A sparse Bayesian learning vector acoustic direction finding method based on orthogonal acoustic intensity flux

Abstract

The application discloses a sparse Bayesian learning vector acoustic direction finding method based on orthogonal acoustic intensity flow, and belongs to the technical field of array signal processing. First, an orthogonal acoustic intensity flow data model is constructed, an acoustic intensity flow is obtained by cross spectrum of sound pressure and vibration velocity channels, and acoustic energy flow density is obtained by acoustic pressure autospectrum. Then, a joint probability density distribution function is established by means of a sparse Bayesian learning model. Finally, according to maximum log-Bayes evidence estimation of signal power, spectral peak search is performed on the signal power estimation value, and the direction estimation of the target is realized. The method uses acoustic intensity and acoustic intensity flow as input, has the effect of suppressing isotropic noise and reduces the calculation amount. When the hyperparameters are updated for the first time, a deconvolution algorithm is introduced to avoid the judgment error of the number of signal sources and the direction of arrival caused by the proximity of two targets. Moreover, the method has good direction estimation accuracy and direction resolution capability, and can maintain good performance under the condition of low signal-to-noise ratio.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically to a sparse Bayesian learning vector acoustic direction finding method based on orthogonal acoustic intensity current. Background Technology

[0002] Due to the wide directivity of single-vector hydrophones, how to ensure the estimation accuracy while achieving high resolution of the algorithm estimation results is a continuous research direction for horizontal direction finding algorithms for single-vector hydrophones.

[0003] Some methods introduce traditional high-resolution processing methods for sound pressure arrays into single-vector hydrophone signal processing, such as MUSIC and MVDR. This method greatly improves the spatial resolution of the estimation results, but the performance deteriorates significantly as the signal-to-noise ratio decreases, especially the estimated spectral peaks will degrade sharply. At the same time, some subspace-based algorithms require prior knowledge of the number of signal sources, which is difficult to obtain in practice.

[0004] Another approach is to introduce sparse methods into single-vector hydrophone signal processing. By utilizing the noise-independent nature of sound pressure and vibration velocity, a covariance matrix of sound pressure and vibration velocity is constructed, and a linear model is built based on this matrix for sparse representation. Taking the sparse Bayesian learning algorithm as an example, although high-resolution estimation results are obtained, the number of targets and their orientations need to be estimated during the iteration process. The quality of the search results will seriously affect the algorithm's performance.

[0005] Therefore, combining existing solutions, how to obtain high-resolution estimation results under low signal-to-noise ratio conditions and achieve stable performance improvement is an unsolved problem. Summary of the Invention

[0006] In view of this, the present invention provides a sparse Bayesian learning vector acoustic direction finding method based on orthogonal acoustic intensity flow, which has good azimuth estimation accuracy and azimuth resolution, and can maintain good performance under low signal-to-noise ratio conditions.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0008] Step 1: Obtain the sound intensity flow by cross-spectrum of sound pressure and channel vibration velocity of the vector hydrophone, and obtain the sound intensity in the direction of the incoming wave by the self-spectrum of the sound pressure channel.

[0009] Step 2: Based on the signal structure of acoustic intensity flow and acoustic intensity, establish a sparse dictionary matrix and construct an orthogonal acoustic intensity flow signal model.

[0010] Step 3: Based on the orthogonal acoustic intensity current signal model, construct a sparse Bayesian learning model to obtain a probabilistic description of the incoming wave direction estimation.

[0011] Step 4: Based on the sparse Bayesian model, the hyperparameters and noise variance are estimated iteratively in alternating steps. In the first iteration, the deconvolution algorithm is used to separate the aliased target and obtain the signal estimates in each direction, while also estimating the number of signal sources. The iteration is terminated according to the convergence condition or the upper limit of the number of iterations, and the obtained hyperparameters are the target orientation estimation results.

[0012] Further, step 1 includes the following specific steps: utilizing the fact that sound pressure and vibration velocity signals are noise-independent, noise reduction is achieved by cross-spectral processing of sound pressure and vibration velocity; wherein the target signal is S, and the sound intensity flow includes sound intensity flow I. x I y I x I is obtained by taking the real part of the conjugate multiplication of the sound pressure P and the X-channel vibration velocity signal of the vector hydrophone. y The sound pressure P is obtained by multiplying the sound pressure P by the Y-channel vibration velocity signal of the vector hydrophone and taking the real part. The sound intensity I is obtained by multiplying the sound pressure itself by its own conjugate.

