Multi-element microphone array sound source localization method based on GS-RBF and time delay estimation

Abstract

The invention relates to a multivariate microphone array sound source localization method based on GS-RBF and time delay estimation, and belongs to the technical field of sound source localization, and the method comprises the following steps: S1, building a near-field model of a fault sound source, and carrying out the design of a microphone array; s2, calculating a time difference of arrival (TDOA) matrix based on a generalized cross-correlation phase transformation algorithm GCPHAT; s3, constructing a sound source localization model based on an RBF neural network; and S4, optimizing the sound source positioning model based on a grid search algorithm GS, and positioning the sound source by using the optimized model. According to the method, the rapidity and accuracy of fault sound source positioning during unmanned aerial vehicle inspection are ensured, the anti-noise performance and the spatial resolution capability in a complex environment are considered, and an efficient and reliable technical solution is provided for detection of hidden faults of the power transmission line.

Description

Technical Field

[0001] The invention belongs to the technical field of sound source localization, and relates to a multi-microphone array sound source localization method based on GS-RBF and time delay estimation. Background Art

[0002] The safe and stable operation of transmission lines is the basic guarantee for the reliability of power systems. Traditional transmission line inspections mostly rely on manual inspections, which are inefficient and limited by the experience of inspectors and the complexity of the on-site environment. There are certain safety hazards and risks of missed inspections.

[0003] To solve the above problems, sound source localization technology has gradually become one of the key means of detecting hidden faults in transmission lines. The acoustic signal generated by partial discharge has strong specificity. Sound source localization technology can accurately locate partial discharge faults through spatial positioning and time delay analysis of acoustic signals, significantly improving the detection capability of hidden defects. The design of the acoustic field sensor array is crucial to the performance of the sound source localization system, and the geometric structure of the sensor array directly affects the accuracy and scope of application of the sound source localization. Existing studies have shown that reasonable array geometry design can improve the robustness and accuracy of positioning in complex background noise and multipath interference environments.

[0004] There are many traditional methods for sound source localization based on microphone arrays, such as the time delay difference based sound source localization algorithm (TDOA), the sound source localization method based on maximum output power controllable beamforming (GCC), the sound source localization method based on high-resolution spectrum estimation (MUSIC), etc. Among them, the sound source localization algorithm based on time delay difference is widely used in many fields because of its simple principle and real-time positioning. However, the TDOA positioning algorithm usually needs to solve a nonlinear equation group, especially in the case of multiple sensors, the amount of calculation may be very large. With the development of machine learning, the emergence of neural networks provides a good solution to complex nonlinear problems. In 2006, Harbin Institute of Technology proposed a sound source localization method based on neural networks. By simulating the sound source position of multiple microphone arrays, the neural network is used to estimate the position of the sound source, achieving high-precision sound source localization. In 2014, Shanghai Jiaotong University proposed the use of convolutional neural networks (CNN) for sound source localization. Studies have shown that this method can significantly improve the accuracy of sound source localization in complex environments. In 2021, the Korea Advanced Institute of Science and Technology proposed a sound source localization method based on the radial basis function (RBF) neural network. Through RBF network training, the estimation of the sound source position was optimized, especially in the case of high environmental noise. RBF (Radial Basis Function) neural network has the characteristics of short training time and high nonlinear mapping characteristics. Using RBF neural network as an algorithm tool has become an efficient solution. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a multi-microphone array sound source localization method based on GS-RBF and time delay estimation, using a two-dimensional multi-microphone array to adapt to the characteristics of wide bandwidth and high signal-to-noise ratio in the transmission line detection scene, and for the near-field spherical sound source model, a sound source localization method combining the generalized cross-correlation phase transform (GCC_PHAT) algorithm is proposed, and accurate positioning is achieved by calculating the arrival time difference (TDOA) matrix combined with the RBF neural network model optimized by the grid search algorithm (GS). This method takes into account the noise resistance and spatial resolution in complex environments, and provides an efficient and reliable technical solution for the detection of hidden faults in transmission lines.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A multi-microphone array sound source localization method based on GS-RBF (Grid Search-Radial basis function) and time delay estimation comprises the following steps:

[0008] S1: Establish a near-field model of the fault sound source and design the microphone array;

[0009] S2: Calculate the time difference of arrival (TDOA) matrix based on the generalized cross correlation phase transform algorithm GCC_PHAT (Generalized Cross Correlation Phase Transform);

[0010] S3: Construct a sound source localization model based on RBF neural network;

[0011] S4: Optimize the sound source localization model based on the grid search algorithm GS, and use the optimized model to locate the sound source.

