An underwater target positioning method based on underwater acoustic particle velocity polarization processing

Abstract

The application discloses a kind of underwater target positioning methods based on underwater acoustic particle velocity polarization processing.The method includes: arranging vector hydrophone array and carrying out underwater acoustic signal acquisition, and write the vector received signal of vector hydrophone array into tensor form;The tensor received signal of vector hydrophone array is carried out high-order singular value decomposition and the noise subspace of each dimension information matrix is solved by truncation to n module expansion left singular matrix;Array manifold matrix of vector hydrophone array is constructed and is written into polarization array manifold tensor;Azimuth-polarization two-dimensional spectrum search is carried out using array manifold tensor and noise subspace, and the azimuth and polarization parameters of the detected target are obtained from two-dimensional spectrum peak value.The underwater target positioning method provided by the application can accurately estimate the polarization parameters and the angle of arrival of incident signal, which helps to complete the underwater acoustic signal information based on frequency, wave number, mode and other characteristics by means of polarization parameters, and significantly improves the underwater target detection capability.

Description

Technical Field

[0001] This invention relates to vector hydrophone signal processing technology and underwater target detection, specifically to an underwater target localization method based on underwater acoustic particle velocity polarization processing. Background Technology

[0002] In real-world ocean waveguides, due to factors such as boundaries, medium inhomogeneity, and coherent multiple sources, the vibration direction of particles deviates from the direction of sound wave propagation, exhibiting a phenomenon similar to polarization. Traditional underwater acoustic models, which are dominated by sound pressure, fail to acknowledge this objective microscopic phenomenon and fact, making it impossible to achieve true formal uniformity in waveguide environment models for different sound fields.

[0003] A renewed understanding of the physical properties of acoustic particle velocity vectors, especially their polarization characteristics, is of great significance for deepening the fundamental scientific and engineering applications of underwater acoustics. Furthermore, polarization can build an interconnected bridge between underwater acoustics and electromagnetics, optics, and seismology, allowing these disciplines to intersect and jointly promote the development of wave physics and its applications, providing stronger support for solving underwater acoustic problems.

[0004] The acoustic particle velocity vector, in addition to the frequency, wavenumber, and mode characteristics traditionally considered in underwater acoustics, incorporates a new polarization feature. It contains crucial information about the interaction between underwater targets and underwater acoustic waveguides. Measurement and processing of the acoustic particle velocity vector reveal the individual characteristics of both underwater targets and underwater acoustic waveguides. The introduction of acoustic particle velocity polarization unifies the underwater acoustic models that deal with mutual interference from spherical waves, plane waves, and waveguide waves, incorporating different underwater acoustic models into a unified underwater acoustic polarization model. High-dimensional orthogonal decomposition provides relevant information about underwater targets and underwater acoustic waveguides. Compared to the severely mismatched acoustic field models processed by underwater acoustic matching field treatment, the underwater acoustic polarization model is always acoustically matched, shifting the focus from model mismatch to polarization parameter estimation. Tensor quantization and tensor decomposition of the acoustic particle velocity vector polarization contribute to higher information fidelity and processing gain, providing new perspectives and opening up new avenues for solving many underwater acoustic problems. Summary of the Invention

[0005] To address the problem that traditional waveguide environment models for different sound fields cannot achieve true formal uniformity, this invention proposes an underwater target localization method based on underwater acoustic particle velocity polarization processing. This invention establishes an underwater acoustic polarization processing framework based on elliptical geometry invariance and its tensor processing method. It transforms the processing of mode bases such as matched sound fields (modes) based on accurate sound field modeling into a multidimensional parameter estimation problem based on the geometric invariance of polarization ellipses. This reduces the dependence on propagation models and the impact of marine environmental mismatch, significantly improving the detection capability of vector hydrophone arrays for underwater targets in complex marine environments.