[0013] Furthermore, acoustic intensity flow I x I y The sound intensity I is represented as:

[0014] I x (f)=real{P(f)·V x * (f)}=cosθ|S(f)| 2 / ρc

[0015] I y (f)=real{P(f)·V y * (f)}=sinθ|S(f)| 2 / ρc

[0016] I(f)=P(f)·P * (f) / ρc=|S(f)| 2 / ρc

[0017] Among them, I x (f), I y (f) represents the intensity of sound energy transmitted along the X and Y axes of the vector hydrophone, which is the sound intensity flow I. x I y I(f) is the scalar sound intensity, representing the magnitude of the sound wave energy flux density, i.e., the sound intensity I; f is the frequency point of the signal in the spectrum; real{} refers to taking the real part, P(f) is the frequency domain signal of the sound pressure channel, V x (f), V y(f) represents the frequency domain representation of the X and Y channel signals of the vector hydrophone, respectively; the superscript * means conjugate; θ is the direction of the incoming wave; S(f) is the frequency domain representation of the signal; ρ is the density of the medium, and c is the propagation speed of the sound wave in the medium.

[0018] Furthermore, step 2 is specifically divided into the following steps:

[0019] S2-1: At time t, when signal S illuminates the vector hydrophone at a horizontal orientation θ0, the sound intensity and sound intensity flow can be represented by a linear model:

[0020] I f =D0P s (f)+N(f);

[0021] Where I f For observation channel, I f =[I x (f),I y (f),I(f)] T D0 = [cosθ0, sinθ0, 1] T P s (f) represents the signal power. Indicates noise power. For noise-related terms, D0 is a parameter expressing the incident direction, and f is the frequency of the signal S;

[0022] S2-2: Divide the horizontal azimuth [0°, 360°] evenly into M parts to obtain the set of parameters representing the incident azimuth:

[0023] D m =[cosθ m sinθ m ,1] T m = 1, ..., M;

[0024] Where D m Let θ be the parameter of the m-th incident direction. m Let θ represent all possible incident directions of the target after discretization, i.e., the 360° direction is uniformly divided into M azimuths. m This corresponds to the m-th angle; the value of M is set according to the required azimuth accuracy.

[0025] S2-3: Considering multiple frequencies, the acoustic intensity flow model at the location of the single-vector hydrophone is as follows:

[0026] I = DP + N

[0027] in Representing different frequencies f1 to f L The acoustic intensity flow is given by D = [D1,...,D] M] represents the parameters of all possible directions of arrival within the horizontal range, P = [P s (f1),...,P s (f L [)] represents the signal power at each frequency point, N = [N(f1),...,N(f2)] L ] represents the noise at each frequency point, and the set {f1,...,f L} represents the frequency points to be processed, with a total of L frequency points.

[0028] Furthermore, step 3 specifically involves:

[0029] If the signal and noise are uncorrelated, the likelihood probability of the data is...

[0030]

[0031] Where ∏() refers to accumulation, CN() refers to the complex Gaussian probability model, and σ f 2 Here, I represents the noise variance, and I refers to the identity matrix.

[0032] Set the hyperparameter γ = [γ1,...,γ] M To approximate the signal power in each direction, γ1,...,γ M Let Γ = diag(γ1,…,γ) be the signal power in M ​​directions. M If ) = diag(γ), then there is a prior probability

[0033]

[0034] Under the Gaussian assumption, the sparse Bayesian learning model is derived from the prior probability and the likelihood probability, and the probabilistic description p(I) of the incoming wave direction estimation is obtained.

[0035]

[0036] Wherein, the covariance matrix

[0037] Further, step 4 is as follows:

[0038] S4-1: After obtaining the probability description of the incoming wave direction in step 3, define the hyperparameter γ = [γ1,...,γ2]. M Used to approximate signal power in each direction, γ1,...,γ M Given signal power in M ​​directions, the hyperparameter γ is solved by maximizing the log-Bayesian evidence:

[0039]

[0040] Where p(I) is the posterior probability model of observation channel I;

[0041] By iteratively updating the hyperparameters to obtain optimal parameter values, and denoting the current iteration number as k, the update formula obtained by the fixed-point iteration method is as follows:

[0042]

[0043] Where I fl To process frequency f l The observation channel, f l ∈{f1,...,f L}, l=1,...,L,D m H D m The transpose of , with superscripts (k) and (k+1) referring to the results of the k-th and (k+1)-th iterations, respectively;

