Joint estimation method, system and equipment for broadband signal direction and signal source number

Abstract

The invention discloses a joint estimation method, system and equipment for broadband signal direction and signal source number, and belongs to the field of power systems, the method comprises the following steps: converting frequency domain data received by an underwater acoustic array into a sparse representation model based on a multi-frequency over-complete array manifold matrix; and performing iteration based on a probability model, so that the probability model iteratively updates each sparse signal and a current airspace power vector and a current gamma distribution rate vector of each sparse signal in the probability model according to the frequency domain data, the multi-frequency over-complete array manifold matrix and a gamma distribution shape parameter, when an iteration termination condition is satisfied, outputting a spatial domain power estimation vector and a signal source number estimation value; and performing linear approximation post-processing based on the spatial direction point corresponding to the spatial domain power estimation vector to obtain a direction estimation result of the broadband signal, so that the accuracy of the direction and source number estimation result of the broadband signal can be improved by implementing the method and the device.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of underwater acoustic detection, and in particular to a wideband signal direction and source number joint estimation method, system and device. BACKGROUND

[0002] Underwater acoustic array direction finding is a core technology in the field of underwater passive detection, which receives underwater target radiation acoustic signals through hydrophone array to estimate the direction of arrival of the target, and has important applications in the fields of ocean monitoring, underwater communication, etc. However, the underwater environment is complex, the received signal usually has wideband characteristics (including multiple frequency points), and the number of sources is often unknown, which poses a significant challenge to traditional direction finding methods.

[0003] In the current underwater acoustic wideband direction finding research, the classic subspace method needs to know the number of sources in advance, and does not consider the joint estimation of wideband signal direction and source number, and the source number estimation 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 wideband signals. SUMMARY

[0004] The present application provides a wideband signal direction and source number joint estimation method, system and device, which can solve the problem of low estimation accuracy in low signal-to-noise ratio and multi-frequency overlapping scenarios by jointly estimating the direction and source number of wideband signals in underwater passive detection scenarios with unknown source number.

[0005] The present application provides a wideband signal direction and source number joint estimation method, comprising:

[0006] Obtaining the frequency domain data corresponding to the wideband signal received by the underwater acoustic array at different frequency points, and converting the frequency domain data into a sparse representation model based on a multi-frequency overcomplete array manifold matrix, wherein the multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors corresponding to multiple frequency points;

[0007] Iterating based on a probability model to iteratively update each sparse signal in the probability model according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameter, and the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probability model, until the iteration termination condition is met, and outputting the spatial power estimation vector and the source number estimation value, wherein the probability model includes a multi-layer prior probability distribution of each sparse signal and a conditional probability distribution of the frequency domain data;

[0008] Performing linear approximation post-processing on the spatial direction points corresponding to the spatial power estimation vector to obtain the direction estimation result of the wideband signal.

[0009] In the embodiments of the present application, the multi-frequency overcomplete array manifold matrix includes overcomplete array manifold vectors of multiple frequency points, which can sufficiently capture the characteristics of wideband signals at different frequency points. The frequency domain data is converted into a sparse representation model, so that the signal has sparsity in the spatial direction, facilitating subsequent estimation of the signal direction. The probability model of the multi-layer prior probability distribution and the conditional probability distribution can comprehensively consider the relationship between the prior information of the signal and the observation data. By iteratively updating the sparse signal and the related spatial power vector and gamma distribution rate vector, the estimation result is continuously optimized, so that the estimation value gradually approaches 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 and reduce the off-grid deviation, so as to obtain more accurate wideband signal direction estimation results.

[0010] Further, the probability model is updated according to the frequency domain data, the multi-frequency overcomplete array manifold matrix and the gamma distribution shape parameter, and the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probability model, and the specific process is as follows.

[0011] In each iteration process of the probability model, each sparse signal is updated based on the frequency domain data, the multi-frequency overcomplete array manifold matrix, the current spatial power and the noise variance, to obtain an 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] The current spatial power vector is updated 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 the current gamma distribution rate vector is updated based on the updated spatial power vector and the gamma distribution shape parameter, to obtain an updated gamma distribution rate vector.

[0013] A plurality of spectral peaks are extracted from the updated spatial power vector, a multi-frequency point likelihood function increment is calculated based on the updated spatial power vector and the spatial direction point corresponding to each spectral peak, and the number of sources is estimated according to the increment, to obtain an estimated value of the number of sources.

