A matching field localization method for underwater sound sources based on high-order singular value decomposition of tensor signals

Abstract

This invention discloses an underwater sound source matching field localization method based on higher-order singular value decomposition of tensor signals, comprising the following steps: Step 1, reconstructing the spatiotemporal frequency multidimensional data recorded by the vertical receiving array into tensor data; Step 2, calculating the tensor signal subspace based on higher-order singular value decomposition and singular matrix truncation. Since singular value decomposition is performed on the matrix expanded in each dimension of the tensor, noise can be further suppressed, resulting in a more accurate signal subspace and improving the accuracy of target localization; Step 3, specifying the receiving array configuration and inputting marine environmental information such as hydrological conditions, seabed topography, and seabed sediment. This invention, while accurately estimating the target location, has stronger background suppression capabilities and outperforms conventional matching field processing.

Description

Technical fields:

[0001] This invention belongs to the field of signal processing and involves theories such as marine acoustics, tensor signal processing, and underwater acoustic signal processing. Specifically, it relates to an underwater sound source matching field localization method based on high-order singular value decomposition of tensor signals. Background technology:

[0002] Tensors, as high-dimensional arrays, have a well-established theoretical foundation and have seen increasing applications in data processing in recent years. Canonical multivariate tensor decomposition (CMD), the most mature and oldest tensor decomposition method, is widely used in classification tasks in signal processing and data analysis, such as audio and speech processing, biomedicine, chemometrics, and machine learning. The core of algebraic independent component analysis (ACI) is also based on CMD of observation tensors. CMD also has numerous applications in data mining, such as using rank-1 factors to describe and capture the principal components of dynamic complex signals. In wireless communication models, signals transmitted by different users propagate along a line-of-sight and also conform to the rank-1 factor model. Similarly, for array signal processing, the received signal model is also applicable to rank-1 factor model description; therefore, CMD has gradually gained traction in array signal processing.

[0003] Matched field localization focuses on three core components: the sound source, the ocean acoustic channel, and the hydrophone receiving array. The sound source generates the sound signal in the ocean; the ocean acoustic channel refers to the propagation form of the sound source in the ocean, which, together with the sound source, constitutes a defined ocean acoustic field; the hydrophone receiving array receives the sound signal transmitted by the sound source and samples the acoustic field distribution of a given sea area. These three components are closely related and together form a whole. Given any two of these components, the third component can be determined. Matched field localization involves matching the acoustic field measured by the array with the copy fields of sound sources located at all possible positions. The matching field processing involves: sequentially placing an estimated sound source at each point of the search grid, calculating the acoustic field (copy field) of all receiving array elements, and then performing a matching correlation process between this copy field and the data of the measured field. The correlation peak reaches its maximum value when the estimated sound source and the actual sound source are at the same location.

[0004] However, due to the uncertainty and randomness of the marine environment, signal processing techniques must be used to estimate parameters. Matched field technology is widely used in seabed acoustic parameter inversion and underwater target localization. In target localization, compared with other traditional localization methods, the matched field localization algorithm can better combine the signal processing algorithms and physical characteristics of the marine acoustic channel, overcome the adverse effects of sound wave reflection, refraction, and multipath effects on the localization effect, obtain sound source depth information that other methods cannot obtain, and thus achieve target sound source localization. It has shown good localization results in various domestic and international sea trials. However, matched field processing also has certain limitations. Due to the great uncertainty of marine environmental information, and the high sensitivity of matched field processing technology to the environmental parameters used, when the environmental parameters used deviate from the actual marine parameters, the matched field processing will experience mismatch, the processing effect will drop sharply, and it may even fail to complete the matching. In addition, conventional matched field localization requires matching all possible sound source locations, so the computational load is large, especially in the deep-sea environment, where the amount of data to be calculated is even larger, and the computation time will be significantly extended. Summary of the Invention:

[0005] The technical problem to be solved by this invention is to provide an underwater sound source matching field localization method based on high-order singular value decomposition of tensor signals, so as to solve the problems of low tolerance to environmental parameters and large amount of computational data in conventional matching field localization. This method has stronger background suppression ability and better performance than conventional matching field processing.

[0006] The technical solution of this invention is to provide an underwater sound source matching field localization method based on high-order singular value decomposition of tensor signals, comprising the following steps.