[0012] Furthermore, the near-field model of the fault sound source is established in step S1, and the microphone array is designed, which specifically includes the following steps:

[0013] S11: The Fresnel zone formula is used to divide the use range of near-field sources and far-field sources, and the near-field model of the fault sound source is constructed:

[0014]

[0015] Where: r is the distance from the sound source to the sensor; D is the array aperture; λ is the wavelength of the sound source;

[0016] S12: Design of circular microphone array configuration based on fault sound source model:

[0017]

[0018] Where: N is the number of microphones; R is the array radius; (x n ,y n ) is the Cartesian coordinate of the nth microphone.

[0019] Further, the arrival time difference TDOA matrix is ​​calculated based on the generalized cross-correlation phase transform algorithm GCC_PHAT, including the following steps:

[0020] S21: Using an N-element microphone array (M1, M2...M N ) synchronously collects the sound source signal in the space and obtains the corresponding time domain discrete signals x1(n), x2(n)…x N (n);

[0021] S22: Time domain signal x for each pair of microphones i (n) and x j (n)(i,j[1,8],i≠j) performs fast Fourier transform FFT and converts it to the frequency domain to obtain the frequency domain signal representation:

[0022]

[0023] In the formula is Fourier transform;

[0024] S23: Then calculate the cross power spectrum function:

[0025]

[0026] In the formula For X j (ω) conjugation;

[0027] S24: Smooth coherence weighting is performed on the cross power spectrum in the frequency domain to suppress noise and reverberation interference, and finally an inverse Fourier transform is performed to obtain the cross correlation function:

[0028]

[0029] In the formula is the weighting function in the frequency domain;

[0030] S25: Introduce appropriate weighting function according to the actual environment and the characteristics of the received signal;

[0031] S26: In the cross-correlation function R ij (τ) to search for the delay time τ corresponding to the maximum peak max , as the time delay difference TDOA of the two signals:

[0032]

[0033] In the formula, τ ij is the delay output corresponding to the two paths i and j, To find the operation of τ corresponding to the maximum value of the objective function;

[0034] S27: According to the number of microphone array elements, the time delay estimation value τ of all microphone pairs is calculated. ij Organized as a symmetric TDOA matrix T N×N ,in:

[0035]

[0036] Furthermore, the PHAT weighting function is introduced in step S25, and the specific expression is as follows:

[0037]

[0038] Further, the step S3 constructs a sound source localization model based on an RBF neural network, specifically comprising the following steps:

[0039] S31: Extract the upper triangular part of the TDOA matrix to obtain the TDOA features between the microphone pairs, and use the TDOA features as network input samples; the network input sample expression is:

[0040]

[0041] In the formula, is the kth input sample, x kn is the nth element extracted from the upper triangular part of the TDOA matrix in the kth input sample;

[0042] S32: After determining the input sample, select the hidden layer function as a Gaussian function:

[0043]

[0044] In the formula, Euclidean norm, σ is the variance of the Gaussian function, is the center vector of the radial basis function of the i-th hidden node;

[0045] S33: The network output can be obtained by weighted summing according to the activation values ​​in the hidden layer:

[0046]

[0047] Where y is the actual output value of the neural network, w i is the weight from the i-th node in the hidden layer to the output layer, and m is the number of hidden nodes;

[0048] S34: Setting the width spread hyperparameter of the radial basis function, inputting the input sample into the RBF neural network for network training to establish a sound source localization model.

[0049] Further, the step S4 described in which the sound source localization model is optimized based on the grid search algorithm GS specifically includes the following steps:

[0050] S41: List the possible values ​​of the hyperparameter spread to be adjusted for the RBF neural network;

[0051] S42: Use the model prediction mean square error MSE to evaluate the model performance, the expression is:

[0052]

[0053] Where y i is the true value of the i-th sample, is the predicted value of the i-th sample, and n is the number;

[0054] S43: traverse all spread values ​​and perform cross-validation for each spread value;

[0055] S44: According to the cross-validation result, the spread value with the lowest model prediction mean square error (MSE) is selected as the optimal spread value, which is used as the final hyperparameter of the sound source localization model finally established based on the RBF neural network.

