Single vector hydrophone high resolution bearing estimation method

Abstract

The application relates to a high-resolution azimuth estimation method of a single-vector hydrophone, relating to the technical fields of underwater acoustic signal processing and direction of arrival estimation. The sound pressure channel and two orthogonal particle velocity channels of the single-vector hydrophone are pretreated; then combined second-order statistics are constructed in a time domain or a frame statistical domain, and a shift-invariant equivalent beam pattern is designed according to the combined second-order statistics; then the beam output is modeled as an angular domain convolution of a real azimuth distribution and a point spread function; finally, a constraint term is introduced in R-L deconvolution iteration, preferably one-dimensional total variation constraint, to restore a high-resolution azimuth spectrum and complete DOA judgment. The application can not only inherit the high-resolution capability of the combined second-order statistics deconvolution framework of the single-vector hydrophone, but also can suppress the instability of standard R-L deconvolution iteration under low signal-to-noise ratio and non-ideal channel conditions.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing and direction of arrival estimation technology, specifically to a high-resolution azimuth estimation method for a single-vector hydrophone. Background Technology

[0002] Vector hydrophones can simultaneously measure sound pressure and particle velocity information at the same spatial location. Compared to scalar hydrophone systems that rely on array apertures, single-vector hydrophones offer significant advantages in terms of platform size, weight, and deployment complexity, making them particularly suitable for constrained platforms such as small underwater unmanned platforms, buoy nodes, and portable detection devices. For these platforms, a key challenge in engineering applications is how to stably obtain high-resolution azimuth information under limited observation dimensions and low signal-to-noise ratio conditions.

[0003] Existing methods for azimuth estimation of single-vector hydrophones mainly include: methods based on sound intensity or complex sound intensity histograms, scanning beamforming methods, and high-resolution methods based on subspace decomposition. Sound intensity-based methods are simple to implement and robust, but the output often exhibits statistical fluctuations, with a relatively wide main lobe, making it difficult to obtain sufficiently sharp spectral peaks. Conventional beamforming and its variants are relatively stable under non-ideal conditions, but their angular resolution is limited by the equivalent aperture. Subspace methods such as MUSIC have high resolution under ideal conditions, but they usually require prior source number information and are sensitive to insufficient snapshots, model mismatch, and inconsistent channel responses. Wang Yujie et al. proposed a deconvolution azimuth estimation method based on combined second-order statistics of single-vector hydrophones. By jointly using the second-order statistics of the sound pressure channel and the orthogonal particle velocity channel, an equivalent beammap with a narrower main lobe and angular translation invariance is constructed. Then, standard RL deconvolution is used to achieve refined azimuth estimation. This method significantly improves multi-target resolution compared to traditional scanning methods and enhances robustness to inconsistent channel amplitude responses to a certain extent. However, standard RL deconvolution is essentially an unregularized multiplicative iterative deconvolution process. In situations with low signal-to-noise ratios, non-stationary ocean background noise, multipath disturbances, or channel response mismatches, iteration accumulates noise and model errors, easily leading to background spectral floor elevation, enhanced local oscillations, and pseudo-peak growth, thus weakening direction-finding stability and engineering usability. Yang Zehui et al. proposed a deconvolution method incorporating total variational constraints in conventional beamforming scenarios, proving that adding a total variational regularization term to the deconvolution objective function can effectively suppress noise and error accumulation, reduce the azimuth spectrum background level, and improve solution stability. However, this method is geared towards conventional horizontal linear array beamforming problems and is not integrated with combined second-order statistical models for single-vector hydrophones, angle-domain translation-invariant beammap construction methods, or single-element direction-finding scenarios.

[0004] Therefore, a new method is still needed that can both inherit the high resolution of the single-vector hydrophone combined second-order statistical deconvolution framework and suppress the instability of standard RL deconvolution iteration under low signal-to-noise ratio and non-ideal channel conditions.