[0006] The objective of this invention is achieved through the following steps:

[0007] Step 1: Arrange a vector hydrophone array in a uniform linear array underwater to acquire underwater acoustic signals of sound pressure scalar and particle velocity vector;

[0008] Step 2: Obtain the polarization vector of each vector hydrophone and the time delay vector of the vector hydrophone array through underwater acoustic signal acquisition;

[0009] Step 3: Calculate the driving matrix of the vector hydrophone array based on the polarization vector and time delay vector, and reconstruct it into a third-order tensor form to obtain the driving tensor;

[0010] Step 4: Obtain the third-order tensor polarization output information of the vector hydrophone array based on the driving tensor of the vector hydrophone array;

[0011] Step 5: Perform high-order singular value decomposition on the third-order tensor polarization output information of the vector hydrophone array;

[0012] Step 6: Truncate the left singular matrices of the 1-mode, 2-mode, and 3-mode expansions obtained from the higher-order singular value decomposition and solve for the noise subspace matrix in each dimension;

[0013] Step 7: Perform a two-dimensional azimuth-polarization spectrum search using the driving tensor and noise subspace. Determine the azimuth angle and polarization parameters of the target based on the direction of arrival and polarization parameters corresponding to the peaks of the azimuth-polarization spectrum obtained from the search.

[0014] Compared with the prior art, the beneficial effects of the present invention are: the present invention proposes an underwater target positioning method based on the polarization processing of underwater acoustic particle vibration velocity, introduces polarization parameters into the signal model, solves the mismatch of the plane wave model in the short-range model in actual ocean waveguides, and improves the detection accuracy of underwater targets.

[0015] The polarization signal model of this invention can compromise between traditional plane wave processing and classical matched field (mode) processing to better adapt to the actual received sound field. It can make full use of sound field information, especially particle velocity information, while reducing model mismatch caused by spatiotemporal variations in complex environments. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure;

[0017] Figure 1 This is a schematic diagram of the uniform linear array of the vector hydrophone and the polarization ellipse of the underwater acoustic particle vibration velocity at the array element receiving point provided in the embodiment of the present invention.

[0018] Figure 2This is a flowchart of an underwater target localization method based on the polarization processing of underwater acoustic particle vibrations using a vector hydrophone array, provided by an embodiment of the present invention.

[0019] Figure 3 This is a one-dimensional spatial spectrum comparison of the horizontal azimuth estimation results of the underwater target localization method based on the hydrophone array and the traditional long vector MUSIC DOA estimation algorithm based on the plane wave model, provided in the embodiments of the present invention.

[0020] Figure 4 This is a one-dimensional spatial spectrum comparison of the elevation angle estimation results of the underwater target localization method based on the hydrophone array based on the hydrophone array (traditional long vector model and tensor model) and the traditional long vector MUSIC DOA estimation algorithm based on the plane wave model.

[0021] Figure 5 This is a one-dimensional spatial spectrum comparison of the elliptic tilt angle estimation results of the underwater target localization method based on the polarization processing of underwater acoustic particle velocity of the vector hydrophone array provided in this embodiment of the invention, using the traditional long vector model and the tensor model MUSIC DOA-polarization parameter joint estimation algorithm.

[0022] Figure 6 This is a one-dimensional spatial spectrum comparison of the ellipticity angle estimation results of the underwater target localization method based on the polarization processing of underwater acoustic particle velocity of the vector hydrophone array provided in this embodiment of the invention, and the MUSIC DOA-polarization parameter joint estimation algorithm of the traditional long vector model and tensor model.

[0023] Figure 7 This is a two-dimensional spatial spectrum of the DOA estimation result of the traditional long vector model MUSIC DOA-polarization parameter joint estimation algorithm for underwater target localization method based on underwater acoustic particle velocity polarization processing of vector hydrophone array provided in the embodiments of the present invention;

[0024] Figure 8 This is a two-dimensional spatial spectrum of the DOA estimation result of the tensor model MUSIC DOA-polarization parameter joint estimation algorithm of the underwater target localization method based on the hydrophone array and the underwater acoustic particle velocity polarization processing provided in the embodiment of the present invention;

[0025] Figure 9 This is a two-dimensional spatial spectrum of the polarization parameter estimation result of the traditional long vector model MUSIC DOA-polarization parameter joint estimation algorithm for underwater target localization based on the hydrophone array based on the hydrophone array provided in this embodiment of the invention.

[0026] Figure 10This is a two-dimensional spatial spectrum of the polarization parameter estimation result of the tensor model MUSIC DOA-polarization parameter joint estimation algorithm of the underwater target localization method based on the polarization processing of underwater acoustic particle vibration velocity of the vector hydrophone array provided in the embodiment of the present invention;

[0027] Figure 11 This is a comparison chart of the root mean square error of the underwater target localization method based on the hydrophone array and the traditional long vector model and tensor model based on the plane wave model for estimating the horizontal azimuth angle, provided in the embodiments of the present invention.