[0014] The noise variance is updated according to the estimated value of the number of sources, to obtain an updated noise variance, so that the next iteration is performed according to the updated spatial power vector, the updated noise variance and the gamma distribution shape parameter.

[0015] Thus, the sparse signal is updated based on the frequency domain data, the multi-frequency over-complete array manifold matrix, the current spatial domain power and the noise variance, which can better reflect the sparse characteristics of the signal at different frequency points and provide a more accurate basis for subsequent parameter updating. The spatial domain power vector is updated by the current frequency domain mean matrix, the current frequency domain covariance matrix and the gamma distribution rate vector, and the gamma distribution rate vector is updated based on the updated spatial domain power vector and the gamma distribution shape parameter. This step-by-step updating method can more accurately reflect the power distribution and sparsity of the signal, thereby improving the estimation accuracy. The spectral peaks are extracted from the updated spatial domain power vector, and the multi-frequency point likelihood function increment is calculated based on the spectral peaks to estimate the number of signal sources. This method can more accurately determine the number of signal sources. At the same time, the noise variance is updated according to the number of signal sources, which can further improve the accuracy of noise estimation and optimize the entire estimation process.

[0016] Further, the plurality of spectral peaks are extracted from the updated spatial domain power vector, the multi-frequency point likelihood function increment is calculated based on the updated spatial domain power vector and the spatial direction point corresponding to each spectral peak, and the number of signal sources is estimated according to the increment to obtain the signal source number estimation value, specifically:

[0017] The spectral peaks in the updated spatial domain power vector are arranged in descending order of amplitude, and a predetermined number of target spectral peaks are determined in the plurality of spectral peaks arranged in descending order.

[0018] The first intermediate factor and the second intermediate factor related to the spatial direction point and the spatial domain power of the target spectral peak are calculated, and the increment of the multi-frequency point likelihood function is calculated to estimate the number of signal sources by positive increment.

[0019] Thus, in the updated spatial domain power vector, the spectral peak corresponds to the direction with strong signal energy, and the possible direction of the signal source can be preliminarily determined by extracting the spectral peak. The multi-frequency point likelihood function increment is calculated based on the updated spatial domain power vector corresponding to each spectral peak and the spatial direction point, which can comprehensively consider the signal characteristics at different frequency points, making the estimation of the number of signal sources more accurate. Only when the likelihood function increment is positive, the corresponding spectral peak is considered as an effective signal source direction, so that the number of signal sources is estimated according to the number of positive increments. This method avoids misjudging noise or interference signals as signal sources, improving the reliability of the estimation of the number of signal sources.

[0020] Further, the probability model is specifically:

[0021] In the first layer of prior probability distribution, for each snapshot corresponding to each frequency point, the probability density of each sparse signal column obeying a mean value of zero and a variance of the current spatial domain power vector is judged, the probability density corresponding to all sparse signal columns is multiplied, and a first prior probability distribution value is obtained, wherein the first layer of prior probability distribution is a prior probability distribution used for representing the sparse signal.

[0022] In the second layer of prior probability distribution, for each power element in the spatial domain power vector, the first gamma distribution probability density of each power element obeying a first parameter and the current gamma distribution rate vector is judged, the first gamma distribution probability density corresponding to all power elements is multiplied, and a second prior probability distribution value of the current spatial domain power vector is obtained, wherein the second layer of prior probability distribution is used for representing the prior probability distribution of the current spatial domain power vector.

[0023] In the third layer of prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density of each rate element obeying the gamma distribution shape parameter is judged, the second gamma distribution probability density corresponding to all rate elements is multiplied, and a third prior probability distribution value corresponding to the current gamma distribution rate vector is obtained, wherein the third layer of prior probability distribution is used for representing the prior probability distribution of the current gamma distribution rate vector, the distribution of the current gamma distribution rate vector in the second layer of prior probability distribution is controlled by the current gamma distribution shape parameter in the third layer of prior probability distribution, and the variance of the current spatial domain power in the first layer of prior probability distribution is controlled by the current gamma distribution rate vector in the second layer of prior probability distribution.

[0024] In the conditional probability distribution, for each snapshot corresponding to each frequency point, the conditional probability density of each frequency domain data column obeying a mean value of the product of the multi-frequency over-complete array manifold matrix and the corresponding sparse signal column and a second covariance matrix corresponding to the frequency domain data being a product of noise variance and a unit matrix is judged, the conditional probability density corresponding to all frequency domain data columns is multiplied, and a conditional probability distribution value is obtained, wherein the conditional probability distribution value is used for evaluating the matching degree between the frequency domain data and the sparse representation model.

