A small-scale vector hydrophone array beamforming method based on graph theory

Abstract

The present invention provides a small-scale vector hydrophone array beamforming method based on graph theory. The present invention includes constructing a small-scale vector hydrophone array model; constructing a spatial vector noise field model; mapping the small-scale vector hydrophone array to a graph theory space; reconstructing the small-scale vector hydrophone array graph theory model based on the graph theory mapping; and using a joint diagonalization method to process and solve the optimal weight vector of the beamformer. The present invention constructs a high-order subgraph by selecting vertices and edges of different orders, and uses this as the mapping of the high-order differential beamformer in the graph theory space. By optimizing and solving the subgraph, a class of beamformer weights can be obtained; the present invention achieves super-directivity in beamforming while taking into account the robustness of the beamformer; it can achieve a breakthrough in the directivity and white noise gain of the small-scale vector array beamforming, obtain a robust high-gain beam pattern, and improve the small-scale vector array's underwater target detection performance.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater signal processing, in particular to a small-scale vector hydrophone array beamforming method based on graph theory. Background Art

[0002] In the field of underwater target detection, vector hydrophones can measure the sound pressure and three-axis velocity information of water particles synchronously and concurrently. Compared with traditional scalar hydrophones, vector hydrophones have smaller geometric dimensions and greater information acquisition capabilities. The resolution capability of conventional arrays is constrained by the Rayleigh limit, and the spatial size of the array determines the resolution. However, due to the limitations of actual application scenarios, the payload size of underwater platforms needs to be miniaturized, which poses a challenge to the low-frequency detection of underwater acoustic targets. Since the directivity of vector hydrophone arrays does not change with frequency, they still have good direction-finding capabilities at low frequencies under the conditions of the minimum array aperture.

[0003] Existing small-scale vector hydrophone beamformers rarely consider noise coherence between elements and channels in the vector hydrophone array when modeling, which is inconsistent with reality. When considering vector hydrophone noise coherence, the beamformer's white noise gain and directivity are difficult to guarantee. Existing technologies require maximum robustness or super-directivity, but this is inconsistent with actual operating environments. Therefore, a method is needed that considers small-scale vector array noise coherence while balancing beamformer robustness and directivity. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a small-scale vector hydrophone array beamforming method based on graph theory. The present invention can achieve breakthroughs in the directivity and white noise gain of small-scale vector array beamforming, obtain a robust high-gain beam pattern, and improve the detection performance of small-scale vector arrays for underwater targets.

[0005] The technical solution of the present invention is: a small-scale vector hydrophone array beamforming method based on graph theory, comprising the following steps:

[0006] S1), constructing a small-scale vector hydrophone array model;

[0007] S2), constructing a spatial vector noise field model;

[0008] S3), mapping the small-scale vector hydrophone array to a graph theory space; reconstructing a graph theory model of the small-scale vector hydrophone array based on the graph theory mapping;

[0009] S4) Use the joint diagonalization method to solve the optimal weight vector of the beamformer.

[0010] Preferably, in step S1), the small-scale vector hydrophone array model is expressed as:

[0011]

[0012] Where Y is the signal received by the vector hydrophone array, A is the array current of the vector hydrophone array,

[0013] V represents the two-dimensional spatial directivity of a single hydrophone array element, V = [1, cosθ, sinθ] T ; N is the receiving noise of the hydrophone array, j is the imaginary unit, f is the signal frequency, τ i is the time delay of the ith hydrophone relative to the reference point, θ is the beamforming alignment angle, X is the target signal received by the hydrophone array, and T is the offset.

[0014] Preferably, in step S2), if the three velocity components of the vector hydrophone are distributed along the three axes of the rectangular coordinate system, then the normalized noise spectrum matrix of the vector hydrophone at any two points in the three-dimensional isotropic uniform noise field space is:

[0015]

[0016] Among them, the original representations in the matrix are:

[0017]

[0018] Where, d mm′ is the distance between the mth and m′th array elements, subscript and Corresponding to one of the vibration velocities x, y and z respectively and the two remain different, j v (·) is the vth order spherical Bessel function, are the two vectors of hydrophone spacing vector and the normalized noise spectrum matrix The angle between the axes; k is the wave number.

[0019] Preferably, in step S3), mapping the small-scale vector hydrophone array to a graph theory space means considering the vector hydrophone array elements as vertices of an undirected graph, representing the spatial linear difference equations between the array elements with the edges of the undirected graph, and re-deriving the beamforming performance evaluation indicators: beam pattern, white noise gain, and directivity factor in the graph theory space.

