Matrix spatial domain filtering and eigen vector based towed line array sonar array pattern estimation method

Abstract

The application discloses a matrix space domain filtering and feature vector towed line array sonar array shape estimation method, and belongs to the field of array signal processing and sonar technology. The method firstly uses heading sensor measurement information to preliminarily estimate array element positions through an interpolation fitting method; based on the positions, conventional beam forming is carried out to obtain a coarse estimation azimuth angle of a target signal; a space domain matrix filter is constructed with the azimuth as the center to filter received data to suppress interference; finally, a covariance matrix of the filtered data is calculated and feature decomposition is carried out to extract main feature vector phase information, and the heading sensor information is combined to obtain accurate position coordinates of each array element through a coordinate rotation solution to realize array shape estimation. The application can effectively filter out interference in a complex environment with multiple signal incidence, significantly improves the precision and robustness of array shape estimation, and solves the technical bottleneck that the traditional feature vector method fails under multiple interference conditions.

Description

Technical Field

[0001] This invention relates to the fields of array signal processing and sonar signal processing technology, specifically to a method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors. Background Technology

[0002] Compared to traditional shipborne sonar, towed array sonar (towed array) has advantages such as large aperture, distance from noise sources, strong detection capability and controllable working depth. It has been widely used in many fields such as military defense, earthquake early warning and marine exploration, and has become an indispensable and important sonar device.

[0003] However, towed arrays are affected by a variety of complex factors during actual operation. Platform motion, gravity, buoyancy, ocean currents, and surges can all cause the towed array to lose its ideal straight-line formation during towing in water, resulting in array distortion. This distortion leads to changes in the positions of array elements, which is extremely detrimental to array signal processing. For example, in beamforming, the array manifold is a critical parameter, requiring precise element position information to generate the steering vector and ultimately form the beam. When array distortion occurs, if signal processing is still performed based on the assumption of a straight line, its performance will be severely affected, leading to problems such as decreased target detection accuracy and deviations in azimuth estimation.

[0004] Currently, the main array formation estimation methods include interpolation fitting based on heading sensors and eigenvector estimation based on acoustic information. Interpolation fitting estimates the entire array based on measurements from heading sensors at different positions within the array, without needing to consider acoustic factors. It is computationally simple and has fewer constraints, but its estimation accuracy is relatively low. Eigenvector estimation primarily uses the array's received data to calculate the covariance matrix. After eigenvalue decomposition, it utilizes the characteristic that the eigenvectors corresponding to large eigenvalues ​​are in phase with the steering vector to estimate the position information of each array element from the phase information of the eigenvectors, thus achieving array formation estimation. This method offers higher accuracy than interpolation fitting and, combined with heading sensor information, can achieve array formation estimation under conditions of unknown sound source orientation. However, this method can only perform array formation estimation in scenarios with a single signal incident on the array. In practical engineering applications, multiple interference signals often exist, severely affecting the array formation estimation performance of this method. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for estimating the formation of a towed linear array sonar using matrix spatial filtering and eigenvectors. This method can achieve accurate formation estimation of the towed linear array by using matrix spatial filtering to filter out interference signals in scenarios where multiple signals are simultaneously incident on the array, combined with the eigenvector method.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide the following technical solution: a method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors, comprising the following steps: Step S1: Using the heading angle information measured by the heading sensors deployed on the towed linear array, the position coordinates of each array element after distortion are initially estimated by interpolation fitting method; Step S2: Based on the preliminary estimate of the distorted array element position coordinates, perform conventional beamforming processing on the array received data matrix to obtain the azimuth spectrum, and determine the direction with the strongest energy in the azimuth spectrum as the coarse estimate of the azimuth angle of the target signal; Step S3: Construct a spatial matrix filter centered on the coarsely estimated azimuth angle of the target signal, and use the spatial matrix filter to filter the array received data matrix to obtain the data matrix after filtering out interference; Step S4: Calculate the sampling covariance matrix and perform eigenvalue decomposition on the data matrix after filtering out interference; extract the phase information of the eigenvector corresponding to the largest eigenvalue, combine it with the heading sensor information, and obtain the position coordinates of each array element through coordinate rotation calculation to complete the array formation estimation.

