Joint estimation of signal direction and number of sources

Abstract

The application discloses a kind of broadband signal direction and source number joint estimation method, system and equipment, belong to electric power system field, the method is: based on the manifold matrix of multiple frequency overcomplete array, the frequency domain data received by underwater acoustic array is converted into sparse representation model;Based on probability model iteration, so that the probability model according to the frequency domain data, the manifold matrix of the multiple frequency overcomplete array and gamma distribution shape parameter, each sparse signal is iteratively updated, and the current spatial power vector and current gamma distribution rate vector of each sparse signal in the probability model, until meeting the iteration termination condition, output spatial power estimation vector and source number estimate;Linear approximation post-processing is carried out based on the spatial direction point corresponding to the spatial power estimation vector, and the direction estimation result of the broadband signal is obtained, so that the accuracy of broadband signal direction and source number estimation result can be improved by implementing the application.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic detection, and in particular to a method, system, and device for jointly estimating broadband signal direction and the number of signal sources. Background Technology

[0002] Underwater acoustic array direction finding is a core technology in the field of underwater passive detection. It uses a hydrophone array to receive acoustic signals radiated by underwater targets and estimate the direction of arrival of the target waves, making it important for applications in marine monitoring and underwater communication. However, the underwater environment is complex, the received signals usually have broadband characteristics (including multiple frequency points), and the number of signal sources is often unknown, which poses a significant challenge to traditional direction finding methods.

[0003] In current research on broadband underwater acoustic direction finding, the classic subspace method requires prior knowledge of the number of signal sources and does not consider the joint estimation of the direction of the broadband underwater acoustic signal and the number of signal sources. Moreover, the estimation of the number of signal sources usually relies on information theory criteria (such as AIC, MDL) or eigenvalue decomposition. These methods have low accuracy in low signal-to-noise ratio and multi-source overlapping scenarios and are difficult to adapt to the multi-frequency characteristics of broadband signals. Summary of the Invention

[0004] This invention provides a method, system, and device for jointly estimating the direction and number of broadband signals, which can solve the problem of low estimation accuracy in underwater acoustic passive detection scenarios with unknown signal-to-noise ratio and multi-frequency superposition scenarios.

[0005] This invention provides a joint estimation method for broadband signal direction and source number, comprising:

[0006] The frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points are obtained, and the frequency domain data is transformed into a sparse representation model based on the multi-frequency overcomplete array manifold matrix. The multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points.

[0007] The iteration is based on a probabilistic model, which iteratively updates each sparse signal according to the frequency domain data, the multi-frequency overcomplete array manifold matrix, and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probabilistic model, until the iteration termination condition is met, and outputs a spatial power estimation vector and a source number estimation value. The probabilistic model includes a multi-level prior probability distribution of each sparse signal and a conditional probability distribution of the frequency domain data.

[0008] The direction estimation result of the broadband signal is obtained by performing linear approximation post-processing based on the spatial direction point corresponding to the spatial power estimation vector.

[0009] In this embodiment of the invention, the multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors for multiple frequency points, which can fully capture the characteristics of broadband signals at different frequency points. Transforming the frequency domain data into a sparse representation model makes the signal sparse in spatial direction, facilitating subsequent estimation of the signal direction. The probabilistic model of multi-level prior probability distribution and conditional probability distribution can comprehensively consider the relationship between the signal's prior information and the observed data. By iteratively updating the sparse signal and the associated spatial power vector and gamma distribution rate vector, the estimation results are continuously optimized, making the estimated value gradually approach the true value. Finally, linear approximation post-processing is performed on the spatial direction points corresponding to the spatial power estimation vector, which can further improve the accuracy of direction estimation, reduce grid deviation, and thus obtain more accurate broadband signal direction estimation results.

[0010] Further, the step of iteratively updating each of the sparse signals, and the current spatial power vector and current gamma distribution rate vector of each of the sparse signals in the probability model, based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, and the gamma distribution shape parameters, specifically involves:

[0011] In each iteration of the probability model, based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power, and the noise variance, each sparse signal is updated to obtain the updated sparse signal, and the current frequency domain mean matrix and the current frequency domain covariance matrix corresponding to the updated sparse signal are determined.

[0012] Based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector, the current spatial domain power vector is updated to obtain the updated spatial domain power vector. Based on the updated spatial domain power vector and the gamma distribution shape parameter, the current gamma distribution rate vector is updated to obtain the updated gamma distribution rate vector.

[0013] Multiple spectral peaks are extracted from the updated spatial power vector. The multi-frequency likelihood function increment is calculated based on the updated spatial power vector and spatial direction point corresponding to each spectral peak. The number of information sources is estimated based on the increment to obtain the estimated number of information sources.

[0014] The noise variance is updated based on the estimated number of sources to obtain the updated noise variance, and then the next iteration is performed based on the updated spatial power vector, the updated noise variance, and the gamma distribution shape parameters.

[0015] This approach, which updates the sparse signal based on frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power, and the noise variance, better reflects the sparsity characteristics of the signal at different frequency points, providing a more accurate foundation for subsequent parameter updates. Updating the spatial power vector using the current frequency domain mean matrix, the current frequency domain covariance matrix, and the gamma distribution rate vector, and then updating the gamma distribution rate vector based on the updated spatial power vector and the gamma distribution shape parameters, allows for a more accurate reflection of the signal's power distribution and sparsity, thus improving estimation accuracy. Extracting spectral peaks from the updated spatial power vector and calculating the multi-frequency likelihood function increment based on these peaks to estimate the number of signal sources more accurately determines the number of signal sources. Simultaneously, updating the noise variance based on the number of signal sources further improves the accuracy of noise estimation, thereby optimizing the entire estimation process.

[0016] Further, the step of extracting multiple spectral peaks from the updated spatial power vector, calculating the multi-frequency likelihood function increment based on the updated spatial power vector and spatial direction point corresponding to each spectral peak, and estimating the number of sources based on the increment to obtain the estimated number of sources, specifically involves:

[0017] In the updated spatial power vector, each of the spectral peaks is arranged in descending order of amplitude, and a preset number of target spectral peaks are determined from the multiple spectral peaks arranged in descending order.

[0018] Calculate the first and second intermediate factors related to the target spectral peak, spatial direction point, and spatial power, and estimate the number of sources by positive increment based on the increment of the multi-frequency likelihood function.

[0019] In this way, in the updated spatial power vector, spectral peaks correspond to directions with stronger signal energy. By extracting spectral peaks, the possible directions of signal sources can be preliminarily determined. Calculating the likelihood function increment at multiple frequencies based on the updated spatial power vector and spatial direction points corresponding to each spectral peak allows for a comprehensive consideration of signal characteristics at different frequencies, resulting in a more accurate estimation of the number of signal sources. Only when the likelihood function increment is positive is the corresponding spectral peak considered a valid signal source direction, thus estimating the number of signal sources based on the number of positive increments. This method avoids misidentifying noise or interference signals as signal sources, improving the reliability of signal source estimation.