[0025] Thus, through the first layer of prior probability distribution, for each snapshot of each frequency point, the probability density of the sparse signal column is judged to be subject to the mean of zero and the variance of the current spatial power vector, and the first prior probability distribution value is obtained by multiplying the probability densities of all sparse signal columns. This distribution can represent the sparse characteristics of the sparse signal and provide prior information of the signal for subsequent updates. Through the second layer of prior probability distribution, for each power element in the spatial power vector, the first gamma distribution probability density is judged when the power element is subject to the first parameter and the current gamma distribution rate vector, and the second prior probability distribution value is obtained by multiplying the first gamma distribution probability densities of all power elements. This layer of distribution reflects the distribution characteristics of the spatial power and further constrains the update of the spatial power. Through the third layer of prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density is judged when the rate element is subject to the gamma distribution shape parameter, and the third prior probability distribution value is obtained by multiplying the second gamma distribution probability densities of all rate elements. This layer of distribution controls the distribution of the gamma distribution rate vector through the gamma distribution shape parameter, thereby indirectly affecting the update of the spatial power. Through the conditional probability distribution, for each snapshot of each frequency point, the complex Gaussian distribution probability density is judged when the frequency domain data column is subject to the mean of the product of the multi-frequency over-complete array manifold matrix and the corresponding sparse signal column and the second covariance matrix is the product of the noise variance and the unit matrix, and the conditional probability distribution value is obtained by multiplying the conditional probability densities of all frequency domain data columns. This distribution can evaluate the matching degree between the frequency domain data and the sparse representation model and provide the information of the observation data for the iterative update.

[0026] Further, the current spatial power vector is updated 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 the current gamma distribution rate vector is updated based on the updated spatial power vector and the gamma distribution shape parameter 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] wherein, denotes the mean value of the sparse signal at frequency f, is the frequency domain data at frequency f, n k ∈ {1,..., N}, (∑ f ) nn denotes the element of the matrix ∑ f in the n-th row and n-th column, is the conjugate transpose matrix of is the multi-frequency over-complete array manifold matrix at frequency f, is the current spatial domain power vector, γ n is the power element in the current spatial domain power vector, σ 2 is the noise variance, σ 2 I M is the second covariance matrix, (U f ) n· is the element of the matrix U f in the n-th row, is the element of the matrix in the n-th column;

[0034] the updated spatial domain power vector is,

[0035]

[0036] the updated gamma distribution rate vector is,

[0037]

[0038] wherein 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] In this way, the current frequency domain mean value matrix and the diagonal element of the current frequency domain covariance matrix are calculated according to the mean value of the sparse signal at frequency f, the frequency domain data, and the diagonal element of the current frequency domain covariance matrix, thereby providing accurate statistical information for subsequent parameter updating. Based on the current frequency domain mean value matrix, the current frequency domain covariance matrix, and the gamma distribution rate vector, the spatial domain power vector is updated by using specific formulas, so that the power distribution of the signal in different spatial directions can be more accurately reflected. Based on the updated spatial domain power vector and the gamma distribution shape parameter, the gamma distribution rate vector is updated by using specific formulas, thereby 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 increment of the multi-frequency point likelihood function is calculated according to the first intermediate factor and the second intermediate factor, and specifically:

[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 a complex Gaussian distribution, σ 2 is noise variance. Hyper-parameter γ (0) = 1 N×1 is initialized before the iteration of the probability model starts. (0) = 1 N×1 , Fixed parameter h = 0.1.

[0047] In this way, by giving specific forms of the prior probability density function, the probability density function and the conditional probability density function, including the complex Gaussian distribution to which the sparse signal column is subjected, the gamma distribution to which the power element is subjected and the gamma distribution to which the rate element is subjected, the probability model is more in line with the characteristics of the actual signal.

[0048] Further, the spatial direction point corresponding to the spatial domain power estimation vector is linearly approximated and processed to obtain a direction estimation value of the wideband signal, specifically:

[0049]

[0050] wherein, is a direction estimation value of the kth signal direction, are two maximum and sub-maximum power values in the first spectral peak, are the corresponding grid point directions of and .

[0051] In this way, by linear approximation and processing, the power information of two adjacent grid points is utilized, and the direction is estimated by weighted average, so that the accuracy of direction estimation can be further improved. In a complex signal environment, the estimation of the signal direction can be affected by noise and other interference. Linear approximation and processing can reduce the influence of these interferences on the direction estimation through smoothing processing, thereby enhancing the robustness of the method.