[0044] S4-2: The first iteration yields the hyperparameter γ estimate. (2) Afterwards, by D T D(180°) yields the directional functions A(θ) for each direction. m ), where D(180°) = [cos180°, 180°, 1] T m = 1, ..., M; by The energy estimates W(θ) in each direction are obtained. m ), m=1,...,M; using the directional function A(θ m ), For W(θ) m Perform deconvolution operations to obtain the deblurred signal power estimates W in each direction. DCV , for W DCV Perform a spectral peak search and record the number of spectral peaks N and their locations as the target locations and target counts obtained in the first iteration; then, after updating the hyperparameter γ estimate in the k-th iteration, adjust γ... (k+1) Perform a spectral peak search to determine the number and location of targets;

[0045] S4-3: After obtaining the number of targets and their locations, the noise variance The updated formula is as follows:

[0046]

[0047] Where N is the number of information sources and must be less than 3, D N This is a matrix composed of dictionary vectors representing the location of the target.

[0048] Furthermore, in step 4, the iteration is terminated based on the convergence condition or the upper limit of the number of iterations, and the resulting hyperparameters are the target orientation estimation results, as detailed below:

[0049] Let ε minThe iteration termination threshold is defined as follows:

[0050]

[0051] ||·||1 is the symbol for the L1 norm;

[0052] If the above iteration conditions are met after the q-th iteration, the number of signal sources is N, and the direction of arrival is... The orientation of the N spectral peaks in the hyperparameter γ.

[0053] Beneficial effects:

[0054] This invention utilizes the characteristics that sound pressure and vibration velocity channels are noise-independent and in phase. It obtains sound intensity and orthogonal sound intensity flow by multiplying the sound pressure autospectrum and sound pressure velocity conjugate and taking the real part. A sparse Bayesian learning model for azimuth estimation is then established based on this model, and the signal power and noise power in each direction are estimated iteratively. In the first iteration, deconvolution is performed on the result before spectral peak search to avoid two horizontally close targets being identified as a single target in the initial iteration, thus preventing errors in the number of signal sources and azimuth estimation due to the targets being too close. This algorithm uses sound intensity and orthogonal sound intensity flow as input, suppressing noise while reducing computational load. It exhibits good performance at high signal-to-noise ratios and maintains good accuracy while keeping the estimated spectral peak width constant under low signal-to-noise ratio conditions. This method has good azimuth estimation accuracy and azimuth resolution, maintaining good performance even at low signal-to-noise ratios, and has significant engineering application value. Attached Figure Description

[0055] Figure 1 This is a diagram illustrating the method steps of the present invention.

[0056] Figure 2a The curves show the root mean square error of the azimuth estimation as a function of the signal-to-noise ratio. The solid black line represents the method of this invention, and the dashed black line represents the MUSIC algorithm. Figure 2b The curve shows the -3dB beamwidth versus signal-to-noise ratio. The triangular markers represent the method of this invention, and the black dashed line represents the MUSIC algorithm. The number of Monte Carlo trials for each signal-to-noise ratio is 500.

[0057] Figure 3 The table shows the azimuth estimation results of the two targets in the example using the algorithm of this invention, MUSIC, and conventional beamforming algorithms; the solid black line represents the estimation result of the algorithm of this invention; the short black dashed line represents the estimation result of MUSIC; and the dotted black dashed line represents the estimation result of conventional beamforming. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0059] like Figure 1As shown, the sparse Bayesian learning lateral method based on orthogonal acoustic intensity current provided by this invention includes the following steps:

[0060] Step 1: Cross-spectral processing of the sound pressure of the vector hydrophone and the vibration velocities of the X and Y channels yields the sound intensity flow I along the X and Y axes. x I y The acoustic intensity I in the direction of arrival is obtained by self-spectral processing of the sound pressure channel.