[0007] Preferably, step S1 preliminarily estimates the position coordinates of each array element after distortion using an interpolation fitting method, specifically as follows: A towed line array with M uniformly distributed elements and an element spacing of r is arranged. L heading sensors are uniformly distributed in the array. The distorted array shape is obtained by fitting an Nth-order polynomial. The horizontal two-dimensional towed line array is represented as: ; Where x is the x-coordinate of the array element, These are the polynomial coefficients; Let the first The heading angle measurement value of each heading sensor at time t is The relationship between this measurement and the formation is as follows: ; Define the heading vector at time t. ,in Indicates transpose, for the polynomial coefficient vector The coefficient estimates are obtained by performing maximum likelihood estimation. ,in It is an L x N matrix. The expression is: ; in, ( ) indicates the first The x-coordinate values ​​of each heading sensor under the assumption of an undistorted linear array; let Given the polynomial coefficient vectors of the abscissa of each array element. The distorted draggable array will then have the following formation: Substitute the x-coordinates of different array elements to calculate the corresponding y-coordinates. .

[0008] Preferably, step S1, which uses interpolation fitting to initially estimate the position coordinates of each array element after distortion, further includes: Obtain the abscissa polynomial coefficient vector of each array element. Then, the coordinates of P equally spaced points are calculated. The length of the dragging line column is obtained. ; The compression coefficient is obtained by comparing the actual length of the towed line array with the calculated length S. Then the x-coordinate of the i-th element is The x-coordinate of the heading sensor is ,in , The vector representing the x-coordinate of the heading sensor position when there is no distortion; Using the x-coordinate of the heading sensor again Perform polynomial fitting and calculate the corrected polynomial fitting coefficients. The formation is That is, the position coordinates of each distorted array element are initially estimated using the interpolation fitting method, and these coordinates are used as the abscissa. , y-axis .

[0009] Preferably, in step S2, the array received data matrix is ​​subjected to conventional beamforming processing to obtain the azimuth spectrum. The specific formula for calculating the azimuth spectrum is as follows: ; in, For array manifold vectors j is the imaginary unit, and f is the signal frequency. c is the speed of sound. For spatial orientation angle, The array element position coordinates estimated in step S1, Let K be the sampling covariance matrix, and K be the number of snapshots. For array receiving data matrix, This represents the conjugate transpose. Taking the direction of the strongest signal as the target signal direction, the target signal azimuth angle is... .

[0010] Preferably, step S3, which constructs a spatial matrix filter centered on the coarsely estimated azimuth angle of the target signal, specifically involves: Design one A 3D matrix filter G filters the received data X to determine the target signal orientation. Neighborhood is a passband Other directions are stopbands The passband and stopband orientations are discretized separately; a matrix filter is designed using the least squares criterion. ,in It is a matrix formed by concatenating the array manifold vectors in each direction column by column. , For extended array manifold matrices used in least squares design, , This is a matrix formed by concatenating the column vectors of all array manifolds within the passband, i.e. , This represents the number of discrete azimuth grid cells in the passband. For the passband azimuth set, Let j be the j-th discrete azimuth angle within the passband. Corresponding discrete azimuth angle Array manifold vectors; It is a matrix formed by concatenating the vectors of all array manifolds within the stopband, i.e. , This represents the number of discrete azimuth grid cells in the stopband. This is the set of stopband azimuth angles. Let i be the i-th discrete azimuth angle within the stopband. Corresponding discrete azimuth angle The array of manifold vectors.

[0011] Preferably, the specific expression of the least squares criterion is: ; in This represents the Frobenius norm.

[0012] Preferably, step S4 involves calculating the sampling covariance matrix and performing eigenvalue decomposition on the data matrix after interference filtering, specifically as follows: The sampling covariance matrix of the filtered array received data is ,in, This is the sampling covariance matrix of the filtered array received data, with dimensions M×M, where M is the number of array elements. The data matrix after filtering in step S3 is shown, where the superscript H denotes the conjugate transpose and K is the snapshot number; the eigenvalue decomposition of this covariance matrix is ​​then performed. ,in Eigenvalues , These are the eigenvectors.