[0052] Another embodiment of the present application also provides a wideband signal direction and source number joint estimation system, comprising: a sparse module, an iteration module and an estimation module.

[0053] The sparse module is used for acquiring frequency domain data corresponding to wideband signals received by a hydrophone array at different frequency points, and converting the frequency domain data into a sparse representation model based on a multi-frequency over-complete array manifold matrix, wherein the multi-frequency over-complete array manifold matrix comprises over-complete array manifold vectors corresponding to multiple frequency points.

[0054] The iteration module is configured to perform iteration based on a probability model, so that the probability model iteratively updates each sparse signal according to the frequency domain data, the multi-frequency over-complete array manifold matrix and a gamma distribution shape parameter, and the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probability model, until an iteration termination condition is met, and then outputs a spatial power estimation vector and a source number estimation value.

[0055] The estimation module is configured to perform linear approximation post-processing on a spatial direction point corresponding to the spatial power estimation vector, so as to obtain a direction estimation result of the wideband signal.

[0056] The embodiment of the present application can fully capture the characteristics of the wideband signal at different frequency points by means of the multi-frequency over-complete array manifold matrix including over-complete array manifold vectors of multiple frequency points. The frequency domain data is converted into a sparse representation model, so that the signal has sparsity in the spatial direction, which facilitates subsequent estimation of the signal direction. The probability model of the multi-layer prior probability distribution and the conditional probability distribution can comprehensively consider the relationship between the prior information of the signal and the observation data. The sparse signal and the related spatial power vector and the gamma distribution rate vector are iteratively updated, so as to continuously optimize the estimation result and make the estimation value gradually approach the true value. Finally, linear approximation post-processing is performed on the spatial direction point corresponding to the spatial power estimation vector, so as to further improve the accuracy of the direction estimation, reduce the off-grid deviation, and thus obtain a more accurate wideband signal direction estimation value.

[0057] Another embodiment of the present application further provides a terminal device, which comprises 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, the steps of the method for jointly estimating the direction and the source number of the wideband signal are implemented. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings described below are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort.

[0059] Figure 1 is a flowchart of a method for jointly estimating the direction and the source number of a wideband signal provided by an embodiment of the present application;

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

[0061] Figure 3 is a schematic diagram of the change of the azimuth estimation result with the signal-to-noise ratio according to an embodiment of the present application;

[0062] Figure 4 is a schematic diagram of the change of the source number estimation value with the signal-to-noise ratio according to an embodiment of the present application;

[0063] Figure 5 is a structural schematic diagram of a wideband signal direction and source number joint estimation system according to an embodiment of the present application. DETAILED DESCRIPTION

[0064] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present 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 the present application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the present application; the terms “include” and “have” and any variations thereof in the specification and claims of the present application and the above description of drawings are intended to cover non-exclusive inclusion.

[0066] In the description of the embodiments of the present application, the technical terms “first”, “second”, and the like are only used to distinguish different objects, and cannot be understood as indicating or implying relative importance or implicitly indicating the number, specific order or primary and secondary relationship of the indicated technical features. In the description of the embodiments of the present application, the meaning of “a plurality of” is two or more, unless otherwise explicitly and specifically limited.

[0067] Reference herein to “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The appearance of the phrase in various places in the specification does not necessarily all refer to the same embodiment, nor is it necessarily independent or alternative embodiments to other embodiments. It is 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 of the present application, the term "and / or" is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are a "or" relationship.

[0069] In the description of the embodiments of the present application, the term "a plurality of" refers to two or more (including two), and similarly, "a plurality of groups" refers to two or more groups (including two groups), and "a plurality of pieces" refers to two or more pieces (including two pieces).

[0070] In the description of the embodiments of the present application, unless otherwise explicitly specified and limited, the technical terms "mounting", "connecting", "connecting", "fixing" and the like should be understood in a broad sense, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanical connection, or it can be electrical connection; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0071] Reference Figure 1 To solve the problem that the joint estimation method of wideband signal direction and source number in the prior art has low precision in the scene of low signal-to-noise ratio and multiple source overlap, and is difficult to adapt to the multi-frequency characteristics of wideband signals, an embodiment of the present application provides a joint estimation method of wideband signal direction and source number, which comprises steps S101-S103, and specifically comprises:

[0072] Step S101, obtaining frequency domain data corresponding to different frequency points of a wideband signal received by a hydrophone array, and converting the frequency domain data into a sparse representation model based on a multi-frequency overcomplete array manifold matrix, wherein the multi-frequency overcomplete array manifold matrix comprises overcomplete array manifold vectors corresponding to multiple frequency points.