[0007] Step 1: Reconstruct the spatiotemporal frequency multidimensional data recorded by the vertical receiving array into tensor data;

[0008] Step 2: Calculate the tensor signal subspace based on higher-order singular value decomposition and singular matrix truncation. Since singular value decomposition is performed on the matrix expanded in each dimension of the tensor, noise can be further suppressed, resulting in a more accurate signal subspace and improving the accuracy of target positioning.

[0009] Step 3: Clarify the configuration of the receiving array and input marine environmental information such as hydrological conditions, seabed topography, and seabed sediment;

[0010] Step 4: Calculate the broadband copy sound field using the normal mode model sound field calculation program KRAKEN, the ray model sound field calculation program BELLHOP, and the parabolic equation model sound field calculation program RAM, and construct the copy field Green's function matrix G(r,z), where r represents the assumed target distance and z represents the assumed target depth.

[0011] Step 5: Construct the ambiguity surface for matching processing based on the tensor inner product;

[0012] Step 6: Determine the distance and depth of the target by searching for the peak value of the ambiguity surface Y.

[0013] As a preferred option, in the design process of step 1, the N-element vertical receiving array receives the broadband sound field, and the array element dimension, frequency point dimension, and snapshot dimension can be tensed into a third-order tensor. Third-order tensor receives data It can be represented as a basis array Green's function tensor With the multi-shot sound source signal model S∈R K×L The sum of the 3-modulus product and the background noise tensor.

[0014]

[0015] The third-order tensor receives data. In this context, N represents the number of array elements, M represents the number of frequency points, and L represents the number of snapshots; the Green's function tensor of the array... medium element g n,m,k S represents the Green's function of the sound field at the m-th frequency point from the n-th receiver element to the k-th sound source. K×L For multi-shot sound source signal model, This is the background noise tensor.

[0016] As a preferred approach, during the design process in step 2, the third-order tensor... Performing higher-order singular value decomposition, we have

[0017]

[0018] In the formula For tensor The kernel tensor, ×1, ×2, and ×3 are the tensor products of the three dimensions, respectively.

[0019] Considering tensors Singular value decomposition of the n-modulus expansion matrix yields:

[0020]

[0021] Where U1∈R N×N For tensor The left singular matrix of the modulo 1 expansion, U2∈R M×M For tensor The left singular matrix of the 2-modulus expansion, U3∈R L×L For tensor The left singular matrix of the 3-modulus expansion.

[0022] tensor The left singular matrix of the n-modulus expansion is truncated so that the signal correlation matrix is ​​composed of the column vectors of the left singular matrix corresponding to the first M largest singular values, i.e., U 1S ∈R N×M U 2S ∈R M×M U 3S ∈R L×M The noise correlation matrix is ​​composed of the column vectors of the left singular matrix corresponding to the smaller remaining singular values, i.e., U 1N ∈ N×(N-M) U 2N ∈R M×(M-M) U 3N ∈R L×(L-M) .

[0023] Considering that the kernel tensor can be expressed as,

[0024]

[0025] The truncated kernel tensor can be represented as,

[0026]

[0027] In the formula This represents the kernel tensor of the truncated signal.

[0028] The output data of a third-order tensor can be approximated as:

[0029]

[0030] Therefore, the tensor signal subspace of the third-order tensor output data can be obtained as follows:

[0031]

[0032] As a preferred embodiment, in the design process of step 5, the ambiguity surface for target localization is as follows, given the assumed sound source distance r and depth z:

[0033]

[0034] Where ·3 represents the inner product of the tensors in the third dimension, and G(r,z) represents the normalized Green's function matrix. 1,2 Tensor With Green's function matrix G * (r,z)∈R N×M The inner product in the 1st and 2nd dimensions.

[0035] Compared with the prior art, the present invention has the following advantages after adopting the above solution:

[0036] This invention addresses the problems of low tolerance to environmental parameters and massive computational data in conventional matched field localization. By performing singular value decomposition and truncation on the matrix expanded in each dimension of the tensor, a more accurate signal subspace can be obtained, improving the ability to suppress background noise. Its performance is superior to that of conventional matched field processing. Attached image description:

[0037] Figure 1 The processing flow of the underwater sound source matching field localization method based on high-order singular value decomposition of tensor signals;

[0038] Figure 2 A schematic diagram illustrating the construction of a tensor signal model;

[0039] Figure 3 The ambiguity surface of a conventional matching field in existing technology;

[0040] Figure 4 This is the ambiguity surface of the present invention. Detailed implementation method:

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0042] like Figure 1 As shown, the underwater sound source matching field localization method based on high-order singular value decomposition of tensor signals of the present invention includes the following steps.