[0005] This invention utilizes a sound pressure channel and two orthogonal particle velocity channels to construct a combined second-order statistic, establishes a translation-invariant equivalent beammap in the angular domain, and uses Richardson-Lucy (RL) deconvolution with a constraint term to recover the target azimuth distribution; in a preferred embodiment, the constraint term is a one-dimensional total variational regularization term. Summary of the Invention

[0006] To achieve the above objectives, this invention proposes a high-resolution azimuth estimation method for a single-vector hydrophone, relating to the fields of underwater acoustic signal processing and direction-of-arrival (DOA) estimation. First, the sound pressure channel and two orthogonal particle velocity channels of the single-vector hydrophone are preprocessed. Then, a combined second-order statistic is constructed in the time domain or frame-by-frame statistical domain, and a translation-invariant equivalent beammap is designed accordingly. Next, the beam output is modeled as an angular domain convolution of the true azimuth distribution and the point spread function. Finally, a constraint term is introduced into the RL deconvolution iteration, preferably using a one-dimensional total variation constraint, to recover the high-resolution azimuth spectrum and complete the DOA decision. This invention inherits the high-resolution capability of the single-vector hydrophone's combined second-order statistic deconvolution framework and suppresses standard RL deconvolution iteration instability under low signal-to-noise ratio and non-ideal channel conditions.

[0007] A high-resolution azimuth estimation method for single-vector hydrophones, such as Figure 1 As shown, the steps are as follows:

[0008] Step 1: The single-vector earpiece receives multi-channel signals;

[0009] Step 2: Calculate the combined second-order statistics of the multi-channel signals;

[0010] Step 3: Map the combined second-order statistics to the angular domain beam to obtain the equivalent beam, and output the equivalent beam as the point spread function (PSF).

[0011] Step 4: Establish the constrained RL objective function;

[0012] Step 5: Iteratively recover the equivalent beam obtained in Step 3 by constraining the RL objective function;

[0013] Step 6: Output the DOA estimation results to obtain the true orientation distribution of the target.

[0014] Furthermore, in step 1, the method for the single-vector hearing device to receive multi-channel signals is as follows:

[0015] Acquiring underwater target acoustic signals using a single-vector audiometer to obtain sound pressure channel signals. and the vibration velocity channel signals of two orthogonal particles and ;

[0016] ;

[0017] ; (1);

[0018] ;

[0019] in, This represents the radiated acoustic signal of the i-th target at time t; Let represent the incident azimuth angle of the i-th target; These represent the noise components of the sound pressure channel and the two orthogonal particle velocity channels, respectively; N represents the number of targets.

[0020] Furthermore, in step 2, the calculation of the combined second-order statistic is as follows:

[0021] Calculate the combined second-order statistics within each data frame of the multi-channel signal;

[0022] The combined second-order statistics include , , , and Five second-order statistics;

[0023] , , ,

[0024] , ;

[0025] ;

[0026] Where T represents transpose.

[0027] Furthermore, in step 3, the method for obtaining the equivalent beam is as follows:

[0028] Step 3.1, based on the scanning angle Constructing a weighted steering vector ;

[0029] ;

[0030] Where T represents transpose;

[0031] Step 3.2, apply the combined second-order statistics obtained in Step 2. Perform angular domain scanning to obtain the angular domain convolution beam. ;

[0032] During the angular domain scanning process, the angular domain convolution beam Indicates the scanning angle The weighted superposition of responses from each incoming wave direction; the beam pattern is the system's output response at each scanning angle when a single unit intensity point target is located at its true azimuth;

[0033] Step 3.3, Angular Domain Convolution Beam Degenerates into being determined solely by the scan angle The angular response function, determined by the true azimuth, is defined as the equivalent beam. ;

[0034] in, This represents the actual target azimuth. This represents the scan angle variable in a continuous sense. Represents the scan angle variable The first on the discrete scan grid There are several possible values, that is, during project implementation. Equivalent beam This represents a translation-invariant equivalent beammap that is only related to the difference between the scan angle and the true target azimuth angle.

[0035] In discrete scanning, the equivalent beam Written as :

[0036] ;

[0037] The equivalent beam depends only on the difference between the scanning angle and the true target azimuth angle, satisfying the angle-domain translation invariance property. The equivalent beam is expressed as... ;

[0038] in, This represents the difference between the scan angle and the actual target azimuth angle;

[0039] Angular domain convolution beam The equivalent beam The point spread function (PSF) is used to characterize the angular domain response of a unit point target after beamforming. This indicates the true location distribution of the target.

[0040] Furthermore, in step 4, the constrained RL objective function is the RL deconvolution objective function with constraint terms. :

[0041] (2);

[0042] in, For RL data consistency items, For regularization parameters, These are constraint terms.

