Double-seabed horizontal array joint target positioning method based on subspace intersection

Abstract

The invention discloses a double-seabed horizontal array joint target positioning method based on subspace intersection, and the method comprises the steps: synchronously collecting signals transmitted by an underwater sound source through two seabed horizontal arrays, and constructing a signal receiving model; establishing a two-dimensional rectangular coordinate system based on the spatial positions of the two seabed horizontal arrays; in the sea area where the two seabed horizontal arrays are located, acoustic environment parameters are measured; based on a modal theory, substituting the acoustic environment parameters into the normal wave model, and calculating the horizontal wave number of each order of normal wave in the sound field; screening out an effective mode in each order mode corresponding to the horizontal wave number; constructing a covariance matrix of a horizontal array output signal; performing eigenvalue decomposition on the covariance matrix to construct a signal subspace; constructing a modal subspace; the modal subspace and the signal subspace are combined and orthogonal triangular decomposition is carried out so as to solve the estimation result of the two seabed horizontal arrays on the sound source azimuth angle; and estimating the position of the sound source according to the estimation result of the two seabed horizontal arrays on the azimuth angle of the sound source.

Description

Technical Field

[0001] The invention belongs to the field of underwater sound source positioning, and in particular relates to a dual seabed horizontal array joint positioning method based on robust azimuth estimation. Background Art

[0002] With the development of marine engineering and signal processing methods, the rapid and accurate positioning of underwater sound sources is a key technology that needs to be urgently solved. In recent years, the development and progress of equipment level have made underwater detection methods more diverse. Among them, large-aperture linear arrays can obtain a larger detection radius, which is conducive to detecting low signal-to-noise ratio sound sources in complex marine environments. Based on modal theory, compared with other depth layers, at the seabed depth, the amplitude of each order of simple normal wave modes is larger, that is, the contribution of more orders of simple normal wave modes to the sound field is retained. Therefore, the seabed horizontal array can effectively sample more orders of simple normal wave modes, thereby obtaining more sound source information. The multi-station joint target positioning method with the seabed horizontal linear array as the observation node can generate the target position information by combining the target azimuth estimation information of multiple observation nodes at each sampling moment. The azimuth measurement results of multiple observation stations are used to achieve target positioning, mainly by combining the sound source azimuth information provided by each observation node to create a sound source positioning model, thereby solving the sound source position coordinates. This type of method has a small amount of computation and stable performance, and is suitable for the sound source positioning problem based on the azimuth estimation of the seabed horizontal array.

[0003] However, when using horizontal line arrays to estimate the target direction, the traditional direction estimation method based on the plane wave model has certain estimation errors under multi-path conditions, which can easily cause spatial spectrum peak deviation or splitting. The lack of accuracy in the direction estimation results will greatly reduce the accuracy of the multi-station joint positioning algorithm. Summary of the invention

[0004] The present invention proposes a dual seabed horizontal array joint target positioning method based on subspace intersection, which is used to achieve high-resolution azimuth estimation of horizontal array nodes according to the acoustic environment of the test sea area, and then jointly locate the sound source by utilizing the azimuth angle differences estimated by the horizontal arrays at different positions, thereby solving the problems of large computational complexity and low precision existing in traditional methods.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A dual seabed horizontal array joint target positioning method based on subspace intersection, comprising:

[0007] Two seabed horizontal arrays are used to synchronously collect signals from underwater sound sources and build a signal reception model;

[0008] A two-dimensional rectangular coordinate system is established based on the spatial positions of the two seafloor horizontal arrays;

[0009] In the sea area where the two seabed horizontal arrays are located, the acoustic environment parameters are measured;

[0010] Based on modal theory, the acoustic environment parameters are substituted into the simple normal wave model to calculate the horizontal wave number of each order of simple normal waves in the sound field; each order of simple normal waves is obtained based on the decomposition of the signal receiving model;