[0043] Step 1: Reconstruct the spatiotemporal frequency multidimensional data recorded by the vertical receiving array into tensor data;

[0044] Step 2: Calculate the tensor signal subspace based on higher-order singular value decomposition and singular matrix truncation. Since singular value decomposition is performed on the matrix expanded in each dimension of the tensor, noise can be further suppressed, resulting in a more accurate signal subspace and improving the accuracy of target positioning.

[0045] Step 3: Clarify the configuration of the receiving array and input marine environmental information such as hydrological conditions, seabed topography, and seabed sediment;

[0046] Step 4: Calculate the broadband copy sound field using the normal mode model sound field calculation program KRAKEN, the ray model sound field calculation program BELLHOP, and the parabolic equation model sound field calculation program RAM, and construct the copy field Green's function matrix G(r,z), where r represents the assumed target distance and z represents the assumed target depth.

[0047] Step 5: Construct the ambiguity surface for matching processing based on the tensor inner product;

[0048] Step 6: Determine the distance and depth of the target by searching for the peak value of the ambiguity surface Y.

[0049] Figure 2A schematic diagram of a vertical array tensor signal model is given, and the third-order tensor receives the data. It can be represented as a basis array Green's function tensor With the multi-shot sound source signal model S∈ K×L The sum of the 3-modulus product and the background noise tensor.

[0050]

[0051] The third-order tensor receives data. In this context, N represents the number of array elements, M represents the number of frequency points, and L represents the number of snapshots; the Green's function tensor of the array... medium element g n,m,k S represents the Green's function of the sound field at the m-th frequency point from the n-th receiver element to the k-th sound source. K×L For multi-shot sound source signal model, This is the background noise tensor.

[0052] As a preferred approach, during the design process in step 2, the third-order tensor... Performing higher-order singular value decomposition, we have

[0053]

[0054] In the formula For tensor The kernel tensor, ×1, ×2, and ×3 are the tensor products of the three dimensions, respectively.

[0055] Considering tensors Singular value decomposition of the n-modulus expansion matrix yields:

[0056]

[0057] Where U1∈R N×N For tensor The left singular matrix of the modulo 1 expansion, U2∈R M×M For tensor The left singular matrix of the 2-modulus expansion, U3∈R L×L For tensor The left singular matrix of the 3-modulus expansion.

[0058] tensor If the left singular matrix of the n-modulus expansion is truncated, then the signal correlation matrix consists of the column vectors of the left singular matrix corresponding to the first M largest singular values, i.e., U 1S ∈R N×M U 2S ∈R M×M U 3S ∈R L×M The noise correlation matrix is ​​composed of the column vectors of the left singular matrix corresponding to the smaller remaining singular values, i.e., U1N ∈ N×(N-M) U 2N ∈R M×(M-M) U 3N ∈R L ×(L-M) .

[0059] Considering that the kernel tensor can be expressed as,

[0060]

[0061] The truncated kernel tensor can be represented as,

[0062]

[0063] In the formula This represents the kernel tensor of the truncated signal.

[0064] The output data of a third-order tensor can be approximated as:

[0065]

[0066] Therefore, the tensor signal subspace of the third-order tensor output data can be obtained as follows:

[0067]

[0068] In this embodiment, the simulation conditions are as follows: a typical Pekeris waveguide, a sea depth of 100m, good hydrology, and a fine sandy seabed. A 32-element vertical receiving array with an element spacing of 2m and a first element depth of 20m is used. The target depth is set to 50m, the distance to the target is 5km, and the vertical receiving array receives line spectrum data at five frequencies: 100Hz, 125Hz, 150Hz, 175Hz, and 200Hz. The number of snapshots is 20, and the input signal-to-noise ratio is -5dB.