[0043] Furthermore, in step 5, the method for iteratively recovering the equivalent beam is as follows:

[0044] The true orientation distribution of the target is recovered by using constrained RL multiplicative iteration;

[0045] First, estimate the current azimuth spectrum of the j-th iteration. Convolution is performed to obtain the predicted beam ;

[0046] Then, calculate the result of the next iteration according to the update formula with constraints. And introduce a small stability constant. and the lower limit of the denominator To avoid division by zero or numerical divergence in flat regions;

[0047] (3);

[0048] in, This represents the predicted beam obtained by convolving the current azimuth spectrum estimate with the point spread function. Let represent the updated azimuth spectrum estimate obtained in the (j+1)th iteration, where j represents the iteration number, and ∇·(·) represents the divergence operator.

[0049] Furthermore, in step 6, the process of obtaining the true location distribution of the target is as follows:

[0050] First, the iteration is terminated when the set number of iterations is reached or the relative change between two adjacent iterations is less than a preset threshold, and the recovered azimuth spectrum is obtained.

[0051] Then, the recovered azimuth spectrum is normalized, local peak search is performed, and minimum peak spacing is determined to output the DOA estimation results of one or more targets.

[0052] Finally, based on different signal-to-noise ratio conditions, the regularization parameter λ is adaptively selected using an error-resolution trade-off criterion to balance azimuth estimation accuracy and main lobe compression capability, thereby obtaining the true azimuth distribution of the target. .

[0053] An electronic device, characterized in that it comprises: one or more processors; a memory; one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs being configured to perform the above-described single-vector hydrophone high-resolution azimuth estimation method.

[0054] A computer-readable storage medium, characterized in that the computer-readable storage medium stores program code, which can be called by a processor to execute the above-described single-vector hydrophone high-resolution azimuth estimation method.

[0055] Compared with the prior art, the technical effects of the present invention are as follows:

[0056] This invention utilizes a single-vector hydrophone sound pressure channel and two orthogonal particle velocity channels to construct a combined second-order statistic, establishing an equivalent beammap with a narrower main lobe and satisfying the angular domain translation invariance condition. This transforms the single-element azimuth scanning problem into an angular domain deconvolution problem with a known point spread function, overcoming the shortcomings of conventional beamforming, such as a wide main lobe and limited angular resolution. Furthermore, this invention introduces constraint terms into the Richardson-Lucy deconvolution process, preferably one-dimensional total variational regularization terms, combined with non-negative multiplicative corrections, small stability constants, and lower bounds on the denominator. This invention effectively suppresses noise accumulation, background spectral bottom elevation, local oscillations, and spurious peak growth under conditions of low signal-to-noise ratio, non-stationary marine background noise, multipath disturbances, and channel response mismatch, thereby improving the stability and reliability of azimuth spectrum recovery. Furthermore, this invention achieves high-resolution DOA estimation for both single and multi-target sources without requiring a pre-defined number of sound sources, and can adaptively select regularization parameters to balance azimuth estimation accuracy with main lobe compression capability. Therefore, it possesses higher angular resolution, stronger adaptability to low signal-to-noise ratio, better robustness to channel response mismatch, and greater engineering application value. Attached Figure Description

[0057] Figure 1 This is a flowchart of the high-resolution azimuth estimation of a single-vector hydrophone based on constrained RL deconvolution according to the present invention;

[0058] Figure 2 A block diagram illustrating the principle of combined second-order statistical beamforming and constrained RL deconvolution;

[0059] Figure 3 This is a schematic diagram comparing the directivity of different equivalent beam patterns. Detailed Implementation

[0060] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0061] Step 1: Establish a two-dimensional horizontal signal model for a single-vector hydrophone. Under the far-field plane wave assumption, the single-vector hydrophone simultaneously measures sound pressure and particle velocities in two orthogonal directions. For the two-dimensional case considering only horizontal DOA estimation, we assume... Three independent sound sources are incident, with horizontal angles of respectively... Then the receiving model can be represented by equation (1). Where, This is the sound pressure level channel output. , These are two orthogonal vibration velocity channels for output. , , These represent the noise components of each channel. In practical engineering, channel amplitude and phase compensation, mechanical noise threshold elimination, and segmented windowing processing can also be added. For broadband targets, statistics can be constructed for each frequency band or time frame and incoherent accumulation can be performed; for narrowband targets, they can be processed directly according to a fixed frequency band.