[0028] Figure 12 This is a comparison of the root mean square error of the elevation angle estimation results of the underwater target localization method based on the hydrophone array based on the vibration velocity polarization of underwater acoustic particles (traditional long vector model and tensor model) and the traditional long vector MUSIC DOA estimation algorithm based on the plane wave model provided in the embodiments of the present invention.

[0029] Figure 13 This is a comparison of the root mean square error of the elliptic tilt angle estimation results of the underwater target localization method based on the polarization processing of underwater acoustic particle velocity using a vector hydrophone array, provided in this embodiment of the invention.

[0030] Figure 14 This is a comparison chart of the root mean square error of the ellipticity angle estimation results of the underwater target localization method based on the polarization processing of underwater acoustic particle velocity using a vector hydrophone array, as provided in this embodiment of the invention. The ellipticity angle estimation results are compared between the traditional long vector model and the tensor model MUSIC DOA-polarization parameter joint estimation algorithm. Detailed Implementation

[0031] To make the above-mentioned objectives, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] Combination Figure 1 and Figure 2 The underwater target localization method based on underwater acoustic particle velocity polarization processing proposed in this invention first establishes a particle velocity polarization signal model. The polarization vector, composed of hydrophone sound pressure and particle velocity components including DOA parameters and polarization ellipse parameters, along with the time delay vector of the uniform linear array of the vector hydrophone, is used to establish a driving vector through the Kronecker product. This vector is then reconstructed into a driving tensor. Based on this driving tensor, the received signal is transformed into a third-order tensor. Higher-order singular value decomposition is used to obtain the polarization signal subspace and noise subspace of each dimension of the tensor. Combining this with the traditional MUSIC algorithm, a signal processing method based on underwater acoustic polarization is proposed to estimate the DOA of the incident signal and the polarization parameters of the polarization ellipse of the particle velocity polarization ellipse at the receiving array element position.

[0033] Combination Figure 2 The underwater target localization method based on the polarization processing of underwater acoustic particle velocity using a vector hydrophone array in this embodiment includes the following steps:

[0034] Step 1: Vector hydrophone array arrangement and polarization driving vector construction.

[0035] An array of M four-component vector hydrophones is deployed in a uniform linear array in an underwater environment. Each vector hydrophone can simultaneously measure the sound pressure signal (scalar) and the X / Y / Z components (vectors) of particle velocity. Using the vector hydrophone array to acquire underwater acoustic signals, the polarization driving vector composed of the sound pressure and particle velocity components of a single vector hydrophone is constructed as follows:

[0036]

[0037] Where u is the polarization vector of a single vector hydrophone, u x The polarization component in the X-axis direction, u y The polarization component in the Y-axis direction, u z Let θ be the polarization component along the Z-axis, and θ∈[-π,π] be the horizontal azimuth angle of the vector hydrophone. Let α be the pitch angle of the vector hydrophone, β∈[-π / 2,π / 2] be the elliptic tilt angle of the vector hydrophone, and α∈[-π / 4,π / 4] be the ellipticity angle of the vector hydrophone.

[0038] Step 2: Construct the time delay vector of the vector hydrophone array.

[0039] Since the vector hydrophone array is a uniform linear array, its array delay vector 'a' is specifically:

[0040]

[0041] Where λ is the wavelength of the incident signal, d is the spacing between adjacent vector hydrophones in the array, and M is the number of vector hydrophones.

[0042] Step 3: Construct the driving tensor of the array.