[0061] In this embodiment of the invention, a narrowband incoherent signal is incident from a horizontal azimuth θ0 onto a two-dimensional single-vector hydrophone. The sound intensity and sound intensity flux at the location of the single-vector hydrophone are then:

[0062] I x (f l )=real{P(f l )·V x * (f l )}=cosθ0|S(f l )| 2 / ρc

[0063] I y (f l )=real{P(f l )·V y * (f l )}=sinθ0|S(f l )| 2 / ρc

[0064] I(f l )=P(f l )·P * (f l ) / ρc=|S(f l )| 2 / ρc

[0065] Among them, I x (f), I y (f) represents the intensity of sound energy transmitted along the X and Y axes of the vector hydrophone, respectively; I(f) is the scalar sound intensity, representing the magnitude of the sound wave energy flux density; f is the frequency point of the signal in the spectrum; real{*} refers to taking the real part; P(f) is the frequency domain signal of the sound pressure channel; V x (f), V y(f) represents the frequency domain representation of the X and Y channel signals of the vector hydrophone. * indicates conjugate; θ is the direction of arrival of the signal; S(f) is the frequency domain representation of the signal; ρ is the density of the medium, and c is the speed of sound in the medium. The X and Y axes are derived from the X and Y axes in the xy-plane coordinate system. The X and Y channels are the signal channels of the vector sensor corresponding to the X and Y axis directions. Usually, the X and Y directions, as well as the Z-axis direction of the vector hydrophone, are marked at the factory. l ∈[f1,...,f L ] indicates the processing frequency points, and there are a total of L frequency points.

[0066] Based on the above equation, the sound intensity I and the orthogonal sound intensity flow I are obtained. x I y .

[0067] Step 2: Based on the signal structure of acoustic intensity flow and acoustic intensity, establish a sparse dictionary matrix and construct an orthogonal acoustic intensity flow signal model.

[0068] The sound intensity and sound intensity flow can be represented by a linear model:

[0069] I fl =D0P s (f l )+N(f l )

[0070] Where I fl =[I x (f l ),I y (f l ),I(f l )] T D0 = [cosθ0, sinθ0, 1] T P s (f l () represents signal power. Indicates noise power, n I , Let D0 be a noise-related term, representing the parameter indicating the incident azimuth. A sparse dictionary is then constructed based on this. The horizontal azimuth [0°, 360°] is uniformly divided into M parts, resulting in the parameter set D representing the incident azimuth. m =[cosθ m sinθ m ,1] T ,m=1,...,M. Let D be... m Let M be the parameter for the m-th incident direction. The value of M is set according to the required azimuth accuracy. When a higher accuracy is required, M can be set to 3601, i.e., 0.1° per division. If only an approximate azimuth is needed, take 361, i.e., 1° per division. θ mThe discretized target incident direction, i.e., the 360° direction, is uniformly divided into M azimuths, corresponding to M angles.

[0071] Considering multiple frequencies, the acoustic intensity flow model at the location of the single-vector hydrophone is as follows:

[0072] I = DP + N

[0073] in Describing the acoustic intensity flux at different frequencies, D = [D1,...,D2] M ] represents the parameters of all possible directions of arrival within the horizontal range, P = [P s (f1),...,P s (f L [)] represents the signal power at each frequency point, N = [N(f1),...,N(f2)] L ] represents the noise at each frequency point, and the set {f1,...,f L} represents the frequency points to be processed, with a total of L frequency points.

[0074] Step 3: Based on the orthogonal acoustic intensity current signal model, construct a sparse Bayesian learning model to obtain a probabilistic description of the incoming wave direction estimation.

[0075] If signal power and noise are independent, the data likelihood probability can be written as:

[0076]

[0077] Where ∏(*) refers to accumulation, CN(*) refers to the complex Gaussian probability model, and σ f 2 The noise variance is I, where I represents the identity matrix.

[0078] Introduce hyperparameters γ = [γ1,...,γ M Variational approximation is performed on the signal power in each direction, γ1,...,γ M Let M be the signal power in each direction. Then the diagonal covariance matrix Γ = diag(γ1,...,γ) M The prior model of ) can be written as:

[0079]

[0080] Under the Gaussian assumption, Bayesian evidence is derived from prior probability and likelihood probability.

[0081]

[0082] Solving for the hyperparameter γ by maximizing the log-Bayesian evidence:

[0083]

[0084] Step 4: Based on the sparse Bayesian model, iteratively estimate the hyperparameters and noise variance to obtain signal estimates in each direction, and simultaneously estimate the number of signal sources; terminate the iteration according to the convergence condition or the upper limit of the number of iterations, and the obtained hyperparameters are the target orientation estimation results.

[0085] By iteratively updating the hyperparameters to obtain optimal parameter values, and denoting the current iteration number as k, the update formula obtained by the fixed-point iteration method is as follows:

[0086]

[0087] Where I fl To process frequency f l The observation channel, f l ∈{f1,...,f L}, l=1,...,L,D m H D m The transpose of .