[0011] Based on the horizontal wavenumbers of each order of simple normal waves, the effective modes in each order mode corresponding to the horizontal wavenumber are screened out;

[0012] Based on the signal receiving model, the covariance matrix of the horizontal array output signal is constructed; the signal subspace is constructed by performing eigenvalue decomposition on the covariance matrix; based on the horizontal wavenumbers of each order of effective modes, the modal subspace is constructed;

[0013] The modal subspace is combined with the signal subspace and orthogonal triangular decomposition is performed to obtain the estimation results of the azimuth of the sound source for two seabed horizontal arrays;

[0014] According to the azimuth estimation results of the sound source by two seabed horizontal arrays, the position of the sound source is estimated based on the established two-dimensional rectangular coordinate system.

[0015] Furthermore, the method of synchronously collecting signals emitted by underwater sound sources using two seabed horizontal arrays to construct a signal receiving model includes:

[0016] For an N-element seafloor horizontal array with an element spacing of d, the receiving depth is z r , the horizontal distance between the nth array element and the sound source is r n (n=1,2,...,N); there are S sound sources in the space at the same time, the signal angular frequency is ω, and the signal received by the nth element of the horizontal array is:

[0017]

[0018] In the formula, p s (ω,r n ,z r ) represents the sound pressure value of the sth sound source signal received by the horizontal array. The magnitude of the sound pressure value is related to the signal angular frequency ω and the horizontal distance r from the sound source. n , receiving depth z r There is a functional relationship; σ(ω) represents Gaussian white noise; at the lth snapshot, the received signal vector on the horizontal array is expressed as: x l (ω)=[x1(ω),x2(ω),...,x N (ω)] T .

[0019] Furthermore, the two-dimensional rectangular coordinate system is established based on the spatial positions of the two seabed horizontal arrays, including:

[0020] The line connecting the midpoints of the two seabed horizontal arrays is determined as the x-axis, and the midpoint of any one of the seabed horizontal arrays is used as the coordinate origin, and the x-axis is rotated 90° horizontally as the y-axis to construct a two-dimensional rectangular coordinate system; thus, the coordinates of the two seabed horizontal arrays are (x1, y1) and (x2, y2), respectively.

[0021] Furthermore, in the sea area where the two seabed horizontal arrays are located, the acoustic environment parameters are measured as inputs of the simple normal wave model. These parameters include:

[0022] The measuring device is arranged near the seabed horizontal array, and the sound velocity profile is measured on-site using a temperature chain, CTD or XBT probe device; the acoustic characteristics of the seabed sediments are acquired by seabed sampling, in-situ measurement, and inversion of seabed geoacoustic parameters to obtain the sound velocity, density and acoustic attenuation coefficient of the seabed sediments.

[0023] Furthermore, the method of screening out effective modes in modes of each order corresponding to the horizontal wavenumbers based on the horizontal wavenumbers of each order of simple normal waves includes:

[0024] According to the sound velocity profile in the water body and the seabed sound velocity c s , the reflection mode and the inversion mode are selected as the effective modes; among them, the horizontal wave number k of the reflection mode m Need to satisfy ωc s <k m <ωc max , the horizontal wave number k of the inversion mode m Need to satisfy ωc max <k m <ωc min , c max and c min Respectively represent the maximum and minimum values ​​of the sound speed in water; the selected effective modal order is expressed as: m = 1, 2, ..., M e , M e is the maximum order of the effective modes screened out.