[0020] Furthermore, the probability model is specifically as follows:

[0021] In the first-level prior probability distribution, for each snapshot corresponding to each frequency point, it is determined that each sparse signal column follows a probability density with a mean of zero and a variance equal to the current spatial power vector. The probability densities corresponding to all sparse signal columns are multiplied to obtain the first prior probability distribution value. The first-level prior probability distribution is a prior probability distribution used to characterize the sparse signal.

[0022] In the second-level prior probability distribution, for each power element in the spatial power vector, the first gamma distribution probability density when each power element follows the first parameter and the current gamma distribution rate vector is determined, and the first gamma distribution probability density corresponding to all power elements is multiplied to obtain the second prior probability distribution value of the current spatial power vector. The second-level prior probability distribution is used to characterize the prior probability distribution of the current spatial power vector.

[0023] In the third-level prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density when each rate element follows the gamma distribution shape parameter is determined. The second gamma distribution probability densities corresponding to all rate elements are multiplied to obtain the third prior probability distribution value corresponding to the current gamma distribution rate vector. The third-level prior probability distribution is used to characterize the prior probability distribution of the current gamma distribution rate vector. The distribution of the current gamma distribution rate vector in the second-level prior probability distribution is controlled by the current gamma distribution shape parameter in the third-level prior probability distribution. The variance of the current spatial power in the first-level prior probability distribution is controlled by the current gamma distribution rate vector in the second-level prior probability distribution.

[0024] In the conditional probability distribution, for each snapshot corresponding to each frequency point, it is determined that each frequency data column follows a complex Gaussian distribution probability density with a mean of the product of the multi-frequency overcomplete array manifold matrix and the corresponding sparse signal column, and the second covariance matrix corresponding to the frequency data is the product of the noise variance and the identity matrix. The conditional probability densities corresponding to all frequency data columns are multiplied together to obtain the conditional probability distribution value, wherein the conditional probability distribution value is used to evaluate the degree of matching between the frequency data and the sparse representation model.

[0025] Thus, through the first-layer prior probability distribution, for each snapshot corresponding to each frequency point, it is determined that the sparse signal sequence follows a probability density with a mean of zero and a variance equal to the current spatial power vector. The probability densities corresponding to all sparse signal sequences are multiplied to obtain the first prior probability distribution value. This distribution characterizes the sparsity of the sparse signal, providing prior information for subsequent updates. Through the second-layer prior probability distribution, for each power element in the spatial power vector, it is determined that it follows a first gamma distribution probability density when it conforms to the first parameter and the current gamma distribution rate vector. The first gamma distribution probability densities corresponding to all power elements are multiplied to obtain the second prior probability distribution value. This layer reflects the distribution characteristics of spatial power and further constrains the update of spatial power. Through the third-layer prior probability distribution, for each rate element in the current gamma distribution rate vector, it is determined that it follows a second gamma distribution probability density when it conforms to the gamma distribution shape parameter. The second gamma distribution probability densities corresponding to all rate elements are multiplied to obtain the third prior probability distribution value. This layer controls the distribution of the gamma distribution rate vector through the gamma distribution shape parameter, thereby indirectly affecting the update of spatial power. By using conditional probability distributions, for each snapshot at each frequency point, the corresponding frequency domain data column is determined to follow a complex Gaussian distribution with a mean of the product of the multi-frequency overcomplete array manifold matrix and the corresponding sparse signal column, and a second covariance matrix that is the product of the noise variance and the identity matrix. The conditional probability distribution value is obtained by multiplying the conditional probability densities corresponding to all frequency domain data columns. This distribution can assess the degree of matching between the frequency domain data and the sparse representation model, providing information from observational data for iterative updates.

[0026] Further, the step of updating the current spatial power vector based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector to obtain an updated spatial power vector, and then updating the current gamma distribution rate vector based on the updated spatial power vector and the gamma distribution shape parameters to obtain an updated gamma distribution rate vector, specifically:

[0027] The current frequency domain mean matrix is:

[0028]

[0029] The diagonal elements of the current frequency domain covariance matrix are:

[0030]

[0031] Γ = diag(γ);

[0032]

[0033] in, This represents the mean of the sparse signal at frequency f. For frequency domain data at frequency f, n k ∈{1,...,N}, (∑ f ) nn Represents matrix ∑ f The element in the nth row and nth column, yes The conjugate transpose of the matrix. Let f be the matrix of the multi-frequency overcomplete array manifold at frequency f. Let γ be the current spatial power vector. n It is the power element in the current spatial power vector, σ 2 Let σ be the noise variance. 2 I M Let U be the second covariance matrix. f ) n· It is matrix U f The nth row element, It is a matrix The element in the nth column;

[0034] The updated spatial power vector is,

[0035]

[0036] The updated gamma distribution rate vector is:

[0037]

[0038] Where N is the number of spatial direction points, F is the number of frequency points, L is the frequency domain snapshot, and h is the gamma distribution shape parameter.

[0039] By using information such as the mean of the sparse signal at a given frequency, frequency domain data, and the diagonal elements of the current frequency domain covariance matrix, the diagonal elements of the current frequency domain mean matrix and the current frequency domain covariance matrix are calculated, providing accurate statistical information for subsequent parameter updates. Based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the gamma distribution rate vector, the spatial power vector is updated using a specific formula, which can more accurately reflect the power distribution of the signal in different spatial directions. Based on the updated spatial power vector and the gamma distribution shape parameters, the gamma distribution rate vector is updated using a specific formula, further optimizing the estimation of the gamma distribution rate vector and making the entire probability model more consistent with the characteristics of the actual signal.

[0040] Further, the step of calculating the increment of the multi-frequency likelihood function based on the first intermediate factor and the second intermediate factor specifically involves:

[0041]

[0042] in, This represents the estimated number of information sources. and These are the first intermediate factor and the second intermediate factor, representing spatial direction points. Spatial power The relevant function values, Card represents the increment of the likelihood function at multiple frequencies, and card represents the number of k that satisfy the set conditions.

[0043] Based on the updated spatial power vector and spatial direction points, function values ​​related to these spatial direction points are calculated, yielding the first and second intermediate factors. These two factors reflect the signal characteristics in different directions, providing a foundation for calculating the likelihood function increment. Based on the first and second intermediate factors, multi-frequency likelihood function increments are calculated using specific formulas. By considering information from multiple frequency points, the signal characteristics can be more comprehensively evaluated, thereby improving the accuracy of source number estimation. Only when the likelihood function increment is positive is the corresponding spectral peak considered a valid signal source direction, thus estimating the source number based on the number of positive increments. This method effectively avoids misjudgments and improves the reliability of source number estimation.