[0043] The driving vector and time delay vector of the vector hydrophone array are used to construct the driving matrix of the array using the Kronecker product, and then expressed as the driving tensor of the array. The specific calculation formula is as follows:

[0044]

[0045] Where A is the driving matrix, u1, u2, u M Let be the polarization vectors of the 1st, 2nd, and Mth vector hydrophones, and let a be the time delay vector of the vector hydrophone array. Represents the tensor product;

[0046] If the vector hydrophone array is a uniform linear array and the array elements are four-component vector hydrophones, then the tensor of the array manifold is specifically:

[0047]

[0048] in,

[0049] In the formula, k is the number of incident signals received by the vector hydrophone array. Let u be a slice of the array driving tensor of the k-th incident signal in the signal number dimension. xk u yk and u zk θ is the polarization component of the particle velocity polarization vector of the k-th incident signal in the x, y, and z axes. k Let be the horizontal azimuth angle of the k-th incident signal. Let β be the elevation angle of the k-th incident signal. k Let α be the elliptic tilt angle of the polarization ellipse of the particle velocity at the receiving point of the k-th incident signal. k Let be the ellipticity angle of the polarization ellipse of the particle velocity at the receiving point of the k-th incident signal, and M be the number of vector hydrophones in the array.

[0050] Step 4: Obtain the third-order tensor polarization output information of the vector hydrophone array based on the array driving tensor.

[0051] Under L rapid snapshots, the third-order tensor form of the vector hydrophone array output can be expressed as:

[0052]

[0053] in, Output information as a third-order tensor. For array driving tensors, ×3 represents the 3-module tensor product operation. The waveform of the sound source signal. Let K be the Gaussian noise tensor, and K be the total number of incident signals.

[0054] Step 5: Perform high-order singular value decomposition (HOSVD) on the third-order tensor output of the vector hydrophone array;

[0055] The high-order singular value decomposition of the array received signal in tensor form yields:

[0056]

[0057] in, For output signal tensor The kernel tensor, × n U represents the tensor product operation of the nth dimension.n For output signal tensor The left singular matrix of the modulus expansion of n, n = 1, 2, 3. These are the left singular matrices after expansion with modulo 1, 2, and 3, respectively.

[0058] Step 6: Truncate the left singular matrix of the n-modulus expansion obtained by HOSVD and solve for the noise subspace matrix of each dimension;

[0059] By truncating the left singular matrices of the modulo 1, modulo 2, and modulo 3 expansions, we can obtain... That is U nN The noise subspace matrix consists of the column vectors of the matrices corresponding to the smaller singular values ​​remaining after sorting in descending order, excluding the larger singular values ​​corresponding to the number of information sources.

[0060] Step 7: Use the array driving tensor and noise subspace matrix to perform azimuth-polarization two-dimensional spectrum search. The polarization parameter corresponding to the peak of the two-dimensional spectrum is the ellipticity angle and elliptic tilt angle of the polarization ellipse of the particle velocity at that point. The direction of arrival (DOA) value corresponding to the peak is the azimuth angle and elevation angle of the incident signal. The azimuth of the detected target can be determined based on the polarization parameter and the direction of arrival.

[0061] because The column vectors are orthogonal to the 1-mode noise subspace, i.e. The row vectors are orthogonal to the 2-mode noise subspace. Based on the direction of arrival and polarization parameter estimation of the long vector MUSIC algorithm, the joint estimation formula of direction of arrival and polarization parameter MUSIC for underwater target localization method using underwater acoustic particle velocity polarization processing is obtained as follows:

[0062]

[0063] in, For the polarization array manifold tensor, × n U represents the tensor product operation of the nth dimension. nN U is the value of the smaller singular value remaining after sorting in descending order, excluding the larger singular value corresponding to the number of sources. n Noise-related matrices in each dimension, composed of column vectors of the matrix. For U nN The conjugate transpose of;

[0064] The polarization parameters corresponding to the peak value of the azimuth-polarization two-dimensional spectrum are the ellipticity angle and elliptic tilt angle of the polarization ellipse of the particle velocity at that point, and the direction of arrival (DOA) value corresponding to the peak value is the azimuth angle and elevation angle of the incident signal.

[0065] Simulation Examples

[0066] Combination Figures 3 to 14 The vector hydrophone has a uniform linear array with M = 8 elements and d = 0.5 m spacing between elements. The sound source signal has a frequency f. s =10Hz single-frequency signal, sampling frequency f=500Hz, number of snapshots 1000, background noise is zero-mean Gaussian white noise; signal incident horizontal azimuth angle θ=40°, elevation angle The particle velocity polarization ellipse has an elliptic tilt angle β = 30°, an ellipticity angle α = 10°, and a signal-to-noise ratio (SNR) of 0 dB.