[0013] Preferably, the step of extracting the phase information of the eigenvector corresponding to the largest eigenvalue, combining it with the heading sensor information, and obtaining the position coordinates of each array element through coordinate rotation calculation to complete the array formation estimation is as follows: In a single-signal incident scenario, the eigenvectors corresponding to large eigenvalues ​​span the same subspace as the steering vector and have the same phase, i.e.: ; in, Let i be the i-th element in the eigenvector corresponding to the largest eigenvalue. Guide vector The i-th element, Let i be the coordinates of the i-th element. This represents the true azimuth angle of the sound source; The phase difference between adjacent array elements is ,in This indicates the extraction of the principal phase of a complex number. Let the phase of the principal eigenvector corresponding to the j-th array element be denoted by the acoustic path difference. ,get ; Assuming the azimuth angle of the target signal is 90 degrees, the position coordinates of each array element are calculated as follows: ; in,( , Let be the local coordinates of the i-th element under the assumption that the target signal is incident from a 90° direction, where Let be the coordinates along the array baseline direction. is the coordinate in the vertical direction, and r is the spacing between array elements; Calculate the rotation angle ,in For the first The heading angle measured by a heading sensor. , and Assuming the sound source is at a 90-degree angle, and compared to the first... The position coordinates of adjacent array elements of each heading sensor, where L is the total number of heading sensors; Rotate the array obtained when the target signal azimuth is 90 degrees, and substitute the rotation angle into the rotation matrix T to obtain the position coordinates of each array element. This enables the estimation of the formation of the dragging line array.

[0014] The beneficial effects of the above-described technical solution of the present invention are as follows: This invention significantly improves the formation estimation performance of towed linear arrays in complex multi-signal environments by combining matrix spatial filtering and the eigenvector method. Traditional methods are prone to failure under multi-interference conditions, while this invention effectively suppresses interference from non-target directions using a spatial matrix filter, ensuring the accuracy of subsequent eigenvector extraction. This method not only inherits the high-precision advantage of the eigenvector method but also achieves robust formation estimation under conditions of unknown azimuth sound sources through headwind sensor-assisted rotation calculation. In multi-signal interference scenarios, this invention can accurately reconstruct the formation, overcoming the application limitations of traditional methods and possessing significant engineering practical value. Attached Figure Description

[0015] Figure 1 This is a flowchart of the overall formation estimation method; Figure 2 This is a diagram showing the results of the formation estimation. Detailed Implementation

[0016] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0017] This invention proposes a formation estimation method combining matrix spatial filtering and eigenvector analysis for towed linear array sonar. This method enables accurate formation estimation of the towed linear array in scenarios where multiple signals simultaneously incident on the array. It utilizes a matrix spatial filter to remove interference signals and combines this with the eigenvector method. First, using the heading angle information measured by the heading sensor in the array, an interpolation fitting method is used to initially estimate the array shape. Then, a conventional beamforming algorithm is combined to estimate the azimuth, obtaining the approximate direction of the target signal. A matrix filter is constructed, setting the area near the target signal direction as the passband and the remaining directions as the stopband. This filter is used to perform spatial filtering of the received data. After filtering out interference signals, accurate formation estimation can be achieved by combining the eigenvector method with the heading sensor information.

[0018] Combination Figure 1 As shown, the towed linear array sonar array formation estimation method proposed in this invention is divided into two main stages: a preliminary formation estimation stage based on a heading sensor and a precise formation estimation stage based on spatial filtering and feature vectors.

[0019] First, heading angle measurements at each measuring point are acquired using heading sensors deployed on the towed linear array, forming a heading angle matrix. Based on this, a polynomial fitting method is employed, and the polynomial fitting coefficients are obtained through maximum likelihood estimation, providing a preliminary description of the array's curve shape. Considering that the actual element spacing will change after array distortion, the abscissa of each element is further compressed and corrected. Polynomial fitting is then performed again using the corrected abscissas to obtain the corrected fitting coefficients, which are then used to calculate the ordinate of each element, completing the preliminary estimation of the array shape.

[0020] Then, the initially estimated array element position coordinates are substituted into the array's received data matrix, and conventional beamforming techniques are used to calculate the azimuth spectrum. The direction with the strongest energy is extracted as the coarsely estimated azimuth angle of the target signal. The passband is defined centered on this coarsely estimated azimuth angle, and the remaining directions are designated as stopbands. A spatial matrix filter is constructed based on the least squares criterion. This filter is used to perform spatial filtering on the raw received data, effectively suppressing interference signals outside the passband.