[0025] Furthermore, based on the signal receiving model, the covariance matrix of the horizontal array output signal is constructed; by performing eigenvalue decomposition on the covariance matrix, a signal subspace is constructed; based on the horizontal wave number of each order effective mode, a modal subspace is constructed, including:

[0026] Based on the received signal vector x of the lth snapshot l (ω), then under L snapshots, the covariance matrix of the horizontal array output signal is obtained as:

[0027]

[0028] In the formula, the superscript H represents the conjugate transpose; by The eigenvalue decomposition can be written as follows:

[0029]

[0030] in, It means arranging the eigenvalues ​​from large to small, and the diagonal matrix composed of the first S large eigenvalues, represents the signal subspace composed of the eigenvectors corresponding to the first S largest eigenvalues; represents the diagonal matrix composed of the remaining NS small eigenvalues, Represents the noise subspace composed of eigenvectors corresponding to NS small eigenvalues;

[0031] Based on the horizontal wave number k of each effective mode m (m=1,2,...,M e ), the modal subspace corresponding to the search angle θ is defined as:

[0032]

[0033] Among them, span{·} represents the spanned space, i is the imaginary unit and e is the base of natural logarithms.

[0034] Furthermore, the method of combining the modal subspace with the signal subspace and performing orthogonal triangular decomposition to solve the estimation result of the azimuth of the sound source by the two seabed horizontal arrays includes:

[0035] Combining the modal subspace with the signal subspace, we can obtain an N×(M e +S)-order matrix:

[0036]

[0037] After QR decomposition, we get:

[0038]

[0039] in, is the orthogonal matrix obtained by orthogonal decomposition, M e +S)×(M e +S)-order upper triangular matrix, whose diagonal elements for Singular values ​​of ; then the function:

[0040] The peak value corresponds to the estimated azimuth of the sound source.

[0041] Furthermore, the estimation of the position of the sound source based on the two-dimensional rectangular coordinate system established according to the sound source azimuth estimation results of the two seabed horizontal arrays includes:

[0042] The estimated results of the sound source azimuths corresponding to the two seafloor horizontal arrays are: The angle between the end-fire direction of the two seabed horizontal arrays and the positive direction of the x-axis of the two-dimensional rectangular coordinate system is Then for the sound source located at (x, y), the observation equation is:

[0043]

[0044] Thus, the estimated sound source position It can be obtained by solving the following system of equations:

[0045]

[0046] A sound source localization device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the double seabed horizontal array joint target localization method based on subspace intersection is implemented.

[0047] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the dual seafloor horizontal array joint target positioning method based on subspace intersection is implemented.

[0048] Compared with the prior art, the present invention has the following technical features:

[0049] The dual-seafloor horizontal array joint positioning method based on robust azimuth estimation proposed in the present invention is based on the simple normal wave theory and eliminates the azimuth estimation error of the seafloor horizontal array by accurately modeling the simple normal wave wave number, so that the dual-horizontal array joint positioning has practical value. The beneficial effect of the present invention is that by introducing the subspace intersection algorithm, the direction finding accuracy of a single horizontal array node is improved, thereby improving the target positioning accuracy. Compared with the traditional matching field direction finding method, the amount of calculation is greatly reduced, which effectively improves the efficiency of target positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The combination of measured data and simulation results in the entire joint positioning process is given, and the target positioning results are output;

[0051] Figure 2 It is a schematic flow diagram of the method of the present invention;

[0052] Figure 3 is a schematic diagram of a test sea area corresponding to an embodiment of the present invention, and a schematic diagram of a rectangular coordinate system based on a horizontal array position;

[0053] Figure 4 is the positional relationship between two fixed sound sources and two horizontal array direction finding nodes in the space corresponding to the embodiment of the present invention;

[0054] Figure 5 is a typical shallow sea sound velocity profile provided by an embodiment of the present invention;

[0055] Figure 6 It is the wave value of the first 6 normal wave modes calculated based on modal theory;

[0056] Figure 7 is the azimuth estimation result of two seabed horizontal array direction finding nodes corresponding to the embodiment of the present invention at the same time;

[0057] Figure 8 is the joint positioning result at 500 moments corresponding to the embodiment of the present invention;

[0058] Fig. 9 is the positioning root mean square error corresponding to the embodiment of the present invention. DETAILED DESCRIPTION

[0059] To make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described clearly and completely in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiment is only a representative embodiment of the present invention, not all.