[0067] Figures 3 to 6 This is a one-dimensional spatial spectrum comparison of the incident signal DOA parameters and the estimated results of the received point particle velocity polarization ellipse parameters obtained by the underwater target localization method based on the hydrophone array-based underwater acoustic particle velocity polarization processing method. It can be seen from the figure that when the plane wave model estimates the real signal containing polarization, there is an estimation error in the horizontal azimuth angle due to the influence of model mismatch. Since the elevation angle and the polarization ellipse tilt angle are coupled together, the estimation error of the plane wave model in estimating the elevation angle is relatively larger than that in estimating the horizontal azimuth angle.

[0068] Figures 7 to 10 The two-dimensional spatial spectra of the incident signal DOA parameters (traditional long vector model and tensor model) and the estimated results of the polarization ellipse parameters of the received point mass velocity polarization, obtained by the underwater target localization method based on the hydrophone array and the hydrophone array, are shown respectively. Under the same signal-to-noise ratio, both the long vector MUSIC algorithm and the tensor decomposition-based MUSIC algorithm can accurately estimate the polarization parameter information and azimuth information of the signal. The sidelobe performance of the tensor decomposition-based MUSIC algorithm is better than that of the long vector MUSIC algorithm, and the spectral peaks are sharper. When displayed at the same color level, it can be intuitively seen that the tensor decomposition-based MUSIC algorithm has higher resolution, which means that it can provide higher estimation accuracy of the sound source horizontal azimuth / elevation angle DOA parameters and the particle velocity polarization ellipse tilt / ellipticity angle parameters.

[0069] Figures 11 to 14 This is a comparison of the root mean square error of the incident signal DOA parameters and the estimated results of the polarization ellipse parameters of the received point particles obtained by the underwater target localization method based on the hydrophone array and the hydrophone array. To avoid the influence of random errors, 300 Monte Carlo simulations were performed, with the signal-to-noise ratio range set to -20dB:2dB:20dB, and the spatial spectrum estimation step size of the DOA and polarization parameters being 0.5°.

[0070] Depend on Figure 11 and Figure 12It can be seen that the root mean square error of the MUSIC algorithm based on the plane wave model is much larger than that of the MUSIC algorithm based on the underwater acoustic particle velocity polarization model. This is because the non-polarization model processes the real polarized signal, and there is polarization loss due to polarization mismatch, which causes model mismatch and estimation error.

[0071] Depend on Figure 11 and Figure 12 It can be seen that the root mean square error of the MUSIC algorithm based on tensor decomposition is smaller than that of the long vector MUSIC algorithm. This indicates that the signal subspace obtained by the MUSIC algorithm based on tensor decomposition through singular value decomposition of information matrices in each dimension is more accurate than that of the traditional long vector MUSIC algorithm, and therefore has better estimation accuracy.

[0072] In summary, this invention relates to an underwater target localization method based on the polarization processing of underwater acoustic particle vibrations using a vector hydrophone array. The above description sets forth many specific details to provide a thorough understanding of the invention. However, the invention can be implemented in many other ways different from those described herein. Those skilled in the art can make similar improvements without departing from the spirit and principles of the invention. Therefore, this invention is not limited to the specific implementations disclosed above. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed herein, and within the spirit and principles of the invention, should be included within the protection scope of this invention.

Claims

1. A method for underwater target localization based on underwater acoustic particle velocity polarization processing, characterized in that, Includes the following steps: Step 1: Arrange a vector hydrophone array in a uniform linear array underwater to collect underwater acoustic signals of sound pressure scalar and particle velocity vector; Step 2: Obtain the polarization vector of each vector hydrophone and the time delay vector of the vector hydrophone array through underwater acoustic signal acquisition; Step 3: Calculate the driving matrix of the vector hydrophone array based on the polarization vector and time delay vector, and reconstruct it into a third-order tensor form to obtain the driving tensor; Step 4: Obtain the third-order tensor polarization output information of the vector hydrophone array based on the driving tensor of the vector hydrophone array; Step 5: Perform high-order singular value decomposition on the third-order tensor polarization output information of the vector hydrophone array; Step 6: Truncate the left singular matrices of the 1-mode, 2-mode, and 3-mode expansions obtained from the higher-order singular value decomposition to solve for the noise subspace matrix in each dimension; Step 7: Perform a two-dimensional azimuth-polarization spectrum search using the driving tensor and noise subspace. Determine the azimuth angle and polarization parameters of the target based on the direction of arrival and polarization parameters corresponding to the peaks of the azimuth-polarization spectrum obtained from the search.

2. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 1, characterized in that, The vector hydrophone is a four-component vector hydrophone, and the polarization vector of the vector hydrophone in step 2 is specifically: ； in, For a single vector hydrophone, 1 corresponds to the polarization component of the sound pressure scalar channel. The polarization component of the vibration velocity along the X-axis is... The polarization component of the vibration velocity along the Y-axis. The polarization component of the vibration velocity along the Z-axis is... The horizontal azimuth angle of the vector hydrophone. The pitch angle of the vector hydrophone. The elliptical tilt angle of the vector hydrophone. Let be the ellipticity angle of the vector hydrophone.

3. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 2, characterized in that, In step 2, the time delay vector of the vector hydrophone array is specifically: ； in, Let be the time delay vector of the vector hydrophone array. The wavelength of the incident signal is . The spacing between individual vector hydrophones, This represents the number of vector hydrophones.

4. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 3, characterized in that, In step 3, the driving matrix of the vector hydrophone array is calculated based on the polarization vector and the time delay vector. The specific calculation formula is as follows: ； in, For driving matrix, These are the polarization vectors of the 1st, 2nd, and Mth vector hydrophones. Let be the time delay vector of the vector hydrophone array. Represents the tensor product; Reconstruct the driving matrix into a driving tensor, specifically by reconstructing the driving matrix... The driving tensor is obtained by decomposing and reconstructing it according to different incident directions. The expression for the polarization array manifold tensor is: ； in, ； ； ； ； In the formula, k is the number of incident signals received by the vector hydrophone array. This is a slice of the driving tensor signal dimension of the k-th incident signal. , and It represents the polarization components of the particle velocity polarization vector of the k-th incident signal in the x, y, and z axes. Let be the horizontal azimuth angle of the k-th incident signal. Let be the elevation angle of the k-th incident signal. Let be the tilt angle of the polarization ellipse of the particle velocity at the receiving point of the k-th incident signal. Let be the ellipticity angle of the polarization ellipse of the particle velocity at the receiving point of the k-th incident signal, and M be the number of vector hydrophones.

5. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 4, characterized in that, In step 4, the third-order tensor polarization output information of the vector hydrophone array is obtained based on the driving tensor of the vector hydrophone array. The specific formula is as follows: ； in, The output information is a third-order tensor polarization, and L is the number of snapshots during the acquisition process of the vector hydrophone array. For driving tensor, For 3-module tensor product operation, The waveform of the sound source signal. Let K be the Gaussian noise tensor, and K be the total number of incident signals.

6. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 5, characterized in that, In step 5, the third-order tensor polarization output information of the vector hydrophone array is subjected to high-order singular value decomposition, specifically expressed as follows: ； in, The output information is the third-order tensor polarization. For output information tensor The kernel tensor, This represents the tensor product operation in the nth dimension. For output information tensor The left singular matrix of the n-modulus expansion. , , , .

7. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 6, characterized in that, In step 6, the step of truncating the left singular matrices of the 1-mode, 2-mode, and 3-mode expansions obtained from the higher-order singular value decomposition to solve for the noise subspace matrix of each dimension is specifically as follows: Left singular matrices expanded in terms of module 1, module 2, and module 3 respectively , , The signal subspace portion is removed during truncation. After retaining the MK columns, the noise subspace matrix is ​​obtained. , The noise subspace matrix is ​​obtained by retaining the last 4-K columns. , After retaining the LK columns, the noise subspace matrix is ​​obtained. K represents the total number of incident signals.

8. The underwater target localization method based on underwater acoustic particle velocity polarization processing according to claim 7, characterized in that, In step 7, the azimuth angle and polarization parameters of the target are determined based on the direction of arrival and polarization parameters corresponding to the azimuth-polarization two-dimensional spectral peaks obtained from the search. Specifically, the direction of arrival-polarization parameter MUSIC joint estimation formula is used, as follows: ； in, For two-dimensional spectral function values, For the polarization array manifold tensor, For the direction of the wave, For polarization parameters, This represents the tensor product operation of the nth dimension. Expand the left singular matrix in the form of n modulo The corresponding noise subspace matrices in each dimension, , for The conjugate transpose of .

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