[0044] Furthermore, the probability model is used to attach strong sparse prior constraints to the signal, specifically as follows:

[0045]

[0046] in, This is the current spatial power vector. is the current gamma distribution rate vector, and h is the gamma distribution shape parameter. express The prior probability density function of γ is the first-level prior probability distribution; P(γ|ξ) represents the probability density function of γ, which is the second-level prior probability distribution; and P(ξ|h) represents the probability density function of the gamma distribution rate parameter ξ, which is the third-level prior probability distribution. express The conditional probability density function. X represents f The l-th column follows a complex Gaussian distribution with mean 0 and variance γ. Indicates γ n Obey parameters and ξ n The gamma distribution, Gamma(ξ) n |h,h) represents ξ n It follows a gamma distribution with parameter h. The mean is covariance matrix σ 2 IM The complex Gaussian distribution, σ 2 Let γ be the noise variance. Before the iteration of the probability model begins, initialize the hyperparameter γ. (0) =1 N×1 ξ (0) =1 N×1 , The parameter h is fixed at 0.1.

[0047] By providing specific forms of the prior probability density function, the probability density function, and the conditional probability density function, including the complex Gaussian distribution followed by the sparse signal train, the gamma distribution followed by the power element, and the gamma distribution followed by the rate element, the probability model becomes more consistent with the characteristics of the actual signal.

[0048] Furthermore, the spatial power estimation vector based on the... After linear approximation and post-processing of the corresponding spatial direction points, the direction estimate of the broadband signal is obtained, specifically:

[0049]

[0050] in, It is the direction estimate of the k-th signal direction. They are the first The two largest and second largest power values ​​among the spectral peaks. They are and The corresponding grid point orientation.

[0051] This linear approximation post-processing utilizes the power information of two adjacent grid points, estimating the direction through a weighted average, which further improves the accuracy of direction estimation. In complex signal environments, signal direction estimation may be affected by noise and other interference. Linear approximation post-processing can reduce the impact of these interferences on direction estimation through smoothing, thereby enhancing the robustness of the method.

[0052] Another embodiment of the present invention provides a joint estimation system for broadband signal direction and number of sources, comprising: a sparse module, an iterative module, and an estimation module;

[0053] The sparse module is used to acquire frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points, and to convert the frequency domain data into a sparse representation model based on the multi-frequency overcomplete array manifold matrix. The multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points.

[0054] The iterative module is used to perform iteration based on a probability model, so that the probability model iteratively updates each of the sparse signals according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each of the sparse signals in the probability model, until the iteration termination condition is met, and outputs a spatial power estimation vector and a source number estimation value, wherein the probability model includes a multi-level prior probability distribution of each of the sparse signals and a conditional probability distribution of the frequency domain data;

[0055] The estimation module is used to perform linear approximation post-processing based on the spatial direction point corresponding to the spatial power estimation vector to obtain the direction estimation result of the broadband signal.

[0056] This invention, through a multi-frequency overcomplete array manifold matrix including overcomplete array manifold vectors at multiple frequency points, can fully capture the characteristics of broadband signals at different frequency points. Transforming frequency domain data into a sparse representation model makes the signal spatially sparsity, facilitating subsequent signal direction estimation. The probabilistic model using multi-level prior probability distributions and conditional probability distributions comprehensively considers the relationship between prior information of the signal and observed data. By iteratively updating the sparse signal and related spatial power vectors and gamma distribution rate vectors, the estimation results are continuously optimized, gradually approximating the true values. Finally, linear approximation post-processing is applied to the spatial direction points corresponding to the spatial power estimation vector, further improving the accuracy of direction estimation, reducing grid deviation, and thus obtaining more accurate broadband signal direction estimates.

[0057] Another embodiment of the present invention provides a terminal device, including: a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the steps of the joint estimation method for broadband signal direction and number of sources as described in the present invention. Attached Figure Description

[0058] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0059] Figure 1 This is a flowchart illustrating a joint estimation method for broadband signal direction and number of sources provided in an embodiment of the present invention;

[0060] Figure 2 This is a schematic diagram of a normalized spatial spectrum estimation result provided in an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram illustrating the variation of orientation estimation results with signal-to-noise ratio provided by an embodiment of the present invention;

[0062] Figure 4 This is a schematic diagram illustrating the variation of the source number estimate with the signal-to-noise ratio, provided by an embodiment of the present invention.

[0063] Figure 5 This is a schematic diagram of the structure of a joint estimation system for broadband signal direction and number of signal sources provided in an embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0065] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0066] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0067] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0068] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0069] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).

[0070] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0071] See Figure 1 To address the shortcomings of existing methods for jointly estimating the direction and number of broadband signals, which suffer from low accuracy in low signal-to-noise ratio and multi-source overlapping scenarios, and are difficult to adapt to the multi-frequency characteristics of broadband signals, an embodiment of the present invention provides a method for jointly estimating the direction and number of broadband signals, comprising steps S101-S103, specifically including:

[0072] Step S101: Obtain frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points, and convert the frequency domain data into a sparse representation model based on the multi-frequency overcomplete array manifold matrix, wherein the multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points.

[0073] In this embodiment, an underwater acoustic array (such as a uniform linear array) composed of M hydrophones (array elements) is used to receive underwater broadband signals. For example, a 10-element uniform linear sonar array with an element spacing of 1m and a sampling frequency of 3kHz is used. The broadband signal includes multiple frequency components (such as 500Hz to 1000Hz). The true incident directions of three broadband white noise signals with a frequency range of 500-1000Hz are -10.7°, 5.3°, 15.5° = 5dB, and the frequency domain signal-to-noise ratio (SNR) is 0dB. Since the underwater broadband signal is a time-domain signal, the received time-domain signal is preprocessed (e.g., anti-aliasing filtering) to obtain the original time-domain data. Then, a Fourier transform (such as a Fast Fourier Transform, FFT) is used to convert the time-domain data to frequency-domain data, and F frequency points of interest (denoted as f = f1, ..., f) are selected. F For example, selecting a frequency point f = [500, 550, 600, 700, 750, 800, 850, 900, 950, 1000] Hz, and extracting the frequency domain data at each selected frequency point from the broadband signal received by the underwater acoustic array. Among them, Y f It is an M×L dimensional matrix (L is the number of frequency domain snapshots), where each element in the frequency domain data represents the signal amplitude and phase information of a certain array element and a certain snapshot at that frequency point.

[0074] Predefine spatial direction points and establish the multi-frequency overcomplete array manifold matrix corresponding to frequency f. Specifically, within the possible signal wave direction range (e.g., -60° to 60°), N spatial direction points are divided at preset intervals (e.g., 2°), denoted as... For each frequency point f, calculate the corresponding spatial direction point at that frequency point. array manifold vectors in, For an M×1 dimensional complex vector, such as the array manifold vector in a uniform linear array. The m-th element can be represented as:

[0075]

[0076] In the formula, j is the imaginary unit.