[0073] In the embodiment, a hydrophone array (such as a uniform linear array) composed of M hydrophones (array elements) is used to receive an underwater broadband signal, such as a 10-element uniform linear array with an element spacing of 1 m, a sampling frequency of 3 kHz, and the broadband signal including multiple frequency components (such as 500-1000 Hz). The true incident directions of three broadband white noise signals with a frequency range of 500-1000 Hz are -10.7°, 5.3°, and 15.5°, and the frequency domain signal-to-noise ratio SNR is 0 dB. Since the underwater broadband signal is a time-domain signal, the original time-domain data is obtained by preprocessing (such as anti-aliasing filtering) the array-received time-domain signal, and the time-domain data is converted to frequency-domain data by Fourier transform (such as fast Fourier transform FFT). F frequency points (denoted as f = f1,..., f F ), for example, the frequency points f = [500, 550, 600, 700, 750, 800, 850, 900, 950, 1000] Hz, are selected, and the frequency-domain data of the broadband signal received by the hydrophone array at the selected frequency points are extracted, where Y f is an M x L matrix (L is the frequency domain snapshot number), and each element in the frequency-domain data represents the signal amplitude and phase information of a certain element and a certain snapshot at the frequency point.

[0074] A multi-frequency over-complete array manifold matrix corresponding to the frequency f is established by predefining spatial direction points. Specifically, in the range of possible signal incoming direction (such as -60° to 60°), N spatial direction points are divided at a preset interval (such as 2°), denoted as For each frequency point f, the array manifold vector corresponding to each spatial direction point at the frequency point is calculated. wherein, is an M x 1 complex vector, and in the uniform linear array, the mth element of the array manifold vector can be represented as:

[0075]

[0076] wherein j is the imaginary unit.

[0077] The multi-frequency over-complete array manifold matrix is the set of array manifold vectors of all frequency points, covering the spatial domain characteristics of the full frequency domain of the broadband signal. All array manifold vectors of each frequency point f are arranged in columns to obtain the spatial domain over-complete array manifold matrix at the frequency f in the multi-frequency over-complete array manifold matrix, 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 each spatial direction point, it 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 probability model starts iteration, the hyperparameters are initialized, wherein the hyperparameters include the spatial domain power vector, the gamma distribution rate vector and the noise variance, such as γ (0) = 1 N×1 , ξ (0) = 1 N×1 , The fixed parameter h is -0.1. During the iteration process of the probability model, the posterior distribution of the sparse signal is calculated under the probability model framework composed of the multi-layer prior probability distribution and the conditional probability distribution by using the Bayesian theorem, combining the frequency domain data, the multi-frequency over-complete array manifold matrix, the current spatial domain power vector, the noise variance and the gamma distribution shape parameter. Based on the posterior distribution (such as using the maximum a posteriori estimation and the like), the updated sparse signal of each frequency point is obtained, so that the updated sparse signal is more consistent with the frequency domain data under the probability model, that is, the model has a higher explanation probability for the observed frequency domain data. According to the updated sparse signal, the power update value of each spatial direction point is calculated according to the correlation between the sparse signal and the spatial domain power vector in the first layer prior probability distribution (the statistical characteristics of the sparse signal are constrained by the spatial domain power vector), and the relevant probability formula (such as using the characteristics of the gamma distribution) is combined. The elements in the current spatial domain power vector are updated, so that the updated spatial domain power vector can more accurately reflect the signal power of each spatial direction point under the current iteration, and the sparse signal continues to adapt to the frequency domain data and the prior distribution under the updated spatial domain power vector. Based on the updated spatial domain power vector, the update value of each rate element in the current gamma distribution rate vector is calculated according to the constraint relationship between the updated spatial domain power vector and the current gamma distribution rate vector in the second layer prior probability distribution (the elements of the spatial domain power vector are subject to the gamma distribution containing the gamma distribution rate vector parameter), and the probability model derivation formula (such as through the parameter update rule of the gamma distribution) is used. The current gamma distribution rate vector is updated, so that it can better control the distribution shape of the spatial domain power vector to adapt to the requirements of the entire probability model on the signal sparsity and statistical characteristics. The above steps of updating the sparse signal, the current spatial domain power vector and the current gamma distribution rate vector are continuously executed. After each iteration, the iteration number i is i+1, and whether the iteration termination condition is met is checked. If the iteration termination condition is met, the iteration is stopped, and the obtained spatial domain power vector is the spatial domain power estimation vector. The number of significant non-zero elements in the spatial domain power estimation vector is counted as the source number estimation value.

