A tensor enhanced bearing estimation method suitable for high order acoustic field sensor array

Abstract

This application belongs to the field of underwater acoustic array signal processing technology. This application provides a tensor-enhanced azimuth estimation method suitable for high-order acoustic field sensor arrays. The embodiments of this disclosure first construct a received tensor from the received data of the high-order acoustic field sensor array; then, multilinear low-rank modeling is performed on the received tensor, and the optimal first subspace factor matrix in the array dimension and the optimal second subspace factor matrix in the channel dimension are extracted using the HOOI method; next, the received tensor and the angle domain dictionary are synchronously projected into a low-dimensional tensor quantum space; finally, the sparse power spectrum in the angle domain is estimated using a multi-shot sparse Bayesian learning model, thereby obtaining the target azimuth. This method can suppress noise components in each dimension while preserving multidimensional coupling relationships, reducing the data dimensionality of subsequent sparse processing, reducing the influence of dictionary correlation and noise, and obtaining a sharper azimuth spectrum and higher resolution under conditions of low signal-to-noise ratio, low snapshot, and adjacent targets.

Description

Technical Field

[0001] This disclosure relates to the field of underwater acoustic array signal processing technology, and more particularly to a tensor-enhanced azimuth estimation method suitable for high-order acoustic field sensor arrays. Background Technology

[0002] In applications such as passive sonar, underwater target detection, sound source localization, and underwater acoustic communication monitoring, target orientation estimation is one of the key technologies in array signal processing. Traditional acoustic pressure sensor arrays only acquire sound pressure information in space, resulting in limited gain. Vector sensor arrays can simultaneously acquire sound pressure and particle velocity information, improving array performance to some extent, but there is still room for improvement. High-order acoustic field sensor arrays, on the other hand, can extract more acoustic field information and have a simpler structure, thus possessing significant application value in underwater acoustic target orientation estimation.

[0003] Existing azimuth estimation methods mainly include conventional beamforming methods, minimum variance distortionless response methods, MUSIC-type subspace methods, and sparse reconstruction methods. Among them, conventional beamforming methods are simple to implement but have low angular resolution; MUSIC-type methods have high resolution but usually require accurate estimation of the number of sources, and when the signal-to-noise ratio is low or the number of snapshots is insufficient, the covariance matrix estimation error can lead to inaccurate separation of the signal subspace and the noise subspace; sparse reconstruction methods can establish sparse models in the angular domain, but when directly vectorizing the data received by high-order sound field sensor arrays, they are prone to destroying the multidimensional structural information between the array dimension, channel dimension, and time snapshot dimension.

[0004] In practical applications, received signals are often affected by adverse factors such as background noise, limited snapshots, array channel errors, and proximity of targets. Long vector signal models typically unfold the received data from high-order sound field sensor arrays with multi-channel configurations into a two-dimensional matrix, making it difficult to fully utilize the inherent multi-dimensional coupling structure of high-order sound field sensor array data. This leads to problems such as azimuth spectrum broadening, spurious peak enhancement, and decreased resolution of adjacent targets.

[0005] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0007] The purpose of this disclosure is to provide a tensor-enhanced orientation estimation method suitable for high-order acoustic field sensor arrays, thereby overcoming at least to some extent one or more problems caused by the limitations and defects of related technologies.

[0008] According to embodiments of this disclosure, a tensor-enhanced orientation estimation method suitable for high-order acoustic field sensor arrays is provided, comprising: Step S1: Acquire the received data from the high-order sound field sensor array and construct the received data as a received tensor; Step S2: Perform multilinear low-rank modeling on the received tensor to obtain the received tensor in low-rank form; Step S3: Use the HOOI method to perform low-rank decomposition on the low-rank form of the receive tensor to obtain the optimal first subspace factor matrix, the optimal second subspace factor matrix, and the optimal third subspace factor matrix. Step S4: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the received tensor onto the multilinear signal subspace to obtain the projected tensor; Step S5: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the angle domain dictionary onto the multilinear signal subspace to obtain the projection steering vector; Step S6: Construct the signal model in the projection domain of the HOOI subspace based on the projection tensor and the projection steering vector; Step S7: Based on the signal model in the HOOI subspace projection domain, construct a multi-shot sparse Bayesian learning model, use the multi-shot sparse Bayesian learning model to estimate the sparse power spectrum in the angle domain, and determine the target orientation based on the sparse power spectrum in the angle domain.

[0009] Furthermore, the high-order sound field sensor array includes Q Each high-order sound field sensor; the high-order sound field sensors are spaced apart. d A uniformly distributed linear array; each high-order sound field sensor is composed of... M A circular array consisting of several sound pressure sensors.

[0010] Furthermore, the receiving tensor is:

[0011] in, K For the number of sound sources, k For the first k One sound source, To transmit signals from a sound source, L For the number of snapshots, For joint guidance vector, This represents the outer product operation, and N represents the modal noise tensor. The low-rank form of the receive tensor is:

[0012] Where K is the core tensor, The first initial subspace factor matrix, This is the second initial subspace factor matrix. This is the third initial subspace factor matrix; For the product of the nth modulus, ; It is the first multilinear rank. It is the second multilinear rank. It is the third multilinear rank and satisfies: , , ; The number of modal channels for each high-order sound field sensor.