[0056] The beneficial effects of the present invention are as follows: the present invention ensures the rapidity and accuracy of locating the fault sound source during drone inspection, takes into account the anti-noise performance and spatial resolution capability in complex environments, and provides an efficient and reliable technical solution for the detection of hidden faults in power transmission lines.

[0057] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0059] Figure 1 This is a flow chart of the sound source localization method of the present invention;

[0060] Figure 2 configuring a microphone array;

[0061] Figure 3 This is the GCC_PHAT algorithm block diagram;

[0062] Figure 4 It is the RBF neural network structure;

[0063] Figure 5 The grid search algorithm (GS) process is 3000 for the number of simulated sound sources;

[0064] Figure 6 The BP neural network prediction results for the number of simulated sound sources of 3000;

[0065] Figure 7 RBF neural network prediction results for 3000 simulated sound sources. DETAILED DESCRIPTION

[0066] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0067] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0068] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0069] See also Figure 1 to Figure 7 , Figure 1 It is a flow chart of the method of the present invention, such as Figure 1 As shown, the present invention provides a sound source localization method of a multi-microphone array based on a GS-RBF neural network and a time delay estimation algorithm, comprising the following steps:

[0070] Step S1: Establish a two-dimensional eight-element circular microphone array configuration and a near-field fault sound source model:

[0071]

[0072] Where: R is the array radius; (x n ,y n ) is the Cartesian coordinate of the nth microphone.

[0073] Step S2: Using an 8-element microphone array (M1, M2...M8) to obtain the corresponding time domain discrete signals x1(n), x2(n)...x8(n), and obtaining the TDOA matrix based on the GCC_PHAT algorithm, specifically including the following steps:

[0074] S21: Use an N-element microphone array (M1, M2...M8) to synchronously collect sound source signals in the space to obtain corresponding time-domain discrete signals x1(n), x2(n)...x8(n).

[0075] S22: Time domain signal x for each pair of microphones i (n) and x j (n)(i,j∈[1,8],i≠j) is transformed into the frequency domain by fast Fourier transform (FFT) to obtain the frequency domain signal representation:

[0076]

[0077] In the formula is the Fourier transform.

[0078] S23: Then the cross power spectrum function can be obtained:

[0079]

[0080] In the formula For X j (ω) is the conjugate.

[0081] S24: In order to sharpen the peak of the cross-correlation function, the cross-power spectrum is smoothed and coherently weighted in the frequency domain to suppress noise and reverberation interference. Finally, the inverse Fourier transform is performed to obtain the cross-correlation function:

[0082]

[0083] In the formula is the weighting function in the frequency domain.

[0084] S25: In practical applications, a suitable weighting function is introduced according to the actual environment and the characteristics of the received signal. The PHAT weighting function is introduced here, which has strong anti-interference and anti-noise capabilities and can improve the accuracy of delay estimation when the signal-to-noise ratio is high. The specific expression is as follows:

[0085]

[0086] S26: In the cross-correlation function R ij (τ) to search for the delay time τ corresponding to the maximum peak max , as the time delay difference (TDOA) of the two signals:

[0087]

[0088] In the formula, τ ij is the delay output corresponding to the two paths i and j, To find the operation of τ corresponding to the maximum value of the objective function.

[0089] S27: Finally, according to the number of microphone array elements, the time delay estimation value τ of all microphone pairs is calculated. ij Organized as a symmetric TDOA matrix T 8×8 ,in:

[0090]

[0091] Step S3: Establishing a sound source localization model based on the RBF neural network, specifically including the following steps:

[0092] S31: Extract the upper triangular part of the TDOA matrix (i.e. remove the elements on the main diagonal and below it), obtain the TDOA features between the microphone pairs, and use the TDOA features as network input samples. The network input sample expression is:

[0093]

[0094] In the formula, is the kth input sample, x kn is the nth element extracted from the upper triangular part of the TDOA matrix for the kth input sample.

[0095] S32: After determining the input sample, select the hidden layer function as a Gaussian function:

[0096]

[0097] In the formula, Euclidean norm, σ is the variance of the Gaussian function, is the center vector of the radial basis function (Gaussian function) of the i-th hidden node.

