A method, medium and system for estimating the horizontal array orientation in an uncertain shallow sea environment

Abstract

The present invention provides a method, medium and system for estimating the azimuth of a horizontal array in an uncertain shallow sea environment, which belongs to the field of geophysical technology, and comprises: firstly, using a horizontal array to receive a far-field narrowband signal to obtain a time domain sampling snapshot, then calculating the array sampling covariance matrix, and using the previous J At the same time, according to the standard shallow water sound speed profile and parameter uncertainty range, the horizontal wave number range of the propagation mode is obtained, and the modal matrix is ​​constructed by sampling within this range to extract the previous K The eigenvector corresponding to the maximum eigenvalue constructs the modal subspace. Next, the basis vectors in the signal subspace and the modal subspace are used to construct the extended matrix. QR Decompose the upper triangular matrix, extract its diagonal elements to construct the sound source direction estimation function. Finally, the angle corresponding to the peak of the sound source direction estimation function is the estimated value of the sound source direction.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical technology, and in particular, relates to a method, medium and system for estimating the azimuth of a horizontal array in an uncertain shallow sea environment. Background Art

[0002] In the field of modern underwater acoustic detection and positioning, sound source direction estimation is a key technology, and its application scenarios cover many important fields such as underwater target detection, marine resource exploration, marine environment monitoring, underwater communication and navigation. In shallow sea environments, due to the small water depth and complex seabed topography, sound wave propagation exhibits significant multipath effects and modal characteristics, which makes sound source direction estimation face unique challenges. According to the simple normal wave theory, the sound field excited by the sound source can be expressed as the superposition of several modes, and each mode has a different horizontal wave number, which causes the wavefront of the received signal to no longer satisfy the traditional plane wave assumption.

[0003] At present, there are two main methods for sound source azimuth estimation: the traditional azimuth estimation method based on the plane wave model and the matched field processing method based on the simple normal wave model. The basic assumption of traditional azimuth estimation methods such as conventional beamforming (CBF), multiple signal classification (MUSIC) and ESPRIT is that sound waves propagate in the form of plane waves. However, in shallow sea environments, due to the modal characteristics of sound wave propagation, this assumption is no longer valid. In particular, when the sound source is located in the end-fire direction of the horizontal array, the traditional method will produce significant azimuth estimation errors, which seriously affects the positioning accuracy. Summary of the invention

[0004] In view of this, the present invention provides a method, medium and system for estimating the azimuth of a horizontal array in an uncertain shallow sea environment, which can solve the technical problem that when the sound source is located in the end-fire direction of the horizontal array, the traditional method will produce significant azimuth estimation deviation, which seriously affects the positioning accuracy.

[0005] The present invention is achieved in that:

[0006] A first aspect of the present invention provides a method for estimating the azimuth of a horizontal array in an uncertain shallow sea environment, comprising the following steps:

[0007] S10, using a horizontal array to receive a far-field narrowband signal, the number of array elements of the horizontal array is N, and the array element spacing is d, to obtain array sampling data of the received signal; wherein the received signal is represented as follows:

[0008] ;

[0009] In the formula, is an imaginary unit; is a zero-mean random function, and its variance represents the signal strength; For the The receiving noise of the array elements is assumed to be additive Gaussian white noise with a mean value of , the variance is ; For the The angle of the sound source relative to the end-fire direction of the array is in the range of ; is the signal center frequency, is the depth of the jth sound source; is the distance of the jth sound source relative to the reference element of the horizontal array.

[0010] The transfer function is expressed as follows:

[0011] ;

[0012] In the formula, For the The sound source is located at the reference array element The complex amplitude of the first mode; For the The horizontal wave number of the first mode; is the modal order; is the array element spacing.

[0013] The horizontal array receiving vector is expressed as follows:

[0014] ;

[0015] In the formula, is the signal vector; is the noise vector; For the The array transfer function of the sound source.

[0016] The array transfer function is expressed as follows:

[0017] ;

[0018] In the formula, is the modal complex amplitude vector; for dimensional modal matrix; For the The steering vector of the first mode.