[0013] Furthermore, step S3 specifically includes: Define the optimization objective function:

[0014] The constraints are:

[0015] in, Describing the Frobenius norm, This indicates the conjugate transpose. It is the identity matrix; The low-rank receiving tensor is expanded using the first, second, and third modular expansions to obtain the first, second, and third modular expansion matrices, respectively. Perform singular value decomposition on the first, second, and third modular expansion matrices respectively, and take the first three terms of each modular expansion matrix. Using the left singular value vectors as initial values, we obtain the initial first modulus factor matrix, the initial second modulus factor matrix, and the initial third modulus factor matrix; where, n =1,2,3; Fixing the second and third initial subspace factor matrices, the received tensor is projected onto the channel-dimensional subspace and the snapshot-dimensional subspace. The projected received tensor undergoes a first modular expansion and singular value decomposition, and the first... The left singular vectors are used as the updated first subspace factor matrix; Using the fixed and updated first and third initial subspace factor matrices, the received tensor is projected onto the array-dimensional subspace and the snapshot-dimensional subspace. The projected received tensor undergoes a second modular expansion and singular value decomposition, and the first... The left singular vectors are used as the updated second subspace factor matrix; Using the fixed and updated first and second subspace factor matrices, the received tensor is projected onto the array-dimensional subspace and the channel-dimensional subspace. The projected received tensor undergoes a third-mode expansion and singular value decomposition, and the first-order terms are taken. The left singular vectors are used as the updated third subspace factor matrix; Based on the updated first subspace factor matrix, the updated second subspace factor matrix, and the updated third subspace factor matrix, calculate the core tensor and the low-rank reconstruction tensor. The goodness of fit is calculated based on the low-rank reconstruction tensor, and the alternating update process is repeated until the first convergence condition is met, so as to obtain the optimal first subspace factor matrix of the received tensor in the array dimension, the optimal second subspace factor matrix in the channel dimension, and the optimal third subspace factor matrix in the snapshot dimension.

[0016] Furthermore, the first convergence condition is:

[0017]

[0018] in, The goodness of fit for the (t+1)th iteration. The fit at the t-th iteration. The preset threshold, Let be the low-rank reconstruction tensor of the t-th iteration.

[0019] Furthermore, the projection tensor is:

[0020] in, The optimal first subspace factor matrix. This is the optimal second subspace factor matrix.

[0021] Furthermore, step S5 specifically includes: The angular region to be scanned is divided into G discrete angular grids, and the original joint steering vector corresponding to each angular grid is generated. Based on the first and second subspace factor matrices, the joint steering vector of each angle grid is projected to obtain the projected steering vector of each angle grid:

[0022] in, This is a conjugate operation.

[0023] Furthermore, step S6 specifically includes: The projection tensor and projection steering vector are vectorized separately. Based on the vectorized projection tensor and the vectorized projection steering vector, construct the projection subspace domain array received signal matrix and the projection subspace domain steering matrix; Based on the received signal matrix and the steering matrix of the projection subspace array, construct the signal model in the HOOI subspace projection domain:

[0024] in, For the signal matrix received by the projection subspace domain array, The guiding matrix for the projected subspace domain. For the sparse moments in the angular domain to be estimated, This is the projection domain modal noise matrix.

[0025] Furthermore, step S7 specifically includes: A shared power hyperparameter is introduced for each row of the sparse matrix in the angular domain to be estimated; Based on the signal model in the HOOI subspace projection domain and the shared power hyperparameters, a multi-shot sparse Bayesian learning model is constructed. By maximizing the marginal likelihood function of the projected received signal matrix, the power hyperparameters and projection domain noise power corresponding to each angle grid are iteratively updated. Determine whether the second convergence condition is met based on the update amount of the power hyperparameter and the noise power in the projection domain. After the iteration is completed, an angular domain sparse power spectrum is constructed based on the power hyperparameter values ​​corresponding to each angular grid.

[0026] Furthermore, the projection domain noise power is iteratively updated, including: Based on the power hyperparameters of the current iteration and the noise power in the projected domain, calculate the posterior covariance matrix and posterior mean matrix of the sparse coefficient matrix. Update the projection domain noise power based on the posterior mean matrix, posterior covariance matrix, and projected received signal matrix.

[0027] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: In the embodiments of this disclosure, the above method first constructs a receiving tensor from the received data of the high-order sound field sensor array; then, it performs multilinear low-rank modeling on the receiving tensor and uses the HOOI method to extract the optimal first subspace factor matrix in the array dimension and the optimal second subspace factor matrix in the channel dimension; next, it synchronously projects the receiving tensor and the angle domain dictionary into a low-dimensional tensor quantum space; finally, it estimates the sparse power spectrum in the angle domain using a multi-shot sparse Bayesian learning model to obtain the target orientation. On the other hand, it can suppress noise components in each dimension while preserving multidimensional coupling relationships, reduce the data dimension of subsequent sparse processing, reduce the