[0088] In step S103, linear approximation post-processing is performed on the spatial direction point corresponding to the spatial domain power estimation vector to obtain the direction estimation result of the wideband signal.

[0089] In the embodiment, the target spatial domain power estimation vector output after the iteration converges is identified local maximum elements in the normalized spatial spectrum, obtaining a plurality of spectral peaks, each spectral peak corresponding to a predefined spatial direction point These direction points are preliminary estimates of the source direction. Considering that the real source direction may be located between two predefined grids, for each spectral peak, the maximum power value of the spectral peak is extracted and the corresponding spatial direction point and the second largest power value of the spectral peak and the corresponding spatial direction point and are adjacent grid points, wherein ( is the source number estimate), indicates the spectral peak corresponding to the kth source. Considering that the direction point with a larger power value has a higher contribution weight to the real source direction, therefore, for each source k, by weightedly averaging the directions of adjacent grid points, the “off-grid bias” caused by the predefined grid discretization is compensated, so that the estimate is closer to the real source direction, and the final direction estimate is obtained. The high-precision direction estimate of all K sources is calculated as the final direction estimate of the wideband signal.

[0090] As shown in Figure 2 is a normalized spatial spectrum, and the red circles are the real azimuth angles. As shown in Figure 3 is a diagram of the azimuth estimate result changing with the signal-to-noise ratio. As shown in Figure 4 is a diagram of the source number estimate changing with the signal-to-noise ratio.

[0091] The post-processing step of the embodiment effectively reduces the direction estimation error caused by the over-coarse spatial grid division by linearly approximating the information of adjacent grid points, and is especially suitable for the scenario in which the real source direction does not fall on the predefined grid point, and significantly improves the direction finding accuracy.

[0092] The above embodiment discloses a method for jointly estimating the direction and source number of a wideband underwater acoustic signal based on sparse Bayesian learning. In the simulation detection scenario of a uniform linear array and a wideband white noise signal, a multi-frequency sparse representation model of underwater direction finding is constructed, a hierarchical prior probability distribution is established, the updating steps of each parameter and the source number estimation strategy are given, and after iterative estimation, the accuracy of the direction estimation is further improved through linear approximation post-processing.

[0093] As an example of the embodiment, the corresponding spatial direction point is linearly approximated and post-processed based on the spatial power estimation vector to obtain the direction estimate value of the wideband signal, specifically:

[0094]

[0095] wherein, is the direction estimation value of the kth signal direction, are the two largest and the second largest power values in the kth spectral peak, are the corresponding grid point directions.

[0096] As an example of an embodiment of the present application, the probability model is iteratively updated according to the frequency domain data, the multi-frequency over-complete array manifold matrix and the gamma distribution shape parameter, and the current spatial power vector and the current gamma distribution rate vector of each sparse signal in the probability model, specifically:

[0097] In each iteration process of the probability model, each sparse signal is updated based on the frequency domain data, the multi-frequency over-complete array manifold matrix, the current spatial power and the noise variance, to obtain an 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; the current spatial power vector is updated 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 the current gamma distribution rate vector is updated based on the updated spatial power vector and the gamma distribution shape parameter, to obtain an updated gamma distribution rate vector; a plurality of spectral peaks are extracted from the updated spatial power vector, a multi-frequency point likelihood function increment is calculated based on the updated spatial power vector and the spatial direction point corresponding to each spectral peak, and the number of sources is estimated according to the increment, to obtain the number of source estimation value; the noise variance is updated according to the number of source estimation value, to obtain an updated noise variance, so as to perform the next iteration according to the updated spatial power vector, the updated noise variance and the gamma distribution shape parameter.

[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 the present embodiment, the input frequency domain data Y f , the multi-frequency over-complete array manifold matrix , the current spatial power vector γ, and the current noise variance σ 2 . Based on the first layer prior probability distribution of the sparse signal, the sparse signal is subject to a complex Gaussian distribution with a mean of 0 and a variance of γ, and the conditional probability distribution of the frequency domain data (the observation data is subject to a mean of and a variance of σ​​​2 I M The posterior distribution of the sparse signal X is calculated by Bayesian inference for the current frequency domain covariance matrix f The sparse signal X is updated at each frequency point by using maximum a posteriori estimation or variational inference, to obtain an updated sparse signal f Based on the updated sparse signal, the statistical characteristics are calculated, i.e., the current frequency domain mean matrix μ f and the current frequency domain covariance matrix ∑ f The diagonal elements of the current frequency domain covariance matrix (∑ f ) nn (the variance of the nth spatial direction) are taken.