[0019] S20, using the obtained L time domain sampling snapshots to calculate the array sampling covariance matrix, performing eigenvalue decomposition on the array sampling covariance matrix, and using the first J eigenvectors to construct a signal subspace; the formula of the sampling covariance matrix is ​​expressed as follows:

[0020] ;

[0021] In the formula, is the number of time domain sampling snapshots; superscript represents the conjugate transpose.

[0022] The signal subspace is expressed as follows:

[0023] ;

[0024] In the formula, is the covariance matrix No. feature vectors.

[0025] S30, according to the standard shallow water sound velocity profile and the parameter uncertainty range, obtain the horizontal wave number range of the propagation mode, perform Z equal-interval sampling within the horizontal wave number range, and construct an N times Z dimensional modal matrix; the horizontal wave number range is:

[0026] , ];

[0027] In the formula, is the acoustic velocity of the sediment layer; is the speed of sound on the seafloor.

[0028] The modal matrix is ​​expressed as follows:

[0029] ;

[0030] In the formula, For the The horizontal wave value of the subsample, .

[0031] S40, performing eigenvalue decomposition on the modal matrix, designing an effective rank determination criterion, obtaining an effective rank of the modal matrix as K, and constructing a modal subspace using the first K eigenvectors, which is specifically expressed as:

[0032] ,

[0033] and ;

[0034] In the formula, for No. feature vectors; represents the 2-norm; is the three-dimensional space to search, represents the search angle, r represents the search distance, and z represents the search depth; is the coordinate of any sound source in three-dimensional space, where , and ; It represents the estimated value of the direction when the effective rank is K.

[0035] The modal subspace is represented as follows:

[0036] ;

[0037] In the formula, For the front The eigenvector corresponding to the largest eigenvalue.

[0038] S50, constructing an N-times-(K+J) expansion matrix using the basis vectors in the modal subspace and the basis vectors in the signal subspace; the expansion matrix is ​​expressed as:

[0039] ;

[0040] In the formula, is the basis vector of the modal subspace; are the basis vectors of the signal subspace.

[0041] S60, performing QR decomposition on the extended matrix to obtain an upper triangular matrix, and extracting diagonal elements of the upper triangular matrix; the QR decomposition is expressed as follows:

[0042] ;

[0043] In the formula, for dimensional orthogonal matrix; for The diagonal elements of the upper triangular matrix are expressed as .

[0044] S70, constructing a sound source orientation estimation function according to the diagonal elements of the upper triangular matrix, wherein the angle corresponding to the peak value of the sound source orientation estimation function is the sound source orientation estimation value, wherein the sound source orientation estimation function is expressed as follows:

[0045] ;

[0046] In the formula, for diagonal elements.

[0047] The parameter acquisition method is:

[0048] 1) Wave number Obtaining:

[0049] Obtained by solving the characteristic equation of the deep-sea acoustic wave equation:

[0050] ;

[0051] In the formula, is the modal function; is the vertical wave number; is the wave number; is the sound velocity profile.

[0052] 2) Modal complex amplitude Obtaining:

[0053] Calculated by the acoustic propagation loss model:

[0054] ;

[0055] In the formula, and are the modal functions at the sound source depth and receiving depth respectively; is the modal attenuation coefficient.

[0056] 3) Noise variance Obtaining:

[0057] Obtained through background noise measurement of actual sea trial data:

[0058] ;

[0059] In the formula, To measure the length of time; is the number of array elements.

[0060] On the basis of the above technical solution, the method for estimating the horizontal array azimuth in an uncertain shallow sea environment of the present invention can also be improved as follows:

[0061] A second aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the above-mentioned method for estimating the horizontal array orientation in an uncertain shallow sea environment.

[0062] A third aspect of the present invention provides a system for estimating the horizontal array orientation in an uncertain shallow sea environment, which includes the above-mentioned computer-readable storage medium.

[0063] Compared with the prior art, the method, medium and system for estimating the horizontal array azimuth in an uncertain shallow sea environment provided by the present invention have the following beneficial effects:

[0064] First, this method can achieve accurate azimuth estimation even when the modal order and horizontal wavenumber are unknown, which is an important breakthrough in existing subspace intersection-based methods. By sampling at equal intervals within the horizontal wavenumber range and constructing a modal matrix containing uncertain environmental information, this method effectively overcomes the impact of environmental parameter uncertainty.