[0020] Preferably, in step S3), an undirected graph G = (Ve, E) is defined, where Ve = {ve1, ve2, ..., ve M} is a set of M vertices, E is the edge of the undirected graph, E is a subset of V containing two elements, for each subset {vi ,v j}, there is at most one edge; use the symbol v i ~v j Represents v i and v j Two vertices are adjacent; for a set of Q edges, E = {e1, e2, ..., e Q}; therefore,

[0021] As a preference, in step S3), a first-order adjacency matrix B is formed by graph theory. (1) , and transform it with the unit matrix C, and obtain the first-order differential beamforming signal, and then obtain the beam B (h (1) ), white noise gain W(h (1) ), and directivity factor D(h (1) );

[0022]

[0023] Where P is the transformed adjacency matrix, A is the array current of the vector hydrophone array; V represents the two-dimensional spatial directivity of a single hydrophone array element; h (1) is the first-order differential beamforming weight vector, B (1) is the first-order adjacency matrix, C is the identity matrix, and H represents the conjugate transpose.

[0024] Preferably, in step S3), the maximum white noise gain weight and the maximum directivity factor weight of the first-order differential beamforming are obtained by maximizing the white noise gain and the directivity factor, that is:

[0025]

[0026] Where h (1),MWNG The maximum white noise gain weight of the first-order difference beamforming, h (1),MDF is the maximum directivity factor weight of the first-order differential beamforming, θ s is the target azimuth, Γ d is the normalized noise spectrum matrix.

[0027] Preferably, in step S4), the two Hermitian matrices are solved by joint diagonalization method. and The new beamforming and new white noise gain are obtained, and the weight vector of the optimal beamformer is obtained under the constraints, as follows:

[0028]

[0029] Among them, T (1) and Λ(1) They are The eigenvectors and eigenvalues ​​of I M-1 It is an M-1 order unit matrix;

[0030] Then we calculate:

[0031]

[0032] Among them, t (1),1 T (1) The first eigenvector of ;

[0033] is the only non-empty eigenvalue; then we get:

[0034]

[0035] Define the beamformer weight vector h (1),1:P for:

[0036] h (1),1:P =T (1),1:P α;

[0037] Where T (1),1:P =[t (1),1 ,t (1),2 ,...,t (1),P ] is T (1) The 1st to Pth eigenvectors of , α=[α1 α2 ...α P ] T ≠0 is the weight vector coefficient, and 1≤P≤M-1;

[0038] Therefore, the new beamforming is:

[0039]

[0040] In order to satisfy the distortion-free response, Therefore, the new white noise gain is expressed as:

[0041]

[0042] The following constraints are imposed on the new white noise gain:

[0043]

[0044] The optimal weight vector of the beamformer is obtained as:

[0045]

[0046] in,

[0047] When P=1, it is the maximum directivity factor weight vector of the first-order difference of the five-element cross array, and when P=M-1, it is the maximum white noise gain weight vector of the first-order difference of the five-element cross array.

[0048] As a preferred method, in step S3), the transformed adjacency matrix is ​​multiplied by P with the vector hydrophone array receiving signal Y to obtain y (1) :

[0049] y (1) =P T Y=[p0-p1,u0-u1,v0-v1,...,p3-p4,u3-u4,v3-v4] T ;

[0050] Therefore, for the new received signal:

[0051]

[0052] Therefore, the first-order difference beamforming signal is:

[0053]

[0054] Where u0, u1, u3, and u4 are the x-axis velocity signals of the four vector hydrophones, p0, p1, p3, and p4 are the sound pressure signals of the four vector hydrophones, v0, v1, v3, and v4 are the y-axis velocity signals of the four vector hydrophones, and X is the velocity signal of the four vector hydrophones. (1) 、N (1) are the source signal matrix and the noise matrix respectively, is the beamforming weight vector.

[0055] As a preference, in step S3), the first-order adjacency matrix B formed by graph theory (1) Expressed as:

[0056]

[0057] Preferably, in step S3), the converted adjacency matrix P is expressed as:

[0058]

[0059] The beneficial effects of the present invention are:

[0060] 1. The present invention maps a small-scale vector hydrophone array into a graph-theoretic space and uses a joint diagonalization process to solve the optimal weight vector of the beamformer, thereby achieving super-directivity in beamforming while also ensuring the robustness of the beamformer.

[0061] 2. The present invention constructs a high-order subgraph by selecting vertices and edges of different orders. This subgraph serves as the mapping of a high-order differential beamformer in graph theory space. A class of beamformer weights is obtained by optimizing the subgraph. This achieves both super-directional beamforming and robustness.