[0062] Step 2: Identify the main symbols and their meanings. Among them, This indicates that the sound pressure channel receives the signal; , This indicates that the velocity channels of two orthogonal particles receive signals. Indicates the first The incident azimuth angle of the target; , , , , This represents a second-order statistic of the combination; Indicates the scanning angle The corresponding weighted steering vector; This indicates the beam scanning output spectrum; This represents the translation-invariant equivalent beam pattern or point spread function (PSF). Indicates the true azimuth distribution or the azimuth spectrum to be recovered; Indicates the constraint weight parameters; , These represent the numerical stability constant and the lower limit of the denominator, respectively.

[0063] Step 3: Construct combined second-order statistics and form a translation-invariant equivalent beammap. The principle block diagram of combined second-order statistics beamforming and constrained RL deconvolution is shown below. Figure 2 As shown. Within each frame of data, the product average or statistical expectation estimation of the sound pressure channel and the two orthogonal particle velocity channels yields several second-order statistics formed by the combination of multi-channel signals. Unlike methods that only use sound intensity or complex sound intensity histograms, this invention introduces the aforementioned combined second-order statistics to couple the multi-channel second-order information of the single-vector hydrophone into the angular domain scanning model, thereby obtaining stronger directivity than conventional scanning methods. Preferably, a weighted steering vector corresponding to the scanning angle is used to perform a weighted scan on the combined second-order statistics to obtain the angular domain beam output, and an equivalent beammap that satisfies the angular domain translation invariance characteristic is further constructed. This equivalent beammap is only related to the difference between the scanning angle and the true target azimuth angle, and therefore can be directly used as the point spread function (PSF) in subsequent deconvolution processing. Figure 3As shown, by constructing different steering vectors and multiplying them with second-order statistics by different coefficients, different beam outputs and corresponding beam patterns can be obtained.

[0064] Step 4: Establish a constrained RL deconvolution model and update rules. The true multi-target orientation distribution is denoted as... ,in, Indicates the first The intensity weight or average power of a target is used to characterize the magnitude contribution of that target in the true azimuth distribution, and can be written as: This represents the Dirac Delta function, used to convert the first angular region into the second angular region. Each target is represented as being located at its true position. The point target; when hour, and satisfy .therefore, This represents the true azimuth distribution formed by the superposition of multiple point targets according to their respective intensity weights. Correspondingly, the beam output can be expressed as the angular domain convolution of the true target azimuth distribution and the point spread function (PSF): While standard RL iteration can compress the main lobe and improve resolution, it gradually amplifies local noise fluctuations under low signal-to-noise ratio and model mismatch conditions. To improve deconvolution stability, this invention introduces a constraint term in addition to the RL data consistency term, constructing a deconvolution objective function with constraints. The constraint term can be a regularization term that suppresses non-physical oscillations, enhances spectral smoothness, and preserves sharp edges of the target peak; in a preferred embodiment, a one-dimensional total variational regularization term is used.

[0065] Step 5: Establish the RL deconvolution objective function with constraints. Based on the standard RL data consistency term, a regularization parameter λ and constraint terms are introduced to construct the objective function. Wherein, The value λ is used to measure the consistency between the predicted beam generated from the currently estimated azimuth spectrum and the actual observed beam; λ is used to adjust the relative weights between the data fitting term and the constraint term. This is used to impose prior constraints on the recovered spectral shape. In a preferred embodiment, The term is taken as a one-dimensional total variational regularization term, which suppresses non-physical oscillations in the spectral base region, mitigates the continuous amplification of noise during iteration, and tries to prevent the sharp edges of the target azimuth peak from being excessively smoothed. To ensure that the restored result conforms to the actual physical meaning, the implementation also requires that the azimuth spectrum to be restored be... Maintaining non-negativity. By introducing the above constraints into the standard RL framework, the solution stability under low signal-to-noise ratio and model mismatch conditions can be significantly improved while maintaining high resolution.