[0060] The present invention proposes to use the subspace intersection method to perform joint positioning of multiple stations of the seabed horizontal array, thereby effectively improving the target positioning accuracy. Moreover, in the case of accurately calculating the wave number of each order of simple normal waves, the subspace intersection method only needs to perform a one-dimensional search for the sound source direction, which is suitable for low-frequency shallow sea sound fields with a small total number of simple normal waves. Compared with the traditional matching field method, the amount of calculation is greatly reduced.

[0061] Referring to the accompanying drawings, the present invention provides a dual seabed horizontal array joint target positioning method based on subspace intersection, comprising the following steps:

[0062] Step 1: Use two seabed horizontal arrays to synchronously collect signals from underwater sound sources and build a signal reception model.

[0063] For an N-element seafloor horizontal array with an element spacing of d, the receiving depth is z r , the horizontal distance between the nth array element and the sound source is r n (n=1,2,...,N); there are S sound sources in the space at the same time, the signal angular frequency is ω, and the signal received by the nth element of the horizontal array is:

[0064]

[0065] In the formula, ps (ω,r n ,z r ) represents the sound pressure value of the sth sound source signal received by the horizontal array. The magnitude of the sound pressure value is related to the signal angular frequency ω and the horizontal distance r from the sound source. n , receiving depth z r There is a functional relationship; σ(ω) represents Gaussian white noise. Therefore, at the lth snapshot, the received signal vector on the horizontal array can be expressed as: x l (ω)=[x1(ω),x2(ω),...,x N (ω)] T , the superscript T indicates transpose.

[0066] Step 2: Establish a two-dimensional rectangular coordinate system based on the spatial positions of the two seabed horizontal arrays.

[0067] In this step, the line connecting the midpoints of the two seabed horizontal arrays is determined as the x-axis, and the midpoint of any one of the seabed horizontal arrays is used as the coordinate origin, and the x-axis is rotated 90° horizontally as the y-axis to construct a two-dimensional rectangular coordinate system parallel to the horizontal plane; thus, the coordinates of the two seabed horizontal arrays are (x1, y1) and (x2, y2), respectively, where x1=y1=0.

[0068] Step three: Measure acoustic environmental parameters such as sound velocity profile and acoustic characteristics of seabed sediments in the sea area where the two seabed horizontal arrays are located.

[0069] Among them, the measuring device is arranged near the seabed horizontal array, and the sound velocity profile can be measured on-site using devices such as temperature chain, CTD, and XBT probes; the acoustic characteristics of seabed sediments are obtained by seabed sampling, in-situ measurement, and inversion of seabed geoacoustic parameters to obtain the sound velocity, density, and sound attenuation coefficient of seabed sediments.

[0070] Step 4: Based on modal theory, the acoustic signal received by the seabed horizontal array is composed of the superposition of simple normal wave modes of different orders. The simple normal wave model is substituted into the sound velocity profile and seabed sediment acoustic environment parameters described in step 3 to calculate the horizontal wave number k of each order of simple normal wave in the sound field. m (m=1,2,...,M), m is the order of the mode; each order of the simple normal wave is the signal receiving model x of step 1. n (ω) is decomposed.

[0071] Step 5: Based on the horizontal wavenumbers of each order of simple normal waves, the effective modes in the modes of each order corresponding to the horizontal wavenumbers are screened out.

[0072] According to the sound velocity profile in the water body and the seabed sound velocity c s , the reflection mode and the inversion mode are selected as the effective modes; among them, the horizontal wave number k of the reflection mode mNeed to satisfy ωc s <k m <ωc max , the horizontal wave number k of the inversion mode m Need to satisfy ωc max <k m <ωc min , c max and c min Respectively represent the maximum and minimum values ​​of the sound speed in water; the selected effective modal order is expressed as: m = 1, 2, ..., M e , M e is the maximum order of the effective modes screened out.