[0062] 3. The present invention can break through the directivity and white noise gain of small-scale vector array beamforming, obtain a robust high-gain beam pattern, and improve the detection performance of small-scale vector arrays for underwater targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of the process of the present invention;

[0064] Figure 2 Schematic diagram of a five-element cross-vector hydrophone array in an embodiment of the present invention;

[0065] Figure 3 2. The beam pattern of a five-element cross array at 200 Hz and 0.5 m element spacing in an embodiment of the present invention, where (a) CBF, (b) MWNG first-order difference, and (c) MDF first-order difference. DETAILED DESCRIPTION

[0066] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0067] like Figure 1 As shown, this embodiment provides a small-scale vector hydrophone array beamforming method based on graph theory, including the following steps:

[0068] S1), constructing a small-scale vector hydrophone array model;

[0069] The small-scale vector hydrophone array model constructed in this embodiment is expressed as:

[0070]

[0071] Where Y is the signal received by the vector hydrophone array, A is the array current of the vector hydrophone array,

[0072] V represents the two-dimensional spatial directivity of a single hydrophone array element, V = [1, cosθ, sinθ] T ; N is the receiving noise of the hydrophone array, j is the imaginary unit, f is the signal frequency, τ i is the time delay of the ith hydrophone relative to the reference point, θ is the beamforming alignment angle, X is the target signal received by the hydrophone array, and T is the offset.

[0073] S2), constructing a spatial vector noise field model;

[0074] In this embodiment, if the three vibration velocity components of the vector hydrophone are distributed along the three axes of the rectangular coordinate system, then the normalized noise spectrum matrix of the vector hydrophone at any two points in the three-dimensional isotropic uniform noise field space is:

[0075]

[0076] Among them, the original representations in the matrix are:

[0077]

[0078] Where, d mm′ is the distance between the mth and m′th array elements, subscript and Corresponding to one of the vibration velocities x, y and z respectively and the two remain different, j v (·) is the vth order spherical Bessel function, are the two vectors of hydrophone spacing vector and the normalized noise spectrum matrix The angle between the axes; k is the wave number.

[0079] S3), mapping the small-scale vector hydrophone array to a graph theory space; reconstructing a graph theory model of the small-scale vector hydrophone array based on the graph theory mapping;

[0080] In this embodiment, mapping the small-scale vector hydrophone array to the graph space means considering the vector hydrophone array elements as vertices of an undirected graph, expressing the spatial linear difference equations between the elements as edges of the undirected graph, and re-deriving the beamforming performance evaluation indicators: beam pattern, white noise gain, and directivity factor in the graph space. In this embodiment, an undirected graph G = (Ve, E) is defined, where Ve = {ve1, ve2, ..., ve M} is a set of M vertices, E is the edge of the undirected graph, E is a subset of V containing two elements, for each subset {v i ,v j}, there is at most one edge; use the symbol v i ~v j Represents v i and v j Two vertices are adjacent; for a set of Q edges, E = {e1, e2, ..., e Q}; therefore,

[0081] S4) Use the joint diagonalization method to solve the optimal weight vector of the beamformer.

[0082] As a preferred embodiment of the present invention, in step S3), a five-element vector hydrophone is used in the present embodiment, see Figure 2As shown. The first-order adjacency matrix B is formed through graph theory (1) , and transform it with the unit matrix C, and obtain the first-order differential beamforming signal, and then obtain the beam B (h (1) ), white noise gain W(h (1) ), and directivity factor D(h (1) );

[0083]

[0084]

[0085] Where P is the transformed adjacency matrix, A is the array current of the vector hydrophone array; V represents the two-dimensional spatial directivity of a single hydrophone array element; B (1) is the first-order adjacency matrix, C is the identity matrix, h (1) is the first-order differential beamforming weight vector, and H represents the conjugate transpose.

[0086] As a preferred embodiment of this invention, in step S3), by maximizing the white noise gain and the directivity factor, the maximum white noise gain weight and the maximum directivity factor weight of the first-order differential beamforming are obtained, that is:

[0087]

[0088] Where h (1),MWNG The maximum white noise gain weight of the first-order difference beamforming, h (1),MDF is the maximum directivity factor weight of the first-order differential beamforming, θ s is the target azimuth, Γ d is the normalized noise spectrum matrix.