[0088] The first iteration yields the hyperparameter γ estimate. (2) Afterwards, by D T D(180°) yields the directional functions A(θ) for each direction. m ), where D(180°) = [cos180°, 180°, 1] T ,m=1,...,M. From The energy estimates W(θ) in each direction are obtained. m ), m=1,...,M. Use the directional function A(θ) m ) for W(θ) m Perform deconvolution operations to obtain the deblurred signal power estimates W in each direction. DCV , for W DCV A spectral peak search is performed, and the number of peaks N and their locations are recorded as the target locations and target counts obtained in the first iteration. In the subsequent k-th iteration, the hyperparameter γ is estimated and the value of γ is adjusted. (k+1) A spectral peak search is performed to determine the number of targets and their locations. After obtaining the number of sources and the target locations, the noise variance update formula is as follows:

[0089]

[0090] Where N is the number of information sources and must be less than 3, D N This is a matrix composed of dictionary vectors representing the location of the target.

[0091] Let ε min The iteration termination threshold is defined as follows:

[0092]

[0093] If the above iteration conditions are met after the q-th iteration, the number of signal sources is N, and the direction of arrival is... The orientation of the N spectral peaks in the hyperparameter γ.

[0094] The effectiveness of the above method is illustrated below through numerical simulation:

[0095] Two narrowband uncorrelated signals are incident from different directions at angles of 60° and 140°, with an azimuth grid of [0°:1°:360°], corresponding to a sparse dictionary D. m =[cosθ m sinθ m ,1] T ,θ m ∈[0°:1°:360°], m=1,...,361. A multi-signal resolution algorithm (MUSIC) is included as a comparison algorithm in the simulation. Each simulation result is obtained through 500 Monte Carlo experiments. Simulations of horizontal azimuth estimation are performed to address the changes in algorithm performance under different signal-to-noise ratios.

[0096] Depend on Figure 2a and Figure 2b It can be seen that both methods have good accuracy and sharp spectral peaks at high signal-to-noise ratios. As the signal-to-noise ratio decreases, the method proposed in this patent maintains almost no change in the spectral peak width, while the accuracy decreases slowly. In other words, the method proposed in this patent is completely superior to the MUSIC method at low signal-to-noise ratios, and has both good accuracy and maintains sharp spectral peaks under low signal-to-noise ratio conditions.

[0097] Depend on Figure 3 It can be seen that the method proposed in this patent can obtain a more accurate number of information sources through deconvolution calculation, avoiding misjudgment caused by the location of information sources being too close, and reducing the dependence on prior information source number information.

[0098] This invention utilizes the characteristics that sound pressure and vibration velocity channels are noise-independent and in phase. It obtains sound intensity and orthogonal sound intensity flow by multiplying the sound pressure autospectrum and sound pressure velocity conjugate and taking the real part. A sparse Bayesian learning model for estimating the azimuth of incoming waves is then established based on this model, and the signal power and noise power in each direction are estimated iteratively. In the first iteration, the result is deconvolved before spectral peak search to avoid two horizontally close targets being identified as a single target in the initial iteration. This algorithm uses sound intensity and orthogonal sound intensity flow as input, suppressing noise while reducing computational load. It exhibits good performance at high signal-to-noise ratios and maintains good accuracy while keeping the estimated spectral peak width constant under low signal-to-noise ratio conditions.