[0077] Multi-frequency overcomplete array manifold matrix The array manifold vector for all frequency points The set encompasses the spatial characteristics of broadband signals across the entire frequency domain. This includes all array manifold vectors at each frequency point f. Arranged column-wise, the spatial overcomplete array manifold matrix at frequency f in the multi-frequency overcomplete array manifold matrix is ​​obtained, denoted as:

[0078]

[0079] If the number of array elements is M=10, the frequency domain snapshot is L=19, and N=91 is selected as the number of spatial direction points to be estimated, the grid points... The overcomplete array manifold matrix corresponding to this frequency point can be expressed as:

[0080]

[0081] Frequency domain data Y at each frequency point f f The overcomplete array manifold matrix corresponding to frequency point f Association, to provide a foundation for the subsequent construction of sparse representation models, where Y f Reflects the actual received signal of the array at that frequency. This reflects the signal propagation characteristics in different spatial directions at this frequency. By introducing sparse signals at points in each spatial direction, the model is transformed into a sparse representation model, which can be expressed as:

[0082]

[0083] Among them, V f Here is the noise matrix at frequency f. It is a sparse signal at frequency f.

[0084] Step S102: Iterate based on the probability model, so that the probability model iteratively updates each of the sparse signals according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each of the sparse signals in the probability model, until the iteration termination condition is met, and outputs the spatial power estimation vector and the source number estimation value, wherein the probability model includes the multi-level prior probability distribution of each of the sparse signals and the conditional probability distribution of the frequency domain data.

[0085] The iteration stopping condition is that the iteration number i reaches the upper limit of the iteration number τ, or the L2 norm of the spatial power vector in the previous and next iterations satisfies ||γ. (i) -γ (i-1) ||2<∈, where ∈ is the threshold parameter, and ∈=0.001 is taken.

[0086] In this embodiment, the multi-layer prior probability distribution of the probability model may include: a first layer constructed based on the spatial power vector for sparse signals; a second layer constructed based on the gamma distribution rate vector for the spatial power vector; and a third layer constructed based on the gamma distribution shape parameter for the gamma distribution rate vector. The conditional probability distribution of the frequency domain data of the probability model is used to describe the association between the frequency domain data and the sparse signal.

[0087] Before the probabilistic model begins iteration, the hyperparameters are initialized. These hyperparameters include the spatial power vector, the gamma distribution rate vector, and the noise variance, such as γ. (0) =1 N×1 ξ (0) =1 N×1 , The parameter h-0.1 is fixed. During the iterative process of the probabilistic model, Bayes' theorem is used, combined with frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power vector, noise variance, and gamma distribution shape parameters, to calculate the posterior distribution of the sparse signal within the probabilistic model framework composed of multi-level prior probability distributions and conditional probability distributions. Based on the posterior distribution (e.g., using maximum a posteriori estimation), the updated sparse signal for each frequency point is obtained, making the updated sparse signal more consistent with the frequency domain data under the probabilistic model, thus giving the model a higher probability of interpreting the observed frequency domain data. Based on the updated sparse signal, and according to the correlation between the sparse signal and the spatial power vector in the first-layer prior probability distribution (the statistical characteristics of the sparse signal are constrained by the spatial power vector), combined with relevant probability formulas (such as utilizing the characteristics of the gamma distribution), the power update value at each spatial direction point is calculated, and each element in the current spatial power vector is updated. This ensures that the updated spatial power vector more accurately reflects the signal power situation at each spatial direction point under the current iteration, allowing the sparse signal to continue adapting to the frequency domain data and prior distribution under the constraints of the updated spatial power vector. Based on the updated spatial power vector, according to the constraint relationship between the current gamma distribution rate vector and the updated spatial power vector in the second-layer prior probability distribution (the elements of the spatial power vector follow a gamma distribution containing gamma distribution rate vector parameters), and using the derivation formulas of the probability model (such as through the parameter update rules of the gamma distribution), the update value of each rate element in the current gamma distribution rate vector is calculated, and the current gamma distribution rate vector is updated. This allows it to better control the distribution shape of the spatial power vector, adapting to the requirements of the entire probability model for signal sparsity and statistical characteristics. Continue executing the steps described above to update the sparse signal, the current spatial power vector, and the current gamma distribution rate vector. After each iteration, the iteration number is set to i = i + 1. Check if the iteration termination condition is met. If it is met, stop the iteration. The spatial power vector obtained at this time is the spatial power estimation vector. Count the number of significantly non-zero elements in the spatial power estimation vector and use it as the source number estimate.

[0088] Step S103: Perform linear approximation post-processing based on the spatial direction points corresponding to the spatial power estimation vector to obtain the direction estimation result of the broadband signal.

[0089] In this embodiment, the target spatial power estimation vector output after iterative convergence is... Identification The local maxima elements in the matrix yield multiple spectral peaks, each corresponding to a predefined spatial direction point. These orientation points are preliminary estimates of the source orientation. Considering that the true source orientation may lie between two predefined grids, for each spectral peak, the maximum power value of that peak is extracted. and corresponding spatial direction points and the second largest power value of this spectral peak and corresponding spatial direction points and These are adjacent grid points, where... ( (This represents the estimated number of sources), where represents the spectral peak corresponding to the k-th source. Considering that directional points with larger power values ​​have a higher weight in contributing to the true source direction, for each source k, the direction is estimated by weighted averaging of the directions of adjacent grid points to compensate for the "off-grid deviation" caused by the predefined grid discretization. This makes the estimated value closer to the true source direction, resulting in the final direction estimate. Calculate the high-precision direction estimates for all K sources. This serves as the final direction estimation result for broadband signals.

[0090] like Figure 2 The diagram shown illustrates a normalized spatial spectrum estimation result provided in this embodiment. The green curve represents the normalized spatial spectrum, and the red circle represents the true azimuth angle. Figure 3 The diagram shown illustrates how the orientation estimation result varies with the signal-to-noise ratio, as provided in this embodiment. Figure 4 The diagram shown is a schematic representation of how the number of information sources varies with the signal-to-noise ratio in this embodiment.

[0091] This post-processing step in this embodiment effectively reduces the direction estimation error caused by excessively coarse spatial grid division by linearly approximating and fusing the information of adjacent grid points. It is especially suitable for scenarios where the actual source direction does not fall exactly on the predefined grid points, and significantly improves the direction finding accuracy.

[0092] The above embodiments disclose a joint estimation method for the direction and number of sources of underwater acoustic broadband signals based on sparse Bayesian learning. This embodiment uses a simulated detection scenario with a uniform linear array and broadband white noise signals. First, a multi-frequency sparse representation model for underwater acoustic direction finding is constructed, and a hierarchical prior probability distribution is established. Then, the update steps of each parameter and the source number estimation strategy are given. After iterative estimation, the accuracy of direction estimation is further improved by linear approximation post-processing.