[0089] As a preferred embodiment of the present invention, in step S4), the two Hermitian matrices are solved by using the joint diagonalization method. and The new beamforming and new white noise gain are obtained, and the weight vector of the optimal beamformer is obtained under the constraints, as follows:

[0090]

[0091] Among them, T (1) and Λ (1) They are The eigenvectors and eigenvalues ​​of I M-1 It is an M-1 order unit matrix;

[0092] Then we calculate:

[0093]

[0094] Among them, t (1),1 T (1) The first eigenvector of ;

[0095] is the only non-empty eigenvalue; then we get:

[0096]

[0097] Define the beamformer weight vector h (1),1:P for:

[0098] h (1),1:P =T (1),1:P α;

[0099] Among them, T (1),1:P =[t (1),1 ,t (1),2 ,...,t (1),P ] is T (1) The 1st to Pth eigenvectors of , α=[α1 α2... α P ] T ≠0 is the weight vector coefficient, and 1≤P≤M-1;

[0100] Therefore, the new beamforming Z (1) for:

[0101]

[0102] In order to satisfy the distortion-free response, Therefore, the new white noise gain W(h (1),1:P ) is expressed as:

[0103]

[0104] The following constraints are imposed on the new white noise gain:

[0105]

[0106] The optimal weight vector of the beamformer is obtained as:

[0107]

[0108] in,

[0109] When P=1, it is the maximum directivity factor weight vector of the first-order difference of the five-element cross array, and when P=M-1, it is the maximum white noise gain weight vector of the first-order difference of the five-element cross array.

[0110] As a preferred method, in step S3), the transformed adjacency matrix is ​​multiplied by P with the vector hydrophone array receiving signal Y to obtain y(1) :

[0111] y (1) =P T Y=[p0-p1,u0-u1,v0-v1,...,p3-p4,u3-u4,v3-v4] T ;

[0112] Therefore, for the new received signal:

[0113]

[0114] Therefore, the first-order difference beamforming signal is:

[0115]

[0116] Where u0, u1, u3, and u4 are the x-axis velocity signals of the four vector hydrophones, p0, p1, p3, and p4 are the sound pressure signals of the four vector hydrophones, v0, v1, v3, and v4 are the y-axis velocity signals of the four vector hydrophones, and X is the velocity signal of the four vector hydrophones. (1) 、N (1) are the source signal matrix and the noise matrix respectively, is the beamforming weight vector.

[0117] As a preference, in step S3), the first-order adjacency matrix B formed by graph theory (1) Expressed as:

[0118]

[0119] Preferably, in step S3), the converted adjacency matrix P is expressed as:

[0120]

[0121] Figure 3 This example shows the beam pattern of a five-element cross array at 200 Hz and 0.5 m element spacing, including (a) CBF, (b) MWNG first-order difference, and (c) MDF first-order difference. The figure shows that by using the graph-theory-based small-scale vector hydrophone array beamforming method proposed in this invention, a set of weights between the maximum white noise gain and the maximum directivity factor can be formed, achieving both super-directivity and robustness for the small-scale vector hydrophone array.

[0122] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A small-scale vector hydrophone array beamforming method based on graph theory, characterized in that: The following steps are involved: S1), constructing a small-scale vector hydrophone array model; S2), constructing a spatial vector noise field model; S3), mapping the small-scale vector hydrophone array to a graph theory space; reconstructing a graph theory model of the small-scale vector hydrophone array based on the graph theory mapping; Mapping a small-scale vector hydrophone array to a graph space involves treating the vector hydrophone array elements as vertices of an undirected graph, representing the spatial linear difference equations between the elements as edges of the undirected graph, and re-deriving the beamforming performance evaluation indicators: beam pattern, white noise gain, and directivity factor in the graph space. Form the first-order adjacency matrix B through graph theory (1) , and transform it with the unit matrix C, and obtain the first-order differential beamforming signal, and then obtain the beam B (h (1) ), white noise gain W(h (1) ), and directivity factor D(h (1) ); Where R is the transformed adjacency matrix, A is the array manifold of the vector hydrophone array; V represents the two-dimensional spatial directivity of a single hydrophone array element; h (1) is the first-order differential beamforming weight vector, B (1) is the first-order adjacency matrix, C is the identity matrix, H represents the conjugate transpose; Γ d Normalized noise spectrum matrix of the vector hydrophone; S4) Use the joint diagonalization method to solve the optimal weight vector of the beamformer.

2. The graph theory-based small-scale vector hydrophone array beamforming method according to claim 1, characterized in that: In step S1), the small-scale vector hydrophone array model is expressed as: Where Y is the signal received by the vector hydrophone array, A is the array manifold of the vector hydrophone array, V represents the two-dimensional spatial directivity of a single hydrophone array element, V = [1, cosθ, sinθ] T ; N is the receiving noise of the hydrophone array, j is the imaginary unit, f is the signal frequency, τ i is the time delay of the ith hydrophone relative to the reference point, θ is the beamforming alignment angle, X is the target signal received by the hydrophone array, and T is the offset.