[0100] According to the current frequency domain mean matrix μ f , the current frequency domain covariance matrix ∑ f , and the current gamma distribution rate vector ξ, the current spatial domain power vector is updated, specifically, the current spatial domain power vector γ n obeys a gamma distribution with parameters 3 / 2 and ξ n , and the updated spatial domain power vector γ (i) is obtained by solving the maximum a posteriori probability based on the square of the modulus of the row vector of the current frequency domain mean matrix μ f and the diagonal elements of the current frequency domain covariance matrix ∑ f .

[0101] According to the updated spatial domain power vector γ (i) , the gamma distribution shape parameter h (a preset fixed value), and based on the third layer prior probability distribution, the current gamma distribution rate vector ξ n obeys a gamma distribution with parameter h, to obtain an updated gamma distribution rate vector ξ (i) .

[0102] From the updated spatial domain power vector γ (i) , K spectral peaks (local maxima) with the largest amplitudes are selected in descending order, and the corresponding spatial direction points are For each spectral peak k, based on the corresponding spatial direction point and the spatial domain power vector, the multi-frequency point likelihood function increment is calculated (the likelihood function increment is positive, indicating that there is a real source in the direction) is counted as the source number estimate value According to the source number estimate value , the eigenvalues of the second covariance matrix R are calculated wherein is 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. nis the power element in the current spatial domain power vector, σ 2 is the noise variance, σ 2 I M is the second covariance matrix, (U f ) n· is the nth row element of the matrix U f , is the nth column element of the matrix ;

[0114] The updated spatial domain power vector is

[0115]

[0116] The updated gamma distribution rate vector is

[0117]

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

[0119] As an example of an embodiment of the application, the plurality of spectral peaks are extracted from the updated spatial domain power vector, the multi-frequency point likelihood function increment is calculated based on the updated spatial domain power vector and the spatial direction point corresponding to each spectral peak, and the number of sources is estimated according to the increment to obtain the source number estimate value, specifically:

[0120] The spectral peaks in the updated spatial domain power vector are arranged in descending order of amplitude, and a predetermined number of target spectral peaks are determined in the descending order of the plurality of spectral peaks; the first intermediate factor and the second intermediate factor related to the spatial direction points and the spatial domain power of the target spectral peaks are calculated, and the increment of the multi-frequency point likelihood function is calculated according to the calculation, so as to estimate the number of sources by positive increment.

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

[0122] In this embodiment, in the updated spatial domain power vector γ (i)In the method, all local maximum values are screened as spectrum peaks, wherein the local maximum value refers to a position where an element value is greater than adjacent element values on the left and right, and corresponds to a potential source direction. The identified spectrum peaks are sorted in descending order according to their amplitudes (spatial power values) to obtain a descending spectrum peak sequence. A preset number of spectrum peaks are selected from the descending sequence as target spectrum peaks (the preset number can be set according to experience or scene requirements, and is usually greater than an actual possible source number to avoid missing a real source). Each target spectrum peak corresponds to a spatial direction point (k=k, 2,..., K is a preset number, n k is an index of the direction point in the spatial domain grid). For each target spectrum peak k, a first intermediate factor is calculated based on a frequency f corresponding to an over-complete array manifold vector, a conjugate transpose of the array manifold vector, an inverse matrix of a current frequency domain covariance matrix of the frequency domain data, in combination with a corresponding spatial direction point and a spatial power value and a second covariance matrix R f of the frequency domain data to calculate a second intermediate factor For each target spectrum peak k, all frequency point first intermediate factors and second intermediate factors are fused to calculate a multi-frequency point likelihood function increment The increment reflects the degree of improvement in the explanation ability of the probability model to the observation data after introducing the spectrum peak. The number of target spectrum peaks that satisfy (the increment is positive, indicating that the spectrum peak corresponds to a real source and can significantly improve the fitting degree of the model to the data) is counted, and the number is the final source number estimation value.

[0123] The embodiment filters the spectrum peak corresponding to the real source by the positive and negative nature of the likelihood function increment through the above steps, realizes adaptive estimation of the source number, does not need to pre-suppose the source number, and improves the applicability in the unknown source number scene.