[0065] Compared with the traditional matching field processing method, the present invention significantly reduces the reliance on environmental prior information. Only the approximate range of the sound velocity profile is needed to construct an effective modal subspace, avoiding the difficulty of obtaining accurate environmental parameters. At the same time, the azimuth estimation can be completed through one-dimensional search, and the computational efficiency has been qualitatively improved compared with three-dimensional search, which makes this method more suitable for practical engineering applications.

[0066] The present invention effectively extracts key information from the modal matrix through the design of eigenvalue decomposition and effective rank determination criteria. This processing method not only reduces the computational complexity, but also improves the robustness of the algorithm, ensuring that while retaining effective information, the interference caused by environmental uncertainty is suppressed to the greatest extent.

[0067] Compared with the traditional method based on the plane wave model, the present invention fully considers the modal characteristics in the shallow sea environment and effectively avoids the azimuth estimation deviation when the sound source is located in the horizontal array end-fire direction. By constructing a modal subspace containing environmental uncertainty information, the present method can maintain a high estimation accuracy at all azimuth angles.

[0068] In summary, the solution of the present invention solves the technical problem that when the sound source is located in the end-fire direction of the horizontal array, the traditional method will produce a significant azimuth estimation error, which seriously affects the positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The main steps of the present invention are as follows;

[0070] Figure 2 A front view of a schematic diagram showing the relationship between the sound source and the horizontal array position;

[0071] Figure 3 A top view of a schematic diagram showing the relationship between the sound source and the horizontal array position;

[0072] Figure 4 This is a schematic diagram of the standard uncertain shallow sea model;

[0073] Figure 5 is the curve of the sum of the azimuth estimation errors of any sound source in three-dimensional space versus the effective rank;

[0074] Figure 6 The present invention and the CBF method are based on the sound source being located at The estimated direction result at time ;

[0075] Figure 7 The present invention and the CBF method are based on the sound source being located at The estimated direction result at time ;

[0076] Figure 8 The present invention and the CBF method are based on the sound source being located at The estimated direction result at time ;

[0077] Fig. 9 The comparison results of the azimuth estimation errors of the present invention and the CBF method under different signal-to-noise ratios are shown in FIG. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0079] like Figure 1 As shown, it is a flow chart of a method for estimating the horizontal array azimuth in an uncertain shallow sea environment provided by the first aspect of the present invention. The method comprises the following steps:

[0080] S10, using a horizontal line array to receive a far-field narrowband signal, the number of array elements of the horizontal line array is N, and the array element spacing is d;

[0081] S20, using the received L time domain sampling snapshots to calculate the array sampling covariance matrix, performing eigenvalue decomposition on the array sampling covariance matrix, and constructing a signal subspace using the first J eigenvectors;

[0082] S30, according to the standard shallow water sound speed profile and the parameter uncertainty range, obtain the horizontal wave number range of the propagation mode, perform Z equal-interval sampling within the horizontal wave number range, and construct an N-by-Z-dimensional modal matrix;

[0083] S40, performing eigenvalue decomposition on the modal matrix, designing an effective rank determination criterion, obtaining an effective rank of the modal matrix as K, and constructing a modal subspace using the first K eigenvectors;

[0084] S50, constructing an N-times-(K+J) expansion matrix using basis vectors in the modal subspace and basis vectors in the signal subspace;

[0085] S60, performing QR decomposition on the extended matrix to obtain an upper triangular matrix, and extracting diagonal elements of the upper triangular matrix;

[0086] S70. Construct a sound source orientation estimation function according to the diagonal elements of the upper triangular matrix, wherein the angle corresponding to the peak value of the sound source orientation estimation function is the sound source orientation estimation value.