[0069] like Figure 3 and Figure 4 The ambiguity surfaces for target localization using conventional matching fields and the proposed method are presented respectively. From the ambiguity distributions of the conventional matching field and the proposed method, it can be seen that the proposed method, while accurately estimating the target position, has a stronger ability to suppress background noise and outperforms conventional matching field processing. This is because by performing singular value decomposition and truncation on the matrix expanded in each dimension of the tensor, a more accurate signal subspace can be obtained, improving the ability to suppress background noise.

[0070] The above description only illustrates preferred embodiments of the present invention and should not be construed as limiting the scope of the claims. Any equivalent structural or procedural modifications made using this specification are included within the patent protection scope of the present invention.

Claims

1. A method for underwater acoustic source matched field localization based on tensor signal higher order singular value decomposition, characterized in that: The method comprises the following steps, Step 1, reconstructing the time-space-frequency multi-dimensional data recorded by the vertical receiving array into tensor data; Step 2, calculating the tensor signal subspace based on high-order singular value decomposition and singular matrix truncation; Step 3, inputting the configuration of the receiving array and the marine environment information; Step 4, calculating the wideband copy sound field and constructing the copy field Green function matrix G(r, z), wherein r represents the assumed target distance and z represents the assumed target depth; Step 5, constructing the ambiguity surface of the matching processing according to the tensor inner product; Step 6, determining the distance and depth of the target by searching the peak value of the ambiguity surface Y; In the design process of step 5, the ambiguity surface of the target positioning for the assumed sound source distance r and depth z is as follows: where •3 denotes the inner product of the tensor in the 3rd dimension, G(r,z) denotes the normalized Green's function matrix, and 1,2 denotes the inner product of the tensor with the Green's function matrix G * (r,z) ∈ R N×M in the 1st and 2nd dimensions.

2. The underwater acoustic source matched-field localization method based on tensor signal higher-order singular value decomposition according to claim 1, characterized in that: In the design process of Step 1, the N-element vertical linear array receives the broadband sound field, which can be zoned into a three-order tensor in the dimensions of array elements, frequency points and snapshots The three-order tensor receives data It can be represented as a base matrix Green function tensor The 3-mode product of the multi-snapshot sound source signal model S ∈ R K×L and the sum of the background noise tensor, where the third-order tensor receives data where N represents the number of array elements, M represents the number of frequency points, and L represents the number of snapshots; the array Green's function tensor where the element g n,m,k represents the sound field Green's function of the nth receiving array element to the kth sound source at the mth frequency point, S ∈ R K×L is a multi-snapshot sound source signal model, is a background noise tensor.

3. The method of claim 1, wherein: In the design process of Step 2, the third-order tensor is subjected to high-order singular value decomposition, In the formula For tensor The kernel tensor, ×1, ×2, and ×3 are the tensor products of the three dimensions, respectively; and singular value decomposition of the n-mode unfolding matrix of the tensor Tn= UΛVH Where U1∈R N×N For tensor The left singular matrix of the modulo 1 expansion, U2∈R M×M For tensor The left singular matrix of the 2-modulus expansion, U3∈R L×L For tensor The left singular matrix of the 3-mode expansion; and, to the left-singular matrix of the n-mode unfolding of the tensor is truncated so that the signal correlation matrix is composed of column vectors of the left-singular matrix corresponding to the first M largest singular values, i.e. U 1S ∈R N×M , U 2S ∈R M×M , U 3S ∈R L×M and the noise correlation matrix is composed of column vectors of the left-singular matrix corresponding to the remaining smaller singular values, i.e. U 1N ∈ N×(N-M) , U 2N ∈R M×(M-M) , U 3N ∈R L×(L-M) ; Meanwhile, the kernel tensor is represented as The truncated kernel tensor is represented as In the formula denotes the nuclear tensor of the truncated signal; The third-order tensor output data is approximately expressed as: Therefore, the tensor signal subspace of the third-order tensor output data is 4. The method of claim 1, wherein: In step 3, the marine environment information includes hydrological conditions, seabed topography and seabed bottom.

5. The method of claim 1, wherein: In step 4, the calculation of the wideband copy sound field can be realized by the normal mode sound field calculation program KRAKEN, the ray model sound field calculation program BELLHOP and the parabolic equation model sound field calculation program RAM.

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