[0066] Step 6: Recover the azimuth spectrum using constrained RL multiplicative iteration. Let the current iteration result be... First, the predicted beam is calculated by convolution with the PSF. Then, a multiplicative correction term is constructed using the ratio of the observed beam to the predicted beam, and the result of the next iteration is obtained according to equation (3). In practice, the initial azimuth spectrum can preferably be the nonnegated original beam output, or a uniform positive value sequence can be used as the initial value; in each iteration, a forward convolution is first performed to obtain... Then, back projection correction is performed, and the total variation constraint term is embedded into the update formula in the form of denominator correction or gradient penalty. To avoid problems such as excessively small gradient denominators, division by zero, or abnormally amplified update amounts in flat regions, it is preferable to add a small stability constant ε to the total variation term and set a positive lower limit η for the update denominator; if necessary, non-negative truncation and amplitude normalization can also be performed on the spectral values ​​after each update. Through the above multiplicative iteration, the main lobe width can be gradually compressed, the background spectral base reduced, and spurious peak growth suppressed, thereby obtaining a more stable high-resolution azimuth spectrum recovery result than the standard RL.

[0067] Step 7: Set termination conditions and complete DOA decision. The constraint RL iteration terminates when the preset maximum number of iterations is reached, or when the relative change between two adjacent iterations is less than a given threshold. In practice, the Euclidean norm difference, maximum absolute difference, or relative mean square change between two adjacent recovered spectra can be used as convergence criteria. For real-time processing scenarios, a fixed number of iterations can be used to control computational complexity. After iteration, the recovered azimuth spectrum is normalized, and a local peak search is performed across the entire scanning angular domain. For single-target scenarios, the angle corresponding to the maximum spectral peak can be directly used as the DOA output. For multi-target scenarios, multiple candidate peaks can be screened and sorted by combining minimum peak spacing constraints, relative amplitude thresholds, and small peak removal rules to reduce false detections caused by noise spurious peaks. If necessary, consistency checks can be performed on the output azimuth between consecutive time frames to improve the smoothness of the azimuth trajectory and its stability in engineering applications.

[0068] Step 8: Adaptively select the regularization parameter λ. λ can be scanned and selected using an error-resolution tradeoff criterion based on different operating signal-to-noise ratio (SNR) conditions. In practice, a set of candidate λ values ​​can be pre-defined. For each candidate value, steps one through seven are repeated under the same data conditions, and the corresponding root mean square error (RMSE) of azimuth estimation, main lobe width, background spectral base, and number of spurious peaks are statistically analyzed. In a preferred embodiment, the parameter corresponding to the minimum RMSE and its minimum error are first determined. Then, an allowable error threshold is constructed based on the standard error method. A larger λ value is selected from the candidate set that meets the error constraints as the recommended value to maximize the main lobe compression and spectral base suppression capabilities without significantly sacrificing direction-finding accuracy. For application scenarios where the SNR is known or can be estimated, the offline calibration results can be compiled into a parameter lookup table for quick selection of λ based on the current SNR level during online processing. When the working environment is relatively stable, experimentally verified default parameter values ​​can also be directly used.

[0069] Example Description: Example 1 illustrates high-resolution azimuth estimation for a single target. The target emits broadband noise from 300 Hz to 3000 Hz, and the single-vector hydrophone samples at a frequency of 12 kHz, processed in 1-second data frames. Scanning is performed at fixed angular intervals within the azimuth range of 0° to 360°. First, combined second-order statistics are calculated and an equivalent beam output is constructed. Then, RL deconvolution with one-dimensional total variation constraints is used to recover the target azimuth spectrum. Compared to CBF, MVDR, complex intensity histogram, MUSIC, and unconstrained dBF, this invention maintains peak localization accuracy while further reducing the background spectral depth and forming a sharper main peak. Example 2 illustrates a scenario of inconsistent channel amplitude response: Assume the sound pressure channel has an amplitude scaling factor α relative to the vibration velocity channel, with other conditions remaining unchanged. When α deviates from 1, both MUSIC-type methods and standard dBF outputs may exhibit main lobe broadening or background increase. After using the constrained RL deconvolution of this invention, a more concentrated single-peak output can still be formed near the true target azimuth, demonstrating better channel mismatch robustness. Example 3 is an example of adaptive parameter selection: For different signal-to-noise ratio scenarios, λ is scanned under the condition of fixed scanning step size and number of iterations, and the RMSE of the azimuth estimation is statistically analyzed. The above-mentioned standard error method is used to select recommended parameters, which can avoid the parameters being too conservative due to only pursuing the minimum RMSE, and can improve the azimuth spectrum resolution as much as possible without significantly reducing the direction finding accuracy.