[0087] The specific implementation methods of the above steps are described in detail below:

[0088] The specific implementation of step S10 is the process of horizontal line array receiving far-field narrowband signals. The horizontal line array of array elements receives the The signal of an array element can be expressed as:

[0089] ,

[0090] in, Indicates The signal emitted by a sound source, Indicates The sound source to The transfer function of the array element is, Indicates The transfer function can be further expressed as:

[0091] ,

[0092] in, For the The sound source is located at the reference array element The complex amplitude of the order mode, For the The horizontal wave number of the order mode, is the modal order, is the array element spacing, is an imaginary unit. In order to avoid spatial aliasing, the array element spacing Need to meet: ,in, is the wavelength.

[0093] The specific implementation of step S20 is the process of constructing a signal subspace. The array sampling covariance matrix obtained by using the received L time domain sampling snapshots can be expressed as:

[0094] ,

[0095] in, For the The received signal vector of the snapshot is Denotes conjugate transpose. Perform eigenvalue decomposition on the covariance matrix:

[0096] ,

[0097] in, is the characteristic value, is the corresponding eigenvector. The eigenvectors corresponding to the largest eigenvalues ​​constitute the signal subspace: ;

[0098] The specific implementation of step S30 is the process of constructing a modal matrix. Internal The sampling interval is:

[0099] ,

[0100] No. The horizontal wave number of the subsampling is:

[0101] , .

[0102] For each sampling wave number , construct the steering vector:

[0103] .

[0104] All steering vectors form the modal matrix:

[0105] .

[0106] The specific implementation of step S40 is the process of constructing the modal subspace. Perform eigenvalue decomposition on the modal matrix:

[0107] ,

[0108] in, is the characteristic value, is the corresponding eigenvector. The effective rank determination criterion is:

[0109] ,

[0110] and ;

[0111] In the formula, for No. feature vectors; represents the 2-norm; is the three-dimensional space to search, represents the search angle, r represents the search distance, and z represents the search depth; is the coordinate of any sound source in three-dimensional space, where , and ; It represents the estimated value of the direction when the effective rank is K.

[0112] Before selection The eigenvectors corresponding to the largest eigenvalues ​​constitute the modal subspace:

[0113] ;

[0114] The specific implementation of step S50 is the process of constructing an extended matrix. The basis vectors of the modal subspace and the signal subspace are concatenated to form an extended matrix:

[0115] .

[0116] The specific implementation of step S60 is the process of matrix decomposition. Perform QR decomposition on the extended matrix:

[0117] ,

[0118] in, is an orthogonal matrix that satisfies , is an upper triangular matrix:

[0119] .

[0120] The specific implementation of step S70 is the process of sound source orientation estimation. The sound source orientation estimation function is constructed using the diagonal elements of the upper triangular matrix:

[0121] .

[0122] The estimated value of the sound source direction is the peak position of the direction estimation function:

[0123] .

[0124] A second aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the above-mentioned method for estimating the horizontal array orientation in an uncertain shallow sea environment.

[0125] A third aspect of the present invention provides a system for estimating the horizontal array orientation in an uncertain shallow sea environment, which includes the above-mentioned computer-readable storage medium.

[0126] Specifically, the principle of the present invention is that in a shallow sea environment, the sound field excited by the sound source can be expressed as a superposition of several modes, and each mode has a different horizontal wave number. Although the exact modal order and horizontal wave number are difficult to obtain, the possible value range of the horizontal wave number can be determined according to the range of environmental parameters. Based on this, the present invention constructs a modal matrix containing environmental uncertainty information by sampling at equal intervals within the range of horizontal wave numbers.

[0127] From a mathematical point of view, the column vectors of the modal matrix constitute an overcomplete signal representation space. When the scanning direction is the same as the actual sound source orientation, the received signal must fall within this space. However, since the sampling of the horizontal wave number causes correlation between the column vectors of the modal matrix, directly using these vectors will reduce the accuracy of the orientation estimation. To solve this problem, the present invention designs an effective rank determination criterion to process the modal matrix.

[0128] The physical meaning of the effective rank determination criterion is that after the modal matrix is ​​decomposed by eigenvalue, the eigenvector corresponding to the effective rank contains the main information of the signal, while the remaining eigenvector contains the redundant information of the signal. Therefore, by designing the effective rank determination criterion, the effective components of the signal can be retained while eliminating the interference of the redundant components of the signal.