[0073] Step 6: Based on the signal receiving model, construct the covariance matrix of the horizontal array output signal;

[0074] The variance matrix is ​​decomposed into eigenvalues ​​to construct the signal subspace Based on the horizontal wavenumbers of each effective mode, the modal subspace μ(θ) is constructed.

[0075] Based on the received signal vector x of the lth snapshot obtained in step 1 l (ω), then under L snapshots, the covariance matrix of the horizontal array output signal is obtained as:

[0076]

[0077] In the formula, the superscript H represents the conjugate transpose; by the covariance matrix The eigenvalue decomposition can be written as follows:

[0078]

[0079] in, It means arranging the eigenvalues ​​from large to small, and the diagonal matrix composed of the first S large eigenvalues, represents the signal subspace composed of the eigenvectors corresponding to the first S largest eigenvalues; represents the diagonal matrix composed of the remaining NS small eigenvalues, Represents the noise subspace composed of eigenvectors corresponding to NS small eigenvalues;

[0080] Based on the horizontal wave number k of each effective mode m (m=1,2,...,M e ), the modal subspace corresponding to the search angle θ is defined as:

[0081]

[0082] Among them, span{·} represents the spanned space, i is the imaginary unit and e is the base of natural logarithms.

[0083] Step seven, combine the modal subspace with the signal subspace and perform orthogonal triangular decomposition to solve the estimation results of the azimuth of the sound source by the two seabed horizontal arrays.

[0084] Combining the modal subspace with the signal subspace, we can obtain an N×(M e +S)-order matrix:

[0085]

[0086] After QR decomposition, we get:

[0087]

[0088] in, is the orthogonal matrix obtained by orthogonal decomposition, M e +S)×(M e +S)-order upper triangular matrix, whose diagonal elements for Singular values ​​of ; then the function:

[0089] The peak value corresponds to the estimated azimuth of the sound source.

[0090] Step 8: Based on the azimuth estimation results of the two seabed horizontal arrays, the sound source is located based on the established two-dimensional rectangular coordinate system. The position of is estimated.

[0091] For the case of two seafloor horizontal arrays, the estimated sound source azimuths corresponding to the two seafloor horizontal arrays are The angle between the end-fire direction of the two seabed horizontal arrays and the positive direction of the x-axis of the two-dimensional rectangular coordinate system is Then for the sound source located at (x, y), the observation equation is:

[0092]

[0093] Thus, the estimated sound source position It can be obtained by solving the following system of equations:

[0094]

[0095] Compared with the prior art, the present invention is based on a simple normal wave model, which effectively eliminates the target azimuth estimation deviation caused by the plane wave model; compared with the traditional matching field processing direction-finding method, the present invention only needs to search for angles when using the seabed horizontal array for azimuth estimation, which effectively reduces the amount of calculation; the method is simple in principle and easy to implement, and the positioning error is not greatly affected by the depth of the sound source, less environmental information is required, and the positioning efficiency is high; the method is suitable for scenes where multiple targets exist at the same time, and subsequently with the help of a target tracking algorithm, real-time output of multiple target tracks can be achieved in the scene.

[0096] Example:

[0097] According to the receiving signal of the seabed horizontal array and the simulated ocean acoustic environment, Figure 1 The process shown in the figure outputs the target positioning result. The specific operation steps of the algorithm are as follows: Figure 2 Given.

[0098] 1. Refer to Figure 3 In the paper, for the underwater sound source joint positioning transceiver structure, a joint positioning system consisting of two seabed horizontal array observation nodes is established in the shallow sea area with a depth of 100m. Figure 4 In the two-dimensional rectangular coordinate system shown, the coordinates of the two 64-element horizontal arrays are (0,0)m and (960,0)m, and the apertures are both 315m. Assuming that there are two sound sources with a depth of 25m in the space, their coordinates are (1000,4000)m and (5000,10000)m.