3. The graph-theory-based small-scale vector hydrophone array beamforming method according to claim 1, characterized in that: In step S2), if the three vibration velocity components of the vector hydrophone are distributed along the three axes of the rectangular coordinate system, then the normalized noise spectrum matrix of the vector hydrophone at any two points in the three-dimensional isotropic uniform noise field space is: Among them, the original representations in the matrix are: ρ p =j0(kd mm′ ) Where, d mm′ is the distance between the mth and m′th array elements, subscript and Corresponding to one of the vibration velocities x, y and z respectively and the two remain different, j v (·) is the vth order spherical Bessel function, are the two vectors of hydrophone spacing vector and the normalized noise spectrum matrix The angle between the axes; k is the wave number.

4. The graph-theory-based small-scale vector hydrophone array beamforming method according to claim 1, characterized in that: In step S3), define an undirected graph G = (Ve, E), where Ve = {ve1,ve2,…,ve M } is a set of M vertices, E is the edge of the undirected graph, E is a subset of Ve containing two elements, for each subset {ve i ,ve j }, there is at most one edge; symbol ve i ~ve j Represents ve i and ve j Two vertices are adjacent; for a set of Q edges, E = {e1, e2, ..., e Q }; therefore, 5. The graph theory-based small-scale vector hydrophone array beamforming method according to claim 1, characterized in that: In step S3), the maximum white noise gain weight and the maximum directivity factor weight of the first-order differential beamforming are obtained by maximizing the white noise gain and the directivity factor, that is: Where h (1),MWNG is the maximum white noise gain weight of the first-order difference beamforming, h (1),MDF is the maximum directivity factor weight of the first-order differential beamforming, θ s is the target azimuth, Γ d is the normalized noise spectrum matrix.

6. The graph-theory-based small-scale vector hydrophone array beamforming method according to claim 5, characterized in that: In step S4), the two Hermitian matrices are solved by joint diagonalization method. and The new beamforming and new white noise gain are obtained, and the weight vector of the optimal beamformer is obtained under the constraints, as follows: Among them, T (1) and Λ (1) They are The eigenvectors and eigenvalues ​​of I M-1 is the M-1 order unit matrix, where M is the number of vertices; Then we calculate: Among them, t (1),1 T (1) The first eigenvector of ; is the only non-empty eigenvalue; then we get: Define the beamformer weight vector h (1),1:P for: h (1),1:P =T (1),1:P a; Among them, T (1),1:P =[t (1),1 ,t (1),2 ,...,t (1),P ] is T (1) The 1st to Pth eigenvectors of P ] T ≠0 is the weight vector coefficient, and 1≤P≤M-1; Therefore, the new beamforming is: Where V represents the two-dimensional spatial directivity of a single hydrophone array element, V = [1, cosθ, sinθ] T ; N is the noise received by the hydrophone array, X is the target signal received by the hydrophone array; y (1) For new received signals; In order to satisfy the distortion-free response, Therefore, the new white noise gain is expressed as: The following constraints are imposed on the new white noise gain: The optimal weight vector of the beamformer is obtained as: in, When P=1, it is the maximum directivity factor weight vector of the first-order difference of the five-element cross array, and when P=M-1, it is the maximum white noise gain weight vector of the first-order difference of the five-element cross array.

7. The graph theory-based small-scale vector hydrophone array beamforming method according to claim 6, characterized in that: In step S3), the transformed adjacency matrix R is multiplied by the vector hydrophone array received signal Y to obtain y (1) : y (1) =R T Y=[r0-r1,u0-u1,v0-v1,...,r3-r4,u3-u4,v3-v4] T ; Therefore, for the new received signal y (1) have: Therefore, the first-order difference beamforming signal is: Where u0, u1, u3, and u4 are the x-axis velocity signals of the four vector hydrophones, r0, r1, r3, and r4 are the sound pressure signals of the four vector hydrophones, v0, v1, v3, and v4 are the y-axis velocity signals of the four vector hydrophones, and x is the velocity signal of the four vector hydrophones. (1) 、N (1) are the source signal matrix and the noise matrix respectively, is the beamforming weight vector.

8. The graph theory-based small-scale vector hydrophone array beamforming method according to claim 7, characterized in that: In step S3), the first-order adjacency matrix B is formed by graph theory (1) Expressed as: The transformed adjacency matrix R is expressed as:

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