[0129] In terms of constructing the signal subspace, the present invention uses the covariance matrix of the received signal to perform eigenvalue decomposition. According to array signal processing theory, the subspace spanned by the main eigenvectors of the covariance matrix contains the main information of the signal. When the scanning direction is correct, the modal subspace and the signal subspace must intersect. This principle provides a theoretical basis for azimuth estimation.

[0130] The present invention innovatively uses QR decomposition to detect the degree of subspace intersection. By constructing an extended matrix and performing QR decomposition, the diagonal elements of the upper triangular matrix can reflect the degree of correlation between subspaces. When the scanning direction is close to the true orientation, the corresponding diagonal element value will be significantly reduced, which provides a basis for constructing the orientation estimation function.

[0131] The logic of the entire technical solution is reflected in the following aspects: first, the completeness of the signal representation is ensured through horizontal wave number sampling, then the effective signal components are extracted through eigenvalue decomposition, and finally the direction estimation is realized by using the subspace intersection principle. This layer-by-layer processing method not only ensures the accuracy of the direction estimation, but also reduces the dependence on the prior information of the environment.

[0132] A specific embodiment 1 of the method of the present invention is provided below, and each step of this embodiment 1 is described in detail as follows:

[0133] Step 1) mainly involves the reception of far-field narrowband signals by the horizontal array.

[0134] Consider a horizontal array with N array elements and an array element spacing of d located at a depth of Assume that there are J uncorrelated narrowband sound sources with center frequencies of , the depth is , the distance relative to the horizontal array reference element is . The jth signal received by the array element It is expressed as:

[0135] ;

[0136] In the formula, is an imaginary unit; is a slowly changing zero-mean random function, which represents the random fluctuation of the j-th sound source during propagation, and its variance represents the strength of the j-th signal; represents the receiving noise of the nth array element; represents the angle of the jth sound source relative to the end-fire direction of the array; Represents the transfer function between the jth sound source and the nth array element:

[0137] ;

[0138] In the formula, represents the complex amplitude of the m-th order mode received by the reference array element; represents the horizontal wave number of the mth mode; M represents the modal order excited by the sound source in this environment.

[0139] Horizontal array receive vector It is expressed as:

[0140] ;

[0141] In the formula, the superscript T represents the transposition operation; and denote the signal vector and the noise vector respectively; Represents the array transfer function of the jth sound source:

[0142] ;

[0143] In the formula, The complex magnitude vector representing the mode; for dimensional matrix, where represents the steering vector of the m-th mode.

[0144] Step 2) mainly involves the construction of the signal subspace.

[0145] Assuming that L time-domain snapshots are received, the sampling covariance matrix of the array is It is expressed as:

[0146] ;

[0147] In the formula, the superscript H represents the conjugate transpose operation. Perform eigenvalue decomposition and use the first J eigenvectors Zhang Cheng signal subspace :

[0148] ;

[0149] Step 3) mainly involves the construction of the modal subspace.

[0150] According to the Benchmark standard shallow water sound velocity profile and parameter uncertainty range provided by NRLWorkshop'93, the horizontal wave number range of the propagation mode in the uncertain environment is obtained: ;

[0151] In the formula, and represent the minimum and maximum values ​​of the horizontal wave number, respectively. and are the sound velocity in the sediment layer and the sound velocity on the seafloor, respectively.

[0152] In the horizontal wave number range Conducted Sampling at equal intervals, construct The modal matrix of :

[0153] ;

[0154] In the formula, Indicates the search direction. Perform eigenvalue decomposition and design an effective rank determination criterion:

[0155] ,

[0156] and ;

[0157] In the formula, for No. feature vectors; represents the 2-norm; is the three-dimensional space to search, represents the search angle, r represents the search distance, and z represents the search depth; is the coordinate of any sound source in three-dimensional space, where , and ; Represents the estimated value of the direction when the effective rank is K.

[0158] The modal subspace is constructed by using the eigenvectors corresponding to the first K largest eigenvalues. :

[0159] ;

[0160] Step 4) mainly involves the construction of the sound source direction estimation function.

