Kronecker product form containing a steering vector and an inter-frame correlation vector; Design the beamformer as a Kronecker product of a time-domain filter and a spatial-domain filter; estimating inter-frame correlation vectors; Perform beamforming processing on frequency domain signals; Inversely transform the frequency domain output signal into a time domain output signal.

2. The robust super-directional beamforming method based on Kronecker product according to claim 1, wherein: The design of the beamformer includes optimizing the time domain filter by maximizing the white noise gain and optimizing the spatial domain filter by maximizing the directivity factor.

3. The Kronecker product-based robust super-directional beamforming method according to claim 1, wherein: The estimation of the inter-frame correlation vector adopts a time-invariant long-term estimation method, which specifically includes: obtaining a steady-state estimation value of the inter-frame correlation vector based on the first two seconds of the current noisy speech segment through long-term averaging; and applying the steady-state estimation value to the entire speech segment.

4. The robust super-directional beamforming method based on Kronecker product according to claim 1, wherein: The estimation of the inter-frame correlation vector adopts a time-varying recursive adaptive estimation method, which specifically includes: calculating the inter-frame correlation vector of each time-frequency point of the noisy signal; and updating the inter-frame correlation vector online by introducing a forgetting factor.

5. The robust super-directional beamforming method based on Kronecker product according to claim 1, wherein: The estimation of the inter-frame correlation vector adopts a data-driven deep learning estimation method, which specifically includes: using a deep learning network to predict a clean signal from a noisy signal; and performing time-invariant long-term estimation or time-varying recursive adaptive estimation based on the predicted clean signal.

6. The Kronecker product-based robust super-directional beamforming method according to claim 5, wherein: The deep learning network adopts a FullSubNet network structure, which includes a full-band module and a sub-band module, and is used to predict the complex ideal ratio mask from the reference microphone observation signal.

7. The robust super-directional beamforming method based on Kronecker product according to claim 1, wherein: The specific implementation of the beamforming process is: Iterate over each frame of the frequency domain signal of the microphone array; For each frame of frequency domain signal, traverse each frequency point, intercept the frequency point of the current frame and the corresponding frequency point at the previous L time frames to form the target signal; The beamformer is used to perform weighted filtering on the target signal to obtain a frequency domain output signal.

8. The robust super-directional beamforming method based on Kronecker product according to claim 1, wherein: The frequency domain output signal is converted into a time domain signal through inverse short-time Fourier transform.

9. An electronic device, characterized in that: include: one or more processors; a storage device for storing one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the robust super-directive beamforming method based on Kronecker product as claimed in any one of claims 1 to 8.

10. A computer-readable medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the robust super-directional beamforming method based on Kronecker product according to any one of claims 1 to 8 is implemented.

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