[0099] 2. Calculate the wave number of each order of simple normal waves based on the measured sound velocity profile and seabed parameters. Figure 5 The typical shallow sea sound velocity profile shown in the figure has a seabed density of ρ = 1.72 g / cm 3 , sound velocity c = 1600m / s, sound attenuation coefficient α = 0.2dB / λ. Signal frequency 120Hz, the normal wave number is calculated through the normal wave model. After mode screening, M e =6, the wave numbers of the first 6 normal waves are Figure 6 shown.

[0100] 3. Perform direction finding based on the subspace intersection method and obtain the direction finding result θ at each node is (In this example, the node number i = 1, 2, the sound source label s = 1, 2). The azimuth estimation results of the two horizontal array nodes are as follows: Figure 7 As shown in the figure, the step size of the angle scan is 0.025°. The azimuths of the two sound sources measured by node I are 64.05° and 76.325° respectively, and the azimuths of the two sound sources measured by node II are 68.375° and 89.375° respectively.

[0101] 4. Substitute the azimuth estimation results and the position coordinates of the dual horizontal array nodes to solve the positions of the two sound sources: (1064.1, 5178.3) m and (4130.7, 10050.6) m. Figure 8 500 positioning results are given.

[0102] 5. Positioning accuracy analysis. Positioning accuracy is measured by the root mean square error, such as Fig. 9 The average positioning root mean square error of sound source I is 100.1m, and the average positioning root mean square error of sound source II is 448.9m. The simulation results show that the method of the present invention has good target positioning performance.

[0103] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A dual seafloor horizontal array joint target positioning method based on subspace intersection, characterized in that: include: Two seabed horizontal arrays are used to synchronously collect signals from underwater sound sources and build a signal reception model; A two-dimensional rectangular coordinate system is established based on the spatial positions of the two seafloor horizontal arrays; In the sea area where the two seabed horizontal arrays are located, the acoustic environment parameters are measured; Based on modal theory, the acoustic environment parameters are substituted into the simple normal wave model to calculate the horizontal wave number of each order of simple normal waves in the sound field; each order of simple normal waves is obtained based on the decomposition of the signal receiving model; Based on the horizontal wavenumbers of each order of simple normal waves, the effective modes in each order mode corresponding to the horizontal wavenumber are screened out; Based on the signal receiving model, the covariance matrix of the horizontal array output signal is constructed; the signal subspace is constructed by performing eigenvalue decomposition on the covariance matrix; based on the horizontal wave number of each order effective mode, the modal subspace is constructed; The modal subspace is combined with the signal subspace and orthogonal triangular decomposition is performed to obtain the estimation results of the azimuth of the sound source for two seabed horizontal arrays; According to the azimuth estimation results of the sound source by two seabed horizontal arrays, the position of the sound source is estimated based on the established two-dimensional rectangular coordinate system.

2. The dual seafloor horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The method of synchronously collecting signals emitted by underwater sound sources using two seabed horizontal arrays to construct a signal receiving model includes: For an N-element seafloor horizontal array with an element spacing of d, the receiving depth is z r , the horizontal distance between the nth array element and the sound source is r n (n=1,2,...,N); there are S sound sources in the space at the same time, the signal angular frequency is ω, and the signal received by the nth element of the horizontal array is: In the formula, p s (ω,r n ,z r ) represents the sound pressure value of the sth sound source signal received by the horizontal array. The magnitude of the sound pressure value is related to the signal angular frequency ω and the horizontal distance r from the sound source. n , receiving depth z r There is a functional relationship; σ(ω) represents Gaussian white noise; at the lth snapshot, the received signal vector on the horizontal array is expressed as: x l (ω)=[x1(ω),x2(ω),...,x N (ω)] T .

3. The dual seabed horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The two-dimensional rectangular coordinate system is established based on the spatial positions of the two seabed horizontal arrays, including: The line connecting the midpoints of the two seabed horizontal arrays is determined as the x-axis, and the midpoint of any one of the seabed horizontal arrays is used as the coordinate origin, and the x-axis is rotated 90° horizontally as the y-axis to construct a two-dimensional rectangular coordinate system; thus, the coordinates of the two seabed horizontal arrays are (x1, y1) and (x2, y2), respectively.