[0021] The filtered data is used to calculate the sampling covariance matrix and perform eigenvalue decomposition. The eigenvector corresponding to the largest eigenvalue is extracted, and the phase difference between adjacent array elements is calculated, thus obtaining the acoustic path difference between each array element. Assuming the target signal is incident from a 90° direction, the relative position coordinates of each array element are solved. Finally, the rotation angle is calculated using the overall array heading angle information provided by the heading sensor. Through coordinate rotation transformation, the array shape under the 90° assumption is rotated to the actual orientation, ultimately achieving high-precision estimation of the distorted array shape. The above technical solution of this invention specifically includes the following steps: Step 1: Use heading sensor information to interpolate and fit the array shape to achieve a preliminary estimate of the array shape; Consider an M-element uniformly distributed towed linear array with an element spacing of r. L heading sensors are uniformly distributed within the array. If the initial array shape is undistorted, the x-coordinate of each heading sensor is... The x-coordinate of each array element is The distorted formation can then be obtained by fitting an Nth-order polynomial to form a horizontal two-dimensional drag-line formation. It can be represented as Where x represents the x-coordinate of the array element, Let be the polynomial coefficients. Assume the measured value of the heading angle from the heading sensor is... , indicating the first The heading angle measured by each heading sensor at time t, and this measured value is related to the array configuration. The relationship between them can be represented as Define the heading vector at time t. for Define the coefficients of the polynomial fit. The coefficients are obtained by performing maximum likelihood (ML) estimation on them. .in It is an L x N matrix. ,in, ( ) indicates the first The x-coordinate values ​​of each heading sensor under the assumption of an undistorted linear array. Let Given the polynomial coefficient vector The distorted draggable array will then have the following formation: By substituting the x-coordinates of different array elements, the corresponding y-coordinates can be calculated. .

[0022] However, when the array formation is distorted, the heading sensor and the abscissa of each element will also change, so the result of the above equation needs to be corrected. The polynomial coefficients of the abscissa of each element are obtained. Then, the coordinates of P equally spaced points are obtained through calculation. The number of points P is much greater than the number of array elements M, from which the length of the dragging line array can be determined. The compression coefficient is obtained by comparing the actual length of the towed line with the calculated length S. Then the x-coordinate of the i-th element is The x-coordinate of the heading sensor is ,in , This represents the x-coordinate vector of the heading sensor position when there is no distortion. The x-coordinate of the heading sensor is then used again. Polynomial fitting yields The formation is That is, the position coordinates of each array element are initially estimated using the interpolation fitting method, and the x-axis is used as the interpolation fitting method. , y-axis .

[0023] Step 2: Obtain a coarse estimate of the target signal's azimuth using conventional beamforming. Let the array receive data matrix be... Calculate the azimuth spectrum of a conventional beamforming system; azimuth spectrum calculation formula. ,in For array manifold vectors f is the signal frequency. c is the speed of sound. For spatial orientation angle, The coordinates of the array elements estimated in step 1 are as follows. Let K be the sampling covariance matrix, and K be the number of snapshots. Taking the direction of the strongest signal as the target signal direction, then the target signal azimuth angle... .

[0024] Step 3: Construct a matrix filter to filter the received data in the spatial domain.

[0025] Design one A 3D matrix filter G filters the received data X (matrix multiplication), where the target signal orientation is used as the filter. The vicinity is the passband, and other directions are the stopbands. The orientations of the passband and stopband are discretized separately. Let... and These are discrete azimuth grids for the passband and stopband, respectively. To ensure the target signal passes through without distortion and to suppress the stopband signal, this matrix spatial filter must satisfy the following conditions: ,Right now ,in A matrix formed by concatenating the array manifold vectors in each direction column-wise can be represented as: , For extended array manifold matrices used in least squares design, , This is a matrix formed by concatenating the column vectors of all array manifolds within the passband, i.e. , It is a matrix formed by concatenating the vectors of all array manifolds within the stopband, i.e. . This represents the number of discrete azimuth grid cells in the passband. For the passband azimuth set, Let j be the j-th discrete azimuth angle within the passband. Corresponding discrete azimuth angle Array manifold vectors; It is a matrix formed by concatenating the vectors of all array manifolds within the stopband, i.e. , This represents the number of discrete azimuth grids in the stopband. For the stopband azimuth set, Let i be the i-th discrete azimuth angle within the stopband. Corresponding discrete azimuth angle Array manifold vectors.