[0098] S33: The network output can be obtained by weighted summing according to the activation values ​​in the hidden layer:

[0099]

[0100] Where y is the actual output value of the neural network, wi is the weight from the i-th node in the hidden layer to the output layer, and m is the number of hidden nodes.

[0101] S34: Setting the “spread” hyperparameter of the radial basis function, inputting the input sample into the RBF neural network for network training to establish a sound source localization model.

[0102] Step S4: Optimizing the sound source localization model based on a grid search algorithm (GS), specifically comprising the following steps:

[0103] S41: List the possible values ​​of the hyperparameter spread of the RBF neural network to be adjusted, and set the spread to take 30 possible values ​​in the range of 0.1 to 2.

[0104] S42: Select the model prediction mean square error (MSE) to evaluate the model performance. The mean square error (MSE) expression is:

[0105]

[0106] Where y i is the true value of the i-th sample, is the predicted value of the i-th sample, and n is the number.

[0107] S43: Traverse all spread values, perform cross-validation for each spread value, and select the cross-validation fold number as 5, that is, perform 5-fold cross-validation.

[0108] S44: According to the 5-fold cross validation result, the spread value with the lowest model prediction mean square error (MSE) is selected as the optimal spread value, which is used as the final hyperparameter of the sound source localization model established based on the RBF neural network.

[0109] Experimental verification:

[0110] 500, 1000, 1500, 2000, and 3000 simulated sound source samples were randomly generated to establish a sound source localization model based on the RBF neural network. The simulated sound source samples were randomly generated in the Oxyz three-dimensional space: x∈[-2,2], y∈[-2,2], z∈[0,2]. All simulated sound source samples were calculated based on the GCC_PHAT to obtain the TDOA matrix, and then the upper triangular part of the TDOA was extracted as the TDOA feature. The data was divided according to the ratio of 70% training set, 15% validation set, and 15% test set, and the input samples were normalized. After the optimal spread value was obtained using the grid search optimization algorithm, the input samples were input into the RBF neural network for training. At the same time, the sound source localization model based on the BP neural network was established for the above five sample quantities, and the root mean square error of the sound source localization model based on the GS-RBF neural network and the sound source localization model based on the BP neural network was compared to further illustrate the accuracy of the sound source localization of the present invention.

[0111] Table 1 lists the optimal spread values ​​obtained by the grid search algorithm (GS) under five simulated sound source numbers. It can be seen that the optimal spread value decreases when the number of samples is large. Figure 5 Taking 3000 simulated sound sources as an example, the grid search algorithm (GS) process is demonstrated, and the figure shows the change of model prediction error with the spread value. Table 2 lists the test root mean square error (RMSE) values ​​of the sound source localization model established based on the two neural networks under five simulated sound source numbers. It can be seen that the test root mean square error of the sound source localization model based on the GS-RBF neural network under all five simulated sound source numbers is lower than the root mean square error of the sound source localization model based on the BP neural network. Figure 6 and Figure 7 Taking 3000 simulated sound sources as an example, the training results of the sound source localization model based on two neural networks are demonstrated.

[0112] Table 1

[0113] Sample size 500 1000 1500 2000 3000 Optimal spread value 0.231 0.3621 0.1 0.1 0.1655

[0114] Table 2

[0115]

[0116] In the above embodiments, the description's reference to "this embodiment" indicates that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily all refer to the same embodiment.

[0117] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.

[0118] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, any one of the methods in this embodiment is implemented.

[0119] This embodiment also provides an electronic terminal, including: a processor and a memory;

[0120] The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the terminal executes any one of the methods in this embodiment.

[0121] The computer-readable storage medium in this embodiment can be understood by ordinary technicians in this field: all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When the program is executed, the execution includes the steps of the above-mentioned method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

[0122] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication with each other. The memory is used to store computer programs, the communication interface is used to communicate, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes each step of the above method.

[0123] In this embodiment, the memory may include a random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0124] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0125] The present invention can be used in many general or special computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.

[0126] The present invention may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media, including storage devices.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A multi-microphone array sound source localization method based on GS-RBF and time delay estimation, characterized in that: The following steps are involved: S1: Establish a near-field model of the fault sound source and design the microphone array; S2: Calculate the arrival time difference TDOA matrix based on the generalized cross-correlation phase transform algorithm GCC_PHAT; S3: Construct a sound source localization model based on RBF neural network; S4: Optimize the sound source localization model based on the grid search algorithm GS, and use the optimized model to locate the sound source.