[0124] As an example of the embodiment, the calculation of the increment of the multi-frequency point likelihood function according to the first intermediate factor and the second intermediate factor is specifically:

[0125]

[0126] wherein, represents a source number estimation value, and are the first intermediate factor and the second intermediate factor respectively, represent a spatial direction point and a spatial power related function values, represents a multi-frequency point likelihood function increment, and card represents the number of k that satisfies the set condition.

[0127] As an example of an embodiment of the present application, the probability model, in particular:

[0128] In the first layer prior probability distribution, for each snapshot of each frequency point, the probability density of each sparse signal column corresponding to the sparse signal column being subject to a mean value of zero and a variance of the current spatial domain power vector is judged, the probability densities corresponding to all sparse signal columns are multiplied, and a first prior probability distribution value is obtained, wherein the first layer prior probability distribution is a prior probability distribution for representing the sparse signal; in the second layer prior probability distribution, for each power element in the spatial domain power vector, the first gamma distribution probability density of each power element being subject to a first parameter and the current gamma distribution rate vector is judged, the first gamma distribution probability densities corresponding to all power elements are multiplied, and a second prior probability distribution value of the current spatial domain power vector is obtained, wherein the second layer prior probability distribution is used to represent the prior probability distribution of the current spatial domain power vector; in the third layer prior probability distribution, for each rate element in the current gamma distribution rate vector, the second gamma distribution probability density of each rate element being subject to the gamma distribution shape parameter is judged, the second gamma distribution probability densities corresponding to all rate elements are multiplied, and a third prior probability distribution value corresponding to the current gamma distribution rate vector is obtained, wherein the third layer prior probability distribution is used to represent the prior probability distribution of the current gamma distribution rate vector, the distribution of the current gamma distribution rate vector in the second layer prior probability distribution is controlled by the current gamma distribution shape parameter in the third layer prior probability distribution, and the variance of the current spatial domain power in the first layer prior probability distribution is controlled by the current gamma distribution rate vector in the second layer prior probability distribution; in the conditional probability distribution, for each snapshot of each frequency point, the conditional probability density of each frequency domain data column corresponding to the frequency domain data column being subject to a complex Gaussian distribution probability density with a mean value being a product of the multi-frequency over-complete array manifold matrix and the corresponding sparse signal column and a second covariance matrix corresponding to the frequency domain data being a product of a noise variance and a unit matrix is judged, the conditional probability densities corresponding to all frequency domain data columns are multiplied, and a conditional probability distribution value is obtained, wherein the conditional probability distribution value is used to evaluate the matching degree between the frequency domain data and the sparse representation model.

[0129] In the first layer prior probability distribution (prior modeling of the sparse signal), the applicable object is a sparse signal column (X 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 application. The one or more modules can be a series of computer program instruction segments capable of completing a specific function, which are used to describe the execution process of the computer program in the terminal device.

[0141] The terminal device can be a desktop computer, a notebook computer, a palm computer, a cloud server and other computing devices. The terminal device can include, but is not limited to, a processor and a memory.

[0142] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The processor is the control center of the terminal device, and connects all parts of the terminal device through various interfaces and lines.

[0143] On the basis of the above-mentioned method embodiment, another embodiment of the present application provides a computer readable storage medium, including a stored computer program, wherein when the computer program runs, the device where the computer readable storage medium is located executes the wideband signal direction and source number joint estimation method described in any one of the above-mentioned method embodiments of the present application.

[0144] The modules / units integrated in the device / terminal equipment, if realized in the form of software function 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 above-mentioned embodiment methods can also be completed by a computer program instructing related hardware, and the computer program can be stored in a computer readable storage medium. When the computer program is executed by a processor, the steps of each method embodiment can be implemented. The computer program includes computer program code, which can be in the form of source code, object code, executable files or some intermediate forms, etc. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc.

[0145] The above is the preferred embodiment of the present application. It should be pointed out that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, which are also considered within the scope of protection of the present application.

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 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 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: Γ = diag(γ); in, This represents the mean of the sparse signal at frequency f. This is the frequency domain data at frequency f. (∑ 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; The updated spatial power vector is, The updated gamma distribution rate vector is: 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.

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, denoted by , represents the increment of the likelihood function at multiple frequencies, and card represents the number of k that satisfy the set conditions.

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, 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 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 direction estimate of the k-th 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. 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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