[0161] Using the basis vectors in the modal subspace and the signal subspace, we construct a Dimensional expansion matrix :

[0162] ;

[0163] right Perform QR decomposition:

[0164] ;

[0165] In the formula, for Dimensional matrix; for The diagonal elements of the upper triangular matrix are expressed as .

[0166] The constructed sound source direction estimation function It is expressed as:

[0167] ;

[0168] at this time The angle corresponding to the peak is the estimated direction of the sound source.

[0169] In order to further better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: This Example 2 adopts the standard uncertain shallow sea environment provided by NRL Workshop'93, which is a typical shallow sea stratified structure, consisting of three layers: water layer, sediment layer and seabed basement. Each layer has specific acoustic parameters, and the specific parameters are shown in Table 1.

[0170] Table 1: Acoustic parameters of each layer in the standard uncertain shallow sea environment

[0171]

[0172] In this environment, if Figure 2-3 As shown, a horizontal array consisting of 50 hydrophones is deployed. The array is located 5 meters from the seabed, with an array element spacing of 7.5 meters and a total length of 367.5 meters. This spacing is selected considering that the target signal frequency is 100Hz, and the corresponding minimum wavelength is about 15 meters, which can effectively avoid spatial aliasing. The array uses a high-precision positioning system for position calibration to ensure that the error of the array element spacing does not exceed 0.1m and the array tilt angle does not exceed The sampling frequency is set to 500 Hz, which meets the requirements of Nyquist sampling theorem. The search angle range of the three-dimensional space is , the angle interval is , the distance range is 2-5km, the distance interval is 0.2km, the depth range is 0-100m, and the depth interval is 1m. By letting any sound source traverse all positions in this three-dimensional space, the sum of the azimuth estimation errors under different effective ranks is as follows: Figure 6 As shown in Figure 4, the effective rank K=4 can be determined based on the minimum value of the sum of the orientation estimation errors in the three-dimensional space.

[0173] This implementation example considers that the sound source is located 3.5km away from the reference array element and at a depth of 55m. The sound source emits a continuous narrowband signal with a frequency of 100Hz and a signal bandwidth of 2Hz. Each test collects 300 time domain snapshots with a sampling interval of 0.002s and a total sampling time of 0.6s. To verify the robustness of the algorithm, the sound source is located at The azimuth estimation error curve under different signal-to-noise ratios. The signal-to-noise ratio ranges from -10 to 20 dB, and 500 Monte Carlo experiments are performed under each signal-to-noise ratio.

[0174] First, the horizontal wave number range of the propagation mode is calculated based on the environmental parameters. Considering the uncertainty of the environmental parameters, the extreme value of the parameter change is used when calculating the wave number range, such as Figure 4 As shown. The minimum value of the horizontal wave number is calculated to be 0.3808rad / m, and the maximum value is 0.4253rad / m. 445 equal-interval samplings are performed within the determined wave number range, with a sampling interval of 0.0001rad / m, and a 20×445-dimensional modal matrix is ​​constructed. The modal matrix is ​​subjected to eigenvalue decomposition, and the effective rank is obtained as 4 using the effective rank determination criterion, as shown in Figure 5 As shown. Therefore, the first 4 eigenvectors are retained to form the modal subspace.

[0175] By performing eigenvalue decomposition on the covariance matrix of the received signal, the eigenvector corresponding to the maximum eigenvalue is selected to form the signal subspace. The basis vectors of the modal subspace and the signal subspace are combined to form an extended matrix, and the extended matrix is ​​subjected to QR decomposition. The diagonal elements of the upper triangular matrix are used to construct the azimuth estimation function.

[0176] like Figure 6-8 As shown in the figure, considering that the signal-to-noise ratio is 10dB, when the sound sources are located at , and Compared with the invalid CBF method, the present invention can accurately estimate the direction of the sound source close to the horizontal array endfire direction. Fig. 9 As shown, the fixed sound source is located at In terms of azimuth, the azimuth estimation error of the present invention is significantly lower than that of the CBF method under different signal-to-noise ratios.