[0093] As an example of an embodiment of the present invention, the method based on the spatial power estimation vector... After linear approximation and post-processing of the corresponding spatial direction points, the direction estimate of the broadband signal is obtained, specifically:

[0094]

[0095] in, It is the direction estimate of the k-th signal direction. They are the first The two largest and second largest power values ​​among the spectral peaks. They are and The corresponding grid point orientation.

[0096] As an example of an embodiment of the present invention, the step of iteratively updating each of the sparse signals, and the current spatial power vector and current gamma distribution rate vector of each of the sparse signals in the probability model, based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, and the gamma distribution shape parameters, specifically involves:

[0097] In each iteration of the probability model, based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power, and the noise variance, each sparse signal is updated to obtain the updated sparse signal, and the current frequency domain mean matrix and the current frequency domain covariance matrix corresponding to the updated sparse signal are determined. Based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector, the current spatial power vector is updated to obtain the updated spatial power vector, and based on the updated spatial power vector and the gamma distribution shape... The parameters are used to update the current gamma distribution rate vector to obtain an updated gamma distribution rate vector; multiple spectral peaks are extracted from the updated spatial power vector, and the multi-frequency likelihood function increment is calculated based on the updated spatial power vector and spatial direction point corresponding to each spectral peak, and the number of sources is estimated based on the increment to obtain the estimated number of sources; the noise variance is updated based on the estimated number of sources to obtain an updated noise variance, so as to perform the next round of iteration based on the updated spatial power vector, the updated noise variance, and the gamma distribution shape parameters.

[0098] The current frequency domain mean matrix is ​​used to describe the average value of the sparse signal at each frequency point, and the current frequency domain covariance matrix is ​​used to describe the fluctuation characteristics of the sparse signal.

[0099] In this embodiment, the input frequency domain data Y f Multi-frequency overcomplete array manifold matrix Current spatial power vector γ, current noise variance σ 2 Based on the first-level prior probability distribution of the sparse signal, which follows a complex Gaussian distribution with mean 0 and variance γ, and the conditional probability distribution of the frequency domain data (the observed data follows a complex Gaussian distribution with mean 0 and variance γ),... For the mean, σ2 I M Given a complex Gaussian distribution of the current frequency domain covariance matrix, calculate the sparse signal X using Bayesian inference. f The posterior distribution is then determined. The sparse signal X at each frequency point is updated using maximum a posteriori estimation or variational inference. f This yields the updated sparse signal. Based on the updated sparse signal, its statistical properties are calculated: that is, the current frequency domain mean matrix μ. f and the current frequency domain covariance matrix ∑ f Take the diagonal elements (∑) of the current frequency domain covariance matrix. f ) nn (The variance of the nth spatial direction).

[0100] Based on the current frequency domain mean matrix μ f The current frequency domain covariance matrix ∑ f Given the current gamma distribution rate vector ξ, update the current spatial power vector. Specifically, based on the second-layer prior probability distribution, update the current spatial power vector γ. n It follows the parameters 3 / 2 and ξ n The gamma distribution, combined with the current frequency domain mean matrix μ f The sum of the squared magnitudes of the row vectors and the current frequency domain covariance matrix ∑ f The updated spatial power vector γ is obtained by maximizing the posterior probability through the diagonal elements. (i) .

[0101] According to the updated spatial power vector γ (i) The gamma distribution shape parameter h (preset fixed value) is used to determine the current gamma distribution rate vector ξ based on the third-layer prior probability distribution. n The updated gamma distribution velocity vector ξ follows a gamma distribution with parameter h. (i) .

[0102] From the updated spatial power vector γ (i) K spectral peaks (local maxima) with the largest amplitudes were selected and sorted in descending order, corresponding to points in the spatial direction. For each spectral peak k, calculate the increment of the likelihood function at multiple frequencies based on its corresponding spatial direction point and spatial power vector. Statistical satisfaction The number of spectral peaks (where a positive likelihood function increment indicates the presence of a real source in that direction) is used as an estimate of the number of sources. Based on the estimated number of information sources Second covariance matrix eigenvalues in, The second covariance matrix R fThe noise variance σ is obtained by averaging the MK smaller eigenvalues ​​(M is the number of array elements) to calculate the updated noise variance. 2(i) The noise variance is calculated as follows:

[0103]

[0104] The updated spatial power vector γ (i) Gamma distribution velocity vector ξ (i) Noise variance As input for the next iteration, the iteration terminates when the iteration stopping condition is met, and the spatial power estimation vector and the source number estimation value are output.

[0105] This embodiment achieves coordinated updates of sparse signals, hyperparameters, and the number of information sources through multi-layer constraints and iterative optimization of the probabilistic model, ultimately focusing on the spatial characteristics of real information sources.

[0106] As an example of an embodiment of the present invention, the step of updating the current spatial power vector based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector to obtain an updated spatial power vector, and then updating the current gamma distribution rate vector based on the updated spatial power vector and the gamma distribution shape parameter to obtain an updated gamma distribution rate vector, specifically:

[0107] The current frequency domain mean matrix is:

[0108]

[0109] The diagonal elements of the current frequency domain covariance matrix are:

[0110]

[0111] Γ = diag(γ);

[0112]

[0113] in, This represents the mean of the sparse signal at frequency f. For frequency domain data at frequency f, n k ∈{1,...,N}, This represents the diagonal elements of the current frequency domain covariance matrix at frequency f. yes The conjugate transpose of the matrix. Let f be the matrix of the multi-frequency overcomplete array manifold at frequency f. Let γ be the current spatial power vector. nIt is the power element in the current spatial power vector, σ 2 Let σ be the noise variance. 2 I M Let U be the second covariance matrix. f ) n· It is matrix U f The nth row element, It is a matrix The element in the nth column;

[0114] The updated spatial power vector is,

[0115]

[0116] The updated gamma distribution rate vector is:

[0117]

[0118] Where N is the number of spatial direction points, F is the number of frequency points, L is the frequency domain snapshot, (μ f ) n· Representative matrix μ f The nth row element, (∑ f ) nn Representing matrix ∑ f The element in the nth row and nth column, where h is the shape parameter of the gamma distribution.

[0119] As an example of an embodiment of the present invention, the step of extracting multiple spectral peaks from the updated spatial power vector, calculating the multi-frequency likelihood function increment based on the updated spatial power vector and spatial direction point corresponding to each spectral peak, and estimating the number of information sources based on the increment to obtain the estimated number of information sources is as follows:

[0120] In the updated spatial power vector, the spectral peaks are arranged in descending order of amplitude. A preset number of target spectral peaks are determined from the multiple spectral peaks arranged in descending order. The first intermediate factor and the second intermediate factor related to the target spectral peaks and the spatial direction point and spatial power are calculated. Based on the increment of the likelihood function of the multi-frequency point, the number of information sources is estimated by positive increment.