[0026] Solving matrix G can be described as a least squares criterion design problem. ,in Let Frobenius norm be the expression, then the solution to this least squares problem is: Using this matrix filter to filter the received data X, the filtered data is obtained as follows: .

[0027] Step 4: Perform formation estimation using the eigenvector method incorporating heading sensor information. The sampling covariance matrix of the filtered array received data is ,in, This is the sampling covariance matrix of the filtered array received data, with dimensions M×M, where M is the number of array elements. The data matrix after filtering in step S3 is shown, where the superscript H denotes the conjugate transpose and K is the snapshot number; the eigenvalue decomposition of this covariance matrix is ​​then performed. ,in Eigenvalues , These are the eigenvectors.

[0028] In a single-signal incident scenario, the eigenvectors corresponding to large eigenvalues ​​and the steering vector span the same subspace and have the same phase. ,in Let i be the i-th element in the eigenvector corresponding to the largest eigenvalue. Guide vector The i-th element, Let i be the coordinates of the i-th element. This represents the true azimuth angle of the sound source.

[0029] The phase difference between adjacent array elements is , Let the phase of the principal eigenvector corresponding to the j-th array element be denoted by the acoustic path difference. ,get .

[0030] Given that the spacing between adjacent array elements is r and remains constant, find the coordinates of the i-th array element. ,Right now ,in It is a coordinate transformation matrix. These are the array element position coordinates obtained using the eigenvector method when the target signal is incident on the array from 90 degrees.

[0031] Therefore, for signals incident from any direction, the array shape estimation result can be obtained by rotating the array shape estimation result when the source azimuth is 90 degrees. Rotation angle ,in For the first The heading angle (the angle between the array and true north) measured by each heading sensor, where L is the total number of heading sensors. , and Assuming the sound source is at a 90-degree angle, and compared to the first... The position coordinates of adjacent array elements of the heading sensor are obtained. After obtaining the rotation angle, it is substituted into the rotation matrix T. The array estimation result under the condition that the sound source azimuth is 90 degrees is rotated to obtain the final array estimation result.

[0032] The working principle of the present invention is explained below with reference to specific embodiments: (1) A uniform towed linear array of M elements is arranged with an element spacing of r. This array is used to receive and record underwater acoustic signals, and the array outputs a received data matrix X. L heading sensors are uniformly placed on the array, and the heading value at time t is output. ; (2) Estimate the polynomial fitting coefficients . ,in , is the x-coordinate of the L heading sensors when the formation is not distorted, and N is the order of the polynomial fitting; (3) Calculate the length S of the dragging line. Select P sampling points densely, and use... Calculate the coordinates of P points ,in The length of the dragging line column is obtained. ; (4) Calculate the compression coefficient ; (5) Correct the abscissa of each array element. Abscissa of the heading sensor The x-coordinate of the i-th element is ; (6) Calculate the preliminary estimated array element coordinates. Substitute the corrected heading sensor and array element abscissas into step (2) to calculate the corrected polynomial fitting coefficients. reuse Calculate the coordinates of each array element , ; (7) Calculate the azimuth spectrum of conventional beamforming. ,in For array manifold vectors f is the signal frequency. c is the speed of sound. For spatial orientation angle, The initial estimated coordinates of the array elements are as follows: The sampling covariance matrix; (8) Obtain the azimuth of the target signal. The direction of the strongest signal is taken as the direction of the target signal; therefore, the azimuth angle of the target signal is... ; (9) Construct a matrix filter. The passband is defined as the area near the target signal direction. The other directions are stopbands. Matrix filters are designed using the least squares criterion. ,in It is a matrix formed by concatenating the array manifold vectors in each direction column by column. , , This represents the number of discrete azimuth grids in the stopband. (10) Perform spatial filtering on the array received data ; (11) Calculate the sampling covariance matrix of the filtered data. ; (12) Perform eigendecomposition of the covariance matrix and extract the phase information of the eigenvectors corresponding to the principal eigenvalues. ,in Eigenvalues , Let be the eigenvector. Then the phase information of the principal eigenvector is: ; (13) Calculate the phase difference between adjacent array elements ; (14) Calculate the path difference between adjacent array elements. ; (15) Assuming the azimuth angle of the target signal is 90 degrees, calculate the position coordinates of each array element. ; (16) Calculate the rotation angle .in For the first The heading angle (the angle between the array and true north) measured by a heading sensor. , and Assuming the sound source is at a 90-degree angle, and compared to the first... The position coordinates of adjacent array elements of the heading sensor; (17) Rotate the array obtained when the target signal azimuth is 90 degrees. Substitute the rotation angle into the rotation matrix T, then the position coordinates of each array element are obtained. This enables the estimation of the formation of the dragging line array.