4. The dual seabed horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: In the sea area where the two seabed horizontal arrays are located, the acoustic environment parameters are measured as inputs to the simple normal wave model. These parameters include: The measuring device is arranged near the seabed horizontal array, and the sound velocity profile is measured on-site using a temperature chain, CTD or XBT probe device; the acoustic characteristics of the seabed sediments are acquired by seabed sampling, in-situ measurement, and inversion of seabed geoacoustic parameters to obtain the sound velocity, density and acoustic attenuation coefficient of the seabed sediments.

5. The dual seabed horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The method of screening out effective modes in modes of each order corresponding to the horizontal wavenumbers based on the horizontal wavenumbers of each order of simple normal waves includes: According to the sound velocity profile in the water body and the seabed sound velocity c s , select the reflection mode and the inversion mode as the effective modes; among them, the horizontal wave number k of the reflection mode m Need to satisfy ωc s <k m <ωc max , the horizontal wave number k of the inversion mode m Need to satisfy ωc max <k m <ωc min , c max and c min Respectively represent the maximum and minimum values ​​of the sound speed in water; the selected effective modal order is expressed as: m = 1, 2, ..., M e , M e is the maximum order of the effective modes screened out.

6. The dual seabed horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The covariance matrix of the horizontal array output signal is constructed based on the signal receiving model; The signal subspace is constructed by performing eigenvalue decomposition on the covariance matrix; Based on the horizontal wavenumbers of each effective mode, the modal subspace is constructed, including: Based on the received signal vector x of the lth snapshot l (ω), then under L snapshots, the covariance matrix of the horizontal array output signal is obtained as: In the formula, the superscript H represents the conjugate transpose; by the covariance matrix The eigenvalue decomposition can be written as follows: in, It means arranging the eigenvalues ​​from large to small, and the diagonal matrix composed of the first S large eigenvalues, represents the signal subspace composed of the eigenvectors corresponding to the first S largest eigenvalues; represents the diagonal matrix composed of the remaining NS small eigenvalues, Represents the noise subspace composed of eigenvectors corresponding to NS small eigenvalues; Based on the horizontal wave number k of each effective mode m (m=1,2,...,M e ), the modal subspace corresponding to the search angle θ is defined as: Among them, span{·} represents the spanned space, i is the imaginary unit and e is the base of natural logarithms.

7. The dual seafloor horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The method combines the modal subspace with the signal subspace and performs orthogonal triangular decomposition to solve the estimation result of the azimuth of the sound source by two seabed horizontal arrays, including: Combining the modal subspace with the signal subspace, we can obtain an N×(M e +S)-order matrix: After QR decomposition, we get: in, is the orthogonal matrix obtained by orthogonal decomposition, M e +S)×(M e +S)-order upper triangular matrix, whose diagonal elements for Singular values ​​of ; then the function: The peak value corresponds to the estimated azimuth of the sound source.

8. The dual seafloor horizontal array joint target positioning method based on subspace intersection according to claim 1 is characterized in that: The method of estimating the position of the sound source based on the two-dimensional rectangular coordinate system established according to the sound source azimuth estimation results of the two seabed horizontal arrays includes: The estimated results of the sound source azimuths corresponding to the two seafloor horizontal arrays are: The angle between the end-fire direction of the two seabed horizontal arrays and the positive direction of the x-axis of the two-dimensional rectangular coordinate system is Then for the sound source located at (x, y), the observation equation is: Thus, the estimated sound source position It can be obtained by solving the following system of equations:

9. A sound source localization device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, it implements the dual seabed horizontal array joint target positioning method based on subspace intersection according to any one of claims 1-8.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the dual seabed horizontal array joint target positioning method based on subspace intersection according to any one of claims 1 to 8 is implemented.

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