[0121] The second intermediate factor is used to reflect the signal energy contribution of the direction corresponding to the target spectral peak at each frequency point.

[0122] In this embodiment, in the updated spatial power vector γ (i)In the process, all local maxima are selected as spectral peaks. A local maximum is a position where the value of an element is greater than its left and right adjacent elements, corresponding to the direction of a potential signal source. The identified spectral peaks are sorted from largest to smallest according to their amplitude (spatial power value), resulting in a descending order sequence. A predetermined number of peaks are selected from this descending order as target peaks (the predetermined number can be set based on experience or scenario requirements, but is usually greater than the actual number of possible signal sources to avoid missing real signal sources). Each target peak corresponds to a spatial direction point. (k = 1, 2, ..., K is the preset number, n) k (This refers to the index of the direction point in the spatial grid). For each target spectral peak k, based on the overcomplete array manifold vector corresponding to frequency f, the conjugate transpose of the array manifold vector, the inverse of the current frequency domain covariance matrix of the frequency domain data, and its corresponding spatial direction point and spatial power value, the first intermediate factor is calculated. And combined with the second covariance matrix R corresponding to the frequency domain data f Calculate the second intermediate factor For each target spectral peak k, the first intermediate factor is used to fuse all frequency points. Second intermediate factor Calculate the increment of the likelihood function at multiple frequency points This increment reflects the improvement in the probabilistic model's interpretability of the observed data after introducing this spectral peak. It involves statistically analyzing all target spectral peaks that satisfy... The number of (positive increments indicate that the spectral peak corresponds to a real source and can significantly improve the model's fit to the data) is the final estimate of the number of sources.

[0123] This embodiment uses the positive or negative sign of the likelihood function increment to filter the spectral peaks corresponding to the real information sources through the above steps, thereby achieving adaptive estimation of the number of information sources. It does not require prior assumption of the number of information sources, thus improving its applicability in scenarios with unknown number of information sources.

[0124] As an example of an embodiment of the present invention, the step of calculating the increment of the multi-frequency likelihood function based on the first intermediate factor and the second intermediate factor specifically involves:

[0125]

[0126] in, This represents the estimated number of information sources. and These are the first intermediate factor and the second intermediate factor, representing spatial direction points. Spatial power The relevant function values, denoted by , represents the increment of the likelihood function at multiple frequencies, and card represents the number of k that satisfy the set conditions.

[0127] As an example of an embodiment of the present invention, the probability model is specifically as follows:

[0128] In the first-level prior probability distribution, for each snapshot corresponding to each frequency point, the sparse signal column is determined to follow a probability density with a mean of zero and a variance equal to the current spatial power vector. The probability densities corresponding to all sparse signal columns are multiplied to obtain a first prior probability distribution value. This first-level prior probability distribution characterizes the prior probability distribution of the sparse signal. In the second-level prior probability distribution, for each power element in the spatial power vector, the first gamma distribution probability density is determined to follow a first parameter and the current gamma distribution rate vector. The first gamma distribution probability densities corresponding to all power elements are multiplied to obtain a second prior probability distribution value for the current spatial power vector. This second-level prior probability distribution characterizes the prior probability distribution of the current spatial power vector. In the third-level prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density is determined to follow a second gamma distribution probability density with a mean of zero and a variance equal to the current spatial power vector. The second gamma distribution probability density corresponding to all rate elements is multiplied to obtain a second prior probability distribution value for the current spatial power vector. Multiplying the gamma distribution probability densities yields the third prior probability distribution value corresponding to the current gamma distribution rate vector. The third-level prior probability distribution characterizes the prior probability distribution of the current gamma distribution rate vector. The distribution of the current gamma distribution rate vector in the second-level prior probability distribution is controlled by the current gamma distribution shape parameter in the third-level prior probability distribution. The variance of the current spatial power in the first-level prior probability distribution is controlled by the current gamma distribution rate vector in the second-level prior probability distribution. In the conditional probability distribution, for each snapshot corresponding to each frequency point, it is determined that each frequency data column follows a complex Gaussian distribution probability density whose mean is the product of the multi-frequency overcomplete array manifold matrix and the corresponding sparse signal column, and whose second covariance matrix corresponding to the frequency data is the product of the noise variance and the identity matrix. Multiplying the conditional probability densities corresponding to all frequency data columns yields the conditional probability distribution value. This conditional probability distribution value is used to evaluate the degree of matching between the frequency data and the sparse representation model.

[0129] In this embodiment, the first-layer prior probability distribution (prior modeling of sparse signals) is applicable to the sparse signal series (X) corresponding to each frequency point f and each snapshot l. fAssuming each sparse signal sequence follows a complex Gaussian distribution with zero mean and variance equal to the current spatial power vector γ, the probability density value of a single sparse signal sequence is calculated. Since sparse signal sequences at different frequencies and in different snapshots are assumed to be independent, the probability density values ​​of all frequencies (f = 1 to F) and all snapshots (l = 1 to L) are multiplied to obtain the first-level prior probability distribution value. This first-level prior probability distribution constrains the distribution of sparse signals through the spatial power vector γ, making the signal exhibit sparsity in the spatial domain. In the second-level prior probability distribution (prior modeling of the spatial power vector), the applicable object is each element γ in the current spatial power vector γ. n (n = 1 to N, where N is the number of spatial direction points), assuming each power element γ n It follows the first parameter being 3 / 2 and the second parameter being the corresponding element ξ in the current gamma distribution velocity vector ξ. n The gamma distribution, then the individual power element γ n The probability density value when ξ n The greater the sparsity of the control distribution, the greater the spatial power vector γ. n The higher the probability of approaching zero, the more likely all γ values ​​will be to be independent, since each power element is assumed to be independent. n Multiplying the probability density values ​​yields the second-layer prior probability distribution value, which constrains the distribution of γ by ξ, enhancing the sparsity of spatial power and providing a statistical basis for the first-layer prior. In the third-layer prior probability distribution (prior modeling of the gamma distribution rate vector), the applicable object is each element ξ in the current gamma distribution rate vector ξ. n (n = 1 to N), assuming each rate element ξ n If the gamma distribution follows a shape parameter h, where both the shape parameter and rate parameter are gamma distributions, then the individual rate element ξ is calculated. n The probability density value of ξ, and the smaller the probability density value, the better. n The closer the initial value is to zero, the more adjustment space is reserved for subsequent iterations and optimizations. Since each rate element is assumed to be independent, all ξ... n Multiplying the probability density values ​​yields the third-level prior probability distribution value, which provides prior constraints for ξ, indirectly controlling the distribution of γ and the sparse signal, forming a hierarchical sparse constraint chain of "h→ξ→γ→X". In conditional probability distribution (modeling the matching degree between frequency domain data and the model), the applicable objects are the frequency domain data series Y corresponding to each frequency point f and each snapshot l. f1 Assuming each frequency domain data column Y f1 Obtained by a mean-multi-frequency overcomplete array manifold matrix The product of the corresponding sparse signal sequence and the second covariance matrix is ​​the noise variance σ. 2 With the identity matrix I M If the product follows a complex Gaussian distribution, then the calculation of a single frequency domain data series Y is performed. f1Since each frequency domain data column is assumed to be independent, the probability density values ​​of all frequency points and all snapshots are multiplied to obtain the conditional probability distribution value. This quantifies the degree of matching between the observed data and the sparse representation model, providing a "data fitting" basis for iterative optimization. Together with the multi-level prior, it forms the complete framework of Bayesian inference. Furthermore, the third-level prior controls the distribution of ξ through h, the second-level prior controls the distribution of γ through ξ, and the first-level prior controls the distribution of the sparse signal X through γ, forming a hierarchical constraint from hyperparameters to the signal. The conditional probability distribution associates the observed data Y with the sparse signal X. Combined with the product of the multi-level prior, it provides an optimization objective for iteratively updating each parameter, ultimately achieving a joint estimation of the source direction and quantity.