[0033] Specific implementation examples: A 32-element uniform linear array is placed on an arc with a central angle of 30 degrees, with an element spacing of 1.875m. Five heading sensors are evenly distributed on the array. Two far-field narrowband signals exist at 110 degrees and 130 degrees, and a near-field noise signal simulating tugboat noise exists at 30 degrees. The array configuration is estimated using both the eigenvector method and the method presented in this invention. The results are attached. Figure 2As shown in the figure, the three curves correspond to the actual array shape, the estimation result of the method of this invention, and the estimation result of the traditional eigenvector method, respectively. It can be seen that the array shape estimated by the traditional eigenvector method deviates significantly from the true shape and is completely ineffective. In contrast, the method of this invention effectively suppresses interference signals outside the passband by constructing a spatial matrix filter. After filtering, the estimated array shape is highly consistent with the true array shape by combining the phase information of the principal eigenvector with the rotation calculation of the heading sensor. The eigenvector method is highly sensitive to multi-interference environments and fails under such conditions. The method presented in this invention, by constructing a matrix spatial filter, effectively suppresses far-field narrowband interference in the 110-degree and 130-degree directions and near-field tugboat noise in the 30-degree direction within the stopband, significantly reducing the impact of interference on the received data. It effectively purifies the characteristic structure of the covariance matrix, ensuring that the phase of the principal eigenvector is consistent with the phase characteristics of the target signal steering vector. Combined with the heading sensor information for coordinate rotation calculation, it can accurately estimate the array shape under conditions of multi-interference and unknown target orientation, breaking through the performance bottleneck of traditional methods under complex signal conditions.

[0034] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors, characterized in that, Includes the following steps: Step S1: Using the heading angle information measured by the heading sensors deployed on the towed linear array, the position coordinates of each array element after distortion are initially estimated by interpolation fitting method; Step S2: Based on the preliminary estimate of the distorted array element position coordinates, perform conventional beamforming processing on the array received data matrix to obtain the azimuth spectrum, and determine the direction with the strongest energy in the azimuth spectrum as the coarse estimate of the azimuth angle of the target signal; Step S3: Construct a spatial matrix filter centered on the coarsely estimated azimuth angle of the target signal, and use the spatial matrix filter to filter the array received data matrix to obtain the data matrix after filtering out interference; Step S4: Calculate the sampling covariance matrix and perform eigenvalue decomposition on the data matrix after filtering out interference; extract the phase information of the eigenvector corresponding to the largest eigenvalue, combine it with the heading sensor information, and obtain the position coordinates of each array element through coordinate rotation calculation to complete the array formation estimation.

2. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 1, characterized in that, Step S1 involves preliminarily estimating the position coordinates of each array element after distortion using an interpolation fitting method. Specifically: A towed line array with M uniformly distributed elements and an element spacing of r is arranged. L heading sensors are uniformly distributed in the array. The distorted array shape is obtained by fitting an Nth-order polynomial. The horizontal two-dimensional towed line array is represented as: ； Where x is the x-coordinate of the array element, These are the polynomial coefficients; Let the first The heading angle measurement value of each heading sensor at time t is The relationship between the measured heading angle and the formation is as follows: ; Define the heading vector at time t. ,in Indicates transpose, for the polynomial coefficient vector The coefficient estimates are obtained by performing maximum likelihood estimation. ,in It is an L x N matrix. The expression is: ； in, ( ) indicates the first The x-coordinate values ​​of each heading sensor under the assumption of an undistorted linear array; let Given the polynomial coefficient vectors of the abscissa of each array element. The distorted draggable array will then have the following formation: Substitute the x-coordinates of different array elements to calculate the corresponding y-coordinates.

3. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 2, characterized in that, Also includes: Obtain the abscissa polynomial coefficient vector of each array element. Then, the coordinates of P equally spaced points are calculated. The length of the dragging line column is obtained. ; The compression coefficient is obtained by comparing the actual length of the towed line array with the calculated length S. Then the x-coordinate of the i-th element is The x-coordinate of the heading sensor is ,in , The vector representing the x-coordinate of the heading sensor position when there is no distortion; Using the x-coordinate of the heading sensor again Perform polynomial fitting and calculate the corrected polynomial fitting coefficients. The formation is That is, the position coordinates of each distorted array element are initially estimated using the interpolation fitting method, and these coordinates are used as the abscissa. , y-axis .

4. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 1, characterized in that, Step S2 performs conventional beamforming processing on the array received data matrix to obtain the azimuth spectrum. The specific formula for calculating the azimuth spectrum is as follows: ； in, For array manifold vectors, j is the imaginary unit, and f is the signal frequency. c is the speed of sound. For spatial orientation angle, The array element position coordinates estimated in step S1, Let K be the sampling covariance matrix, and K be the number of snapshots. For array receiving data matrix, Representing the conjugate transpose, with the direction of the strongest signal as the target signal direction, the target signal azimuth angle is then... .

5. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 1, characterized in that, Step S3, which constructs a spatial matrix filter centered on the coarsely estimated azimuth angle of the target signal, specifically involves: Design one A 3D matrix filter G filters the received data X to determine the target signal orientation. Neighborhood is a passband Other directions are stopbands The passband and stopband orientations are discretized separately. Design of matrix filters using the least squares criterion ,in It is a matrix formed by concatenating the array manifold vectors in each direction column by column. , For extended array manifold matrices used in least squares design, , This is a matrix formed by concatenating the column vectors of all array manifolds within the passband, i.e. , This represents the number of discrete azimuth grid cells in the passband. For the passband azimuth set, Let j be the j-th discrete azimuth angle within the passband. Corresponding discrete azimuth angle Array manifold vectors; It is a matrix formed by concatenating the vectors of all array manifolds within the stopband, i.e. , This represents the number of discrete azimuth grids in the stopband. For the stopband azimuth set, Let i be the i-th discrete azimuth angle within the stopband. Corresponding discrete azimuth angle Array manifold vectors.

6. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 5, characterized in that, The specific expression for the least squares criterion is as follows: ； in This represents the Frobenius norm.

7. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 1, characterized in that, Step S4 involves calculating the sampling covariance matrix and performing eigenvalue decomposition on the data matrix after interference filtering. Specifically: The sampling covariance matrix of the filtered array received data is ,in, This is the sampling covariance matrix of the filtered array received data, with dimensions M×M, where M is the number of array elements. The data matrix after filtering in step S3 is shown, where the superscript H denotes the conjugate transpose and K is the snapshot number; the eigenvalue decomposition of this covariance matrix is ​​then performed. ,in Eigenvalues , These are the eigenvectors.

8. The method for estimating the configuration of a towed linear array sonar based on matrix spatial filtering and eigenvectors according to claim 1, characterized in that, The phase information of the eigenvector corresponding to the largest eigenvalue is extracted, and combined with the heading sensor information, the position coordinates of each array element are obtained through coordinate rotation calculation to complete the array formation estimation. Specifically: In a single-signal incident scenario, the eigenvectors corresponding to large eigenvalues ​​and the steering vector span the same subspace and have the same phase, i.e.: ； in, Let i be the i-th element in the eigenvector corresponding to the largest eigenvalue. Guide vector The i-th element, Let i be the coordinates of the i-th element. This represents the true azimuth angle of the sound source; The phase difference between adjacent array elements is ,in This indicates the extraction of the principal phase of a complex number. Let the phase of the principal eigenvector corresponding to the j-th array element be denoted by the acoustic path difference. ,get ; Assuming the azimuth angle of the target signal is 90 degrees, the position coordinates of each array element are calculated as follows: ； in,( , Let be the local coordinates of the i-th element under the assumption that the target signal is incident from a 90° direction, where Let be the coordinates along the array baseline direction. is the coordinate in the vertical direction, and r is the spacing between array elements; Calculate the rotation angle ,in For the first The heading angle measured by a heading sensor. , and Assuming the sound source is at a 90-degree angle, and compared to the first... The position coordinates of adjacent array elements of each heading sensor, where L is the total number of heading sensors; Rotate the array obtained when the target signal azimuth is 90 degrees, and substitute the rotation angle into the rotation matrix T to obtain the position coordinates of each array element. This enables the estimation of the formation of the dragged line array.

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