[0070] Scope of Protection: The above embodiments are only used to illustrate the technical concept of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make equivalent substitutions or improvements to the form of the constraint terms, initialization methods, termination criteria, statistical accumulation methods, and peak value decision strategies without departing from the core idea of ​​the present invention, and all such substitutions or improvements should fall within the scope of protection of the present invention. The main symbols and their meanings are shown in Table 1:

[0071] Table 1. Explanation of Symbol Meanings

[0072]

Claims

1. A high-resolution azimuth estimation method for a single-vector hydrophone, characterized in that, The steps include the following: Step 1: The single-vector earpiece receives multi-channel signals; Step 2: Calculate the combined second-order statistics of the multi-channel signals; Step 3: Map the combined second-order statistics to the angular domain beam to obtain the equivalent beam, and output the equivalent beam as the point spread function (PSF). Step 4: Establish the constrained RL objective function; Step 5: Iteratively recover the equivalent beam obtained in Step 3 by constraining the RL objective function; Step 6: Output the DOA estimation results to obtain the true orientation distribution of the target.

2. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 1, the method for the single-vector hearing device to receive multi-channel signals is as follows: Acquiring underwater target acoustic signals using a single-vector audiometer to obtain sound pressure channel signals. and the vibration velocity channel signals of two orthogonal particles and ; ； ； (1)； ； in, This represents the radiated acoustic signal of the i-th target at time t; Let represent the incident azimuth angle of the i-th target; These represent the noise components of the sound pressure channel and the two orthogonal particle velocity channels, respectively; N represents the number of targets.

3. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 2, the calculation of the combined second-order statistic is as follows: Calculate the combined second-order statistics within each data frame of the multi-channel signal; The combined second-order statistics include , , , and Five second-order statistics; ， ， ， ， ； ； Where T represents transpose.

4. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 3, the method for obtaining the equivalent beam is as follows: Step 3.1, based on the scanning angle Constructing a weighted steering vector ; ； Where T represents transpose; Step 3.2, apply the combined second-order statistics obtained in Step 2. Perform angular domain scanning to obtain the angular domain convolution beam. ; Step 3.3, Angular Domain Convolution Beam Degenerates into being determined solely by the scan angle The angular response function, determined by the true azimuth, is defined as the equivalent beam. ; in, This represents the actual target azimuth. This represents the scan angle variable in a continuous sense. Represents the scan angle variable The first on the discrete scan grid One possible value; In discrete scanning, the equivalent beam Written as : ； The equivalent beam is represented as ; in, This represents the difference between the scan angle and the actual target azimuth angle; Angular domain convolution beam The equivalent beam As a point spread function (PSF); This indicates the true location distribution of the target.

5. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 4, the constrained RL objective function is the RL deconvolution objective function with constraint terms. : （2）； in, For RL data consistency items, For regularization parameters, These are constraint terms.

6. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 5, the method for iteratively recovering the equivalent beam is as follows: The true orientation distribution of the target is recovered by using constrained RL multiplicative iteration; First, estimate the current azimuth spectrum of the j-th iteration. Convolution is performed to obtain the predicted beam ; Then, calculate the result of the next iteration according to the update formula with constraints. And introduce a small stability constant. and the lower limit of the denominator To avoid division by zero or numerical divergence in flat regions; （3）； in, This represents the predicted beam obtained by convolving the current azimuth spectrum estimate with the point spread function. Let represent the updated azimuth spectrum estimate obtained in the (j+1)th iteration, where j represents the iteration number, and ∇·(·) represents the divergence operator.

7. The high-resolution azimuth estimation method for a single-vector hydrophone according to claim 1, characterized in that, In step 6, the process of obtaining the true location distribution of the target is as follows: First, the iteration is terminated when the set number of iterations is reached or the relative change between two adjacent iterations is less than a preset threshold, and the recovered azimuth spectrum is obtained. Then, the recovered azimuth spectrum is normalized, local peak search is performed, and minimum peak spacing is determined to output the DOA estimation results of one or more targets. Finally, based on different signal-to-noise ratio conditions, the regularization parameter λ is adaptively selected using the error-resolution trade-off criterion to obtain the true azimuth distribution of the target. .

8. An electronic device, characterized in that, include: One or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs being configured to perform the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program code that can be invoked by a processor to execute the method as described in any one of claims 1 to 7.

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