2. The multi-microphone array sound source localization method based on GS-RBF and time delay estimation according to claim 1, characterized in that: The step S1 of establishing a near-field model of the fault sound source and designing a microphone array specifically includes the following steps: S11: The Fresnel zone formula is used to divide the use range of near-field sources and far-field sources, and the near-field model of the fault sound source is constructed: Where: r is the distance from the sound source to the sensor; D is the array aperture; λ is the wavelength of the sound source; S12: Design of circular microphone array configuration based on fault sound source model: Where: N is the number of microphones; R is the array radius; (x n ,y n ) is the Cartesian coordinate of the nth microphone.

3. The multi-microphone array sound source localization method based on GS-RBF and time delay estimation according to claim 1, characterized in that: The time difference of arrival TDOA matrix is ​​calculated based on the generalized cross-correlation phase transform algorithm GCC_PHAT, including the following steps: S21: Using an N-element microphone array (M1, M2...M N ) synchronously collects the sound source signal in the space and obtains the corresponding time domain discrete signals x1(n), x2(n)…x N (n); S22: Time domain signal x for each pair of microphones i (n) and x j (n)(i,j∈[1,8],i≠j) performs fast Fourier transform FFT and converts it to the frequency domain to obtain the frequency domain signal representation: In the formula is Fourier transform; S23: Then calculate the cross power spectrum function: In the formula For X j (ω) conjugation; S24: Smooth coherence weighting is performed on the cross power spectrum in the frequency domain to suppress noise and reverberation interference, and finally an inverse Fourier transform is performed to obtain the cross correlation function: In the formula is the weighting function in the frequency domain; S25: Introduce appropriate weighting function according to the actual environment and the characteristics of the received signal; S26: In the cross-correlation function R ij (τ) to search for the delay time τ corresponding to the maximum peak max , as the time delay difference TDOA of the two signals: In the formula, τ ij is the delay output corresponding to the two paths i and j, To find the operation of τ corresponding to the maximum value of the objective function; S27: According to the number of microphone array elements, the time delay estimation value τ of all microphone pairs is calculated. ij Organized as a symmetric TDOA matrix T N×N ,in:

4. The multi-microphone array sound source localization method based on GS-RBF and time delay estimation according to claim 1, characterized in that: The PHAT weighting function is introduced in step S25, and the specific expression is as follows:

5. The multi-microphone array sound source localization method based on GS-RBF and time delay estimation according to claim 1, characterized in that: Step S3 constructs a sound source localization model based on an RBF neural network, specifically comprising the following steps: S31: Extract the upper triangular part of the TDOA matrix to obtain the TDOA features between the microphone pairs, and use the TDOA features as network input samples; the network input sample expression is: In the formula, is the kth input sample, x kn is the nth element extracted from the upper triangular part of the TDOA matrix in the kth input sample; S32: After determining the input sample, select the hidden layer function as a Gaussian function: In the formula, Euclidean norm, σ is the variance of the Gaussian function, is the center vector of the radial basis function of the i-th hidden node; S33: The network output can be obtained by weighted summing according to the activation values ​​in the hidden layer: Where y is the actual output value of the neural network, w i is the weight from the i-th node in the hidden layer to the output layer, and m is the number of hidden nodes; S34: Setting the width spread hyperparameter of the radial basis function, inputting the input sample into the RBF neural network for network training to establish a sound source localization model.

6. The multi-microphone array sound source localization method based on GS-RBF and time delay estimation according to claim 1, characterized in that: Step S4 optimizes the sound source localization model based on the grid search algorithm GS, specifically including the following steps: S41: List the possible values ​​of the hyperparameter spread to be adjusted for the RBF neural network; S42: Use the model prediction mean square error MSE to evaluate the model performance, the expression is: Where y i is the true value of the i-th sample, is the predicted value of the i-th sample, and n is the number; S43: traverse all spread values ​​and perform cross-validation for each spread value; S44: According to the cross-validation result, the spread value with the lowest model prediction mean square error (MSE) is selected as the optimal spread value, which is used as the final hyperparameter of the sound source localization model finally established based on the RBF neural network.

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