[0099] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sparse Bayesian learning vector acoustic direction finding method based on orthogonal sound intensity flow, characterized in that, It comprises the following steps: Step 1, the sound intensity flow is obtained by the cross spectrum of the sound pressure and the channel vibration velocity of the vector hydrophone, and the incoming direction sound intensity is obtained by the self spectrum of the sound pressure channel; The step 1 comprises the following specific steps: The noise is irrelevant to the sound pressure and the velocity signal, and the sound pressure and the velocity are cross-spectrally processed to realize noise reduction; wherein the target signal is S, the sound intensity flow includes a sound intensity flow , , is obtained by performing conjugate multiplication on the sound pressure P and the X-channel velocity signal of the vector hydrophone and then taking the real part, is obtained by performing conjugate multiplication on the sound pressure P and the Y-channel velocity signal of the vector hydrophone and then taking the real part, and the sound intensity is obtained by performing conjugate multiplication on the sound pressure itself. The acoustic intensity flow , , acoustic intensity is expressed as: where, , are the transport intensity of acoustic energy along the X, Y axis of the vector hydrophone, i.e. the acoustic intensity flow , , is the scalar acoustic intensity, which describes the acoustic energy flow density, i.e. the acoustic intensity ; f is the frequency point of the signal in the frequency spectrum; denotes taking the real part, is the frequency domain signal of the sound pressure channel, , are the frequency domain expressions of the X, Y channel signals of the vector hydrophone; the superscript means taking the conjugate; is the direction of arrival of the signal; is the frequency domain expression of the signal; is the medium density, is the transmission speed of the acoustic wave in the medium; Step 2, a sparse dictionary matrix is established based on the signal structure of the sound intensity flow and the sound intensity, and an orthogonal sound intensity flow signal model is constructed; The step 2 is specifically divided into the following steps: S2-1: At time t, signal S is in horizontal position When illuminating a vector hydrophone, the acoustic intensity and acoustic intensity flow are expressed as linear models: ； wherein is the observed channel, , , is the signal power, denotes the noise power, is the noise correlation term, is a parameter expressing the incident azimuth, is the signal S frequency; S2-2: horizontally aligning is uniformly divided into M parts, obtaining a parameter set representing the incident orientation: ； wherein is the parameter for the mth incident direction, is the discrete all possible target incident directions, i.e. 360° directions are evenly divided into M azimuths, corresponds to the mth angle; the value of M is set according to the actual required azimuth accuracy; S2-3: considering multiple frequencies, the sound intensity flow model of the position where the single vector hydrophone is located is: where denotes different frequencies f 1 ~f L under the sound intensity flow, denotes the parameter of all possible wave direction in the horizontal range, denotes the signal power of each frequency point, denotes each frequency point noise, set is the frequency point processed, a total of L frequency points; Step 3, according to the orthogonal sound intensity flow signal model, a sparse Bayesian learning model is constructed, and a probability description of the incoming direction estimation is obtained; Step 4, based on the sparse Bayesian model, the hyperparameters and the noise variance are estimated by alternating iteration; wherein the first iteration uses a deconvolution algorithm to separate the aliasing targets, obtains the signal estimation value of each direction, and estimates the number of signal sources at the same time; the iteration is terminated according to the convergence condition or the upper limit of the iteration number, and the obtained hyperparameters are the target direction estimation results.

2. The quadrature steered beamforming method of claim 1, wherein, The step 3 is specifically: If the signal and the noise are not correlated, the likelihood probability of the data is wherein, denotes an accumulation, denotes a complex Gaussian probability model, is the noise variance, denotes the identity matrix; Setting hyperparameters to approximate each directional signal power, for M directional signal powers; let then there is a prior probability Under the Gaussian assumption, the sparse Bayesian learning model is derived from the prior probability and the likelihood probability to obtain the probability description of the DOA estimation ; where the covariance matrix .

3. The quadrature steered beamforming method of claim 2, wherein, The step 4 is specifically as follows: S4-1 : After obtaining the probabilistic description of the DOA in step 3, define the hyperparameters for approximating the power of each directional signal, for M directional signal powers, solve the hyperparameters by maximizing the log-Bayesian evidence : ； wherein the observation channel posterior probability model; The optimal parameter value is obtained by continuously updating the hyperparameters, and the current iteration round is recorded as k, and the updating formula is obtained by the fixed-point iteration method as follows: ； wherein is the processing frequency of the observation channel, , , is the transpose of , the superscripts (k) and (k+1) refer to the results of the kth and (k+1)th iteration, respectively. S4-2: Obtaining hyperparameters in the first iteration estimated value Afterwards, by Obtain the directional functions of each direction ,in ;Depend on Energy estimates in each direction were obtained. Use a directive function , ,right Deconvolution operations are performed to obtain the deblurred signal power estimates in each direction. ,right Perform a peak search and record the number of peaks N and their locations as the target locations and number of targets obtained in the first iteration; then update the hyperparameters in the k-th iteration. After estimating the value, for Perform a spectral peak search to determine the number and location of targets; S4-3: After obtaining the target number and its position, the noise variance The update formula is as follows: Where N is the number of sources and must be less than 3, A matrix of dictionary vectors for the target orientation, .

4. The quadrature steered beamforming method of claim 3, wherein, In the step 4, the iteration is terminated according to the convergence condition or the upper limit of the iteration number, and the obtained hyperparameters are the target direction estimation results, which are specifically as follows: Let is an iteration termination threshold, and the iteration termination condition is: ； is the L1 norm symbol; If the above iteration condition is satisfied after the qth iteration, the number of sources is N, and the direction of arrival The hyperparameters are N spectral peaks.

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