[0130] As an example of an embodiment of the present invention, the probability model is used to attach strong sparse prior constraints to the signal, specifically as follows:

[0131]

[0132] in, This is the current spatial power vector. is the current gamma distribution rate vector, and h is the gamma distribution shape parameter. express The prior probability density function of γ is the first-level prior probability distribution; P(γ|ξ) represents the probability density function of γ, which is the second-level prior probability distribution; and P(ξ|h) represents the probability density function of the gamma distribution rate parameter ξ, which is the third-level prior probability distribution. express The conditional probability density function. X represents f The l-th column follows a complex Gaussian distribution with mean 0 and variance γ. Indicates γ n Obey parameters and ξ n The gamma distribution, Gamma(ξ) n |h,h) represents ξ n It follows a gamma distribution with parameter h. The mean is covariance matrix σ 2 I M The complex Gaussian distribution, σ 2 Let γ be the noise variance. Before the iteration of the probability model begins, initialize the hyperparameter γ. (0) =1 N×1 ξ (0) =1 N×1 , σ 2(0) =10 - 2. Fix parameter h = 0.1.

[0133] like Figure 5 As shown, based on the above method embodiments, corresponding system embodiments are provided; one embodiment of the present invention provides a joint estimation system 500 for broadband signal direction and number of sources, including: a sparse module 501, an iteration module 502 and an estimation module 503;

[0134] The sparse module 501 is used to acquire frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points, and convert the frequency domain data into a sparse representation model based on the multi-frequency overcomplete array manifold matrix. The multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points.

[0135] The iteration module 502 is used to perform iteration based on a probability model, so that the probability model iteratively updates each of the sparse signals according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each of the sparse signals in the probability model, until the iteration termination condition is met, and outputs the spatial power estimation vector and the source number estimation value, wherein the probability model includes the multi-level prior probability distribution of each of the sparse signals and the conditional probability distribution of the frequency domain data;

[0136] The estimation module 503 is used to perform linear approximation post-processing based on the spatial direction point corresponding to the spatial power estimation vector to obtain the direction estimation result of the broadband signal.

[0137] It is understood that the above system embodiments correspond to the method embodiments of the present invention, and can implement the joint estimation method of broadband signal direction and number of sources provided by any of the above method embodiments of the present invention.

[0138] It should be noted that the system embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the system embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0139] Based on the above embodiments of the joint estimation method for broadband signal direction and number of sources, another embodiment of the present invention provides a terminal device, which includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the joint estimation method for broadband signal direction and number of sources according to any embodiment of the present invention.

[0140] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the terminal device.

[0141] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0142] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0143] Based on the above-described method embodiments, another embodiment of the present invention provides a computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to execute the joint estimation method for broadband signal direction and number of sources as described in any of the above-described method embodiments of the present invention.

[0144] The modules / units integrated in the device / terminal equipment, if implemented as software functional units and sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0145] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A joint estimation method for broadband signal direction and number of sources, characterized in that, include: The frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points are obtained, and the frequency domain data is transformed into a sparse representation model based on the multi-frequency overcomplete array manifold matrix. The multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points, and the sparse representation model includes sparse signals corresponding to multiple frequency points. The iteration is based on a probabilistic model, which iteratively updates each sparse signal according to the frequency domain data, the multi-frequency overcomplete array manifold matrix, and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probabilistic model, until the iteration termination condition is met, and outputs a spatial power estimation vector and a source number estimation value. The probabilistic model includes a multi-level prior probability distribution of each sparse signal and a conditional probability distribution of the frequency domain data. The direction estimation result of the broadband signal is obtained by performing linear approximation post-processing based on the spatial direction point corresponding to the spatial power estimation vector.

2. The joint estimation method for broadband signal direction and number of sources as described in claim 1, characterized in that, The step of enabling the probabilistic model to iteratively update each of the sparse signals based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, and the gamma distribution shape parameters, as well as the current spatial power vector and current gamma distribution rate vector of each of the sparse signals in the probabilistic model, specifically involves: In each iteration of the probability model, based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power, and the noise variance, each sparse signal is updated to obtain the updated sparse signal, and the current frequency domain mean matrix and the current frequency domain covariance matrix corresponding to the updated sparse signal are determined. Based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector, the current spatial domain power vector is updated to obtain the updated spatial domain power vector. Based on the updated spatial domain power vector and the gamma distribution shape parameter, the current gamma distribution rate vector is updated to obtain the updated gamma distribution rate vector. Multiple spectral peaks are extracted from the updated spatial power vector. The multi-frequency likelihood function increment is calculated based on the updated spatial power vector and spatial direction point corresponding to each spectral peak. The number of information sources is estimated based on the increment to obtain the estimated number of information sources. The noise variance is updated based on the estimated number of sources to obtain the updated noise variance, and then the next iteration is performed based on the updated spatial power vector, the updated noise variance, and the gamma distribution shape parameters.

3. The joint estimation method for broadband signal direction and number of sources as described in claim 2, characterized in that, The process involves extracting multiple spectral peaks from the updated spatial power vector, calculating the multi-frequency likelihood function increment based on the updated spatial power vector and spatial direction point corresponding to each spectral peak, and estimating the number of information sources based on the increments to obtain the estimated number of information sources. Specifically: In the updated spatial power vector, each of the spectral peaks is arranged in descending order of amplitude, and a preset number of target spectral peaks are determined from the multiple spectral peaks arranged in descending order. Calculate the first and second intermediate factors related to the target spectral peak, spatial direction point, and spatial power, and calculate the increment of the multi-frequency likelihood function based on the first and second intermediate factors to estimate the number of sources through positive increments.