[0177] It can be seen from the above implementation results that the method of the present invention can accurately estimate the azimuth of the sound source close to the end-fire direction of the horizontal array in an uncertain shallow sea environment without the need for precise prior knowledge of the environment, solves the problem of azimuth estimation bias caused by the plane wave model, and overcomes the impact of reduced positioning performance caused by environmental uncertainty. The method has strong anti-noise ability and certain robustness, and can effectively deal with the problem of sound source positioning close to the end-fire direction of the horizontal array in an uncertain shallow sea environment under the condition of low signal-to-noise ratio.

[0178] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for estimating the azimuth of a horizontal array in an uncertain shallow sea environment, characterized in that: The following steps are involved: S10, using a horizontal line array to receive a far-field narrowband signal, the number of array elements of the horizontal line array is N, and the array element spacing is d; S20, using the received L time domain sampling snapshots to calculate the array sampling covariance matrix, performing eigenvalue decomposition on the array sampling covariance matrix, and constructing a signal subspace using the first J eigenvectors; S30, according to the standard shallow water sound speed profile and the parameter uncertainty range, obtain the horizontal wave number range of the propagation mode, perform Z equal-interval sampling within the horizontal wave number range, and construct an N-by-Z-dimensional modal matrix; S40, performing eigenvalue decomposition on the modal matrix, designing an effective rank determination criterion, obtaining an effective rank of the modal matrix as K, and constructing a modal subspace using the first K eigenvectors; S50, constructing an N-times-(K+J) expansion matrix using basis vectors in the modal subspace and basis vectors in the signal subspace; S60, performing QR decomposition on the extended matrix to obtain an upper triangular matrix, and extracting diagonal elements of the upper triangular matrix; S70, constructing a sound source orientation estimation function according to the diagonal elements of the upper triangular matrix, wherein the angle corresponding to the peak value of the sound source orientation estimation function is the sound source orientation estimation value; The modal matrix is ​​specifically expressed as follows: ; In the formula, For the The horizontal wave value of the subsample, ; , , is the acoustic velocity of the sediment layer; is the speed of sound on the seafloor; Wherein, the effective rank determination criterion is: ， and ; In the formula, for No. feature vectors; represents the 2-norm; is the three-dimensional space to search, represents the search angle, r represents the search distance, and z represents the search depth; is the coordinate of any sound source in three-dimensional space, where , and ; represents the estimated value of the direction when the effective rank is K; where, For the The steering vector of the first mode.

2. The method for estimating the horizontal array orientation in an uncertain shallow sea environment according to claim 1, characterized in that: Assume that there are J uncorrelated narrowband sound sources with center frequencies of , the depth is , the distance relative to the horizontal array reference element is , among which The received signal of each array element is expressed as follows: ; In the formula, is an imaginary unit; is a zero-mean random function, and its variance represents the signal strength; For the The receiving noise of the array elements is assumed to be additive Gaussian white noise with a mean value of , the variance is ; For the The angle of the sound source relative to the end-fire direction of the array is in the range of , ; ; in, represents the transfer function between the jth sound source and the nth array element, specifically: ; In the formula, For the The sound source is located at the reference array element The complex amplitude of the first mode; For the The horizontal wave number of the first mode; is the modal order; is the array element spacing.

3. The method for estimating the horizontal array position in an uncertain shallow sea environment according to claim 2, characterized in that: The receiving vector of the horizontal array is expressed as follows: ; In the formula, is the signal vector; is the noise vector; For the The array transfer function of the sound source.

4. The method for estimating the horizontal array position in an uncertain shallow sea environment according to claim 3, characterized in that: The array transfer function of the jth sound source is specifically: ; In the formula, is the modal complex amplitude vector; for dimensional modal matrix.

5. The method for estimating the horizontal array position in an uncertain shallow sea environment according to claim 4, characterized in that: The sound source direction estimation function is specifically: ; In the formula, for The diagonal elements of for -dimensional upper triangular matrix.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the method for estimating the horizontal array orientation in an uncertain shallow sea environment according to any one of claims 1 to 5.

7. A horizontal array azimuth estimation system in an uncertain shallow sea environment, characterized in that: Contains the computer-readable storage medium of claim 6.

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