4. The joint estimation method for broadband signal direction and number of sources as described in claim 1, characterized in that, The probability model is specifically as follows: In the first-level prior probability distribution, for each snapshot corresponding to each frequency point, it is determined that each sparse signal column follows a probability density with a mean of zero and a variance equal to the current spatial power vector. The probability densities corresponding to all sparse signal columns are multiplied to obtain the first prior probability distribution value. The first-level prior probability distribution is a prior probability distribution used to characterize the sparse signal. In the second-level prior probability distribution, for each power element in the spatial power vector, the first gamma distribution probability density when each power element follows the first parameter and the current gamma distribution rate vector is determined, and the first gamma distribution probability density corresponding to all power elements is multiplied to obtain the second prior probability distribution value of the current spatial power vector. The second-level prior probability distribution is used to characterize the prior probability distribution of the current spatial power vector. In the third-level prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density when each rate element follows the gamma distribution shape parameter is determined. The second gamma distribution probability densities corresponding to all rate elements are multiplied to obtain the third prior probability distribution value corresponding to the current gamma distribution rate vector. The third-level prior probability distribution is used to characterize the prior probability distribution of the current gamma distribution rate vector. The distribution of the current gamma distribution rate vector in the second-level prior probability distribution is controlled by the gamma distribution shape parameter in the third-level prior probability distribution. The variance of the current spatial power in the first-level prior probability distribution is controlled by the current gamma distribution rate vector in the second-level prior probability distribution. In the conditional probability distribution, for each snapshot corresponding to each frequency point, it is determined that each frequency data column follows a complex Gaussian distribution probability density with a mean of the product of the multi-frequency overcomplete array manifold matrix and the corresponding sparse signal column, and the second covariance matrix corresponding to the frequency data is the product of the noise variance and the identity matrix. The conditional probability densities corresponding to all frequency data columns are multiplied together to obtain the conditional probability distribution value, wherein the conditional probability distribution value is used to evaluate the degree of matching between the frequency data and the sparse representation model.

5. The joint estimation method for broadband signal direction and number of sources as described in claim 2, characterized in that, The process involves updating the current spatial power vector based on the current frequency domain mean matrix, the current frequency domain covariance matrix, and the current gamma distribution rate vector to obtain an updated spatial power vector. Then, based on the updated spatial power vector and the gamma distribution shape parameters, the current gamma distribution rate vector is updated to obtain an updated gamma distribution rate vector. Specifically: The current frequency domain mean matrix is: ; The diagonal elements of the current frequency domain covariance matrix are: ; ; ; ; in, Indicates sparse signal at frequency The mean at that point, For frequency Frequency domain data at that location, , Indicates the preset quantity. Represents the current frequency domain covariance matrix The OK Column elements, yes The conjugate transpose of the matrix. For frequency The multi-frequency overcomplete array manifold matrix at the location, This is the current spatial power vector. It is the power element in the current spatial power vector. For noise variance, The second covariance matrix, It is a matrix The n row element, It is a matrix The n Column elements; The updated spatial power vector is, ; The updated gamma distribution rate vector is: ; in, N The number of points in spatial directions. The number of frequency points L For frequency domain snapshots, h represents the shape parameter of the gamma distribution.

6. The joint estimation method for broadband signal direction and number of sources as described in claim 3, characterized in that, The step of calculating the increment of the multi-frequency likelihood function based on the first intermediate factor and the second intermediate factor specifically involves: ; ; ; ; in, This represents the estimated number of information sources. and These are the first intermediate factor and the second intermediate factor, representing spatial direction points. Spatial power The relevant function values, This represents the increment of the likelihood function at multiple frequencies. It means that the set conditions are satisfied. The number of This indicates the preset quantity. The number of frequency points f F Indicates the F-th frequency point. L For frequency domain snapshots; It is a multi-frequency overcomplete array manifold The The column, that is, the k-th spectral peak in directional array manifold vectors; It is the model covariance matrix; It is the covariance matrix of the frequency domain data, used to calculate the second intermediate factor; and These are the gamma distribution rate vectors. and spatial power vector The element of the k-th spectral peak.

7. The joint estimation method for broadband signal direction and number of sources as described in claim 4, characterized in that, The probabilistic model is used to attach strong sparse prior constraints to the signal, specifically: ; ; ; ； in, For a sparse signal at frequency f, For frequency Frequency domain data at the location; For frequency The multi-frequency overcomplete array manifold matrix at the location, The element in the l-th column; This is the current spatial power vector. This represents the current gamma distribution rate vector. Gamma distribution shape parameters express The prior probability density function, i.e., the first-level prior probability distribution, express The probability density function, i.e., the second-level prior probability distribution, Represents the gamma distribution rate parameter The probability density function, i.e., the third-level prior probability distribution, express The conditional probability density function; express The The column follows a mean of 0 and a variance of 0. The complex Gaussian distribution, express Obey parameters and gamma distribution, express Obey parameters gamma distribution, Mean The covariance matrix is The complex Gaussian distribution, The noise variance is used; the hyperparameters are initialized before the iteration of the probability model begins. , = , The parameter h is fixed at 0.

1.

8. The joint estimation method for broadband signal direction and number of sources as described in claim 1, characterized in that, The linear approximation post-processing based on the spatial direction points corresponding to the spatial power estimation vector to obtain the direction estimate of the broadband signal is specifically as follows: ; in, It is the first Direction estimate of each signal direction. They are the first The two largest and second largest power values ​​in the estimated spectral peaks, They are The corresponding grid point orientation.

9. A joint estimation system for broadband signal direction and number of sources, characterized in that, include: Sparse module, iterative module, and estimation module; The sparse module is used to acquire frequency domain data of the broadband signal received by the underwater acoustic array at different frequency points, and to convert the frequency domain data into a sparse representation model based on the multi-frequency overcomplete array manifold matrix. The multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points, and the sparse representation model includes sparse signals corresponding to multiple frequency points. The iterative module is used to perform iteration based on a probability model, so that the probability model iteratively updates each of the sparse signals according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameters, as well as the current spatial power vector and the current gamma distribution rate vector of each of the sparse signals in the probability model, until the iteration termination condition is met, and outputs a spatial power estimation vector and a source number estimation value, wherein the probability model includes a multi-level prior probability distribution of each of the sparse signals and a conditional probability distribution of the frequency domain data; The estimation module is used to perform linear approximation post-processing based on the spatial direction point corresponding to the spatial power estimation vector to obtain the direction estimation result of the broadband signal.

10. A terminal device, characterized in that, The system includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein, when the processor executes the computer program, it implements the joint estimation method for broadband signal direction and number of sources as described in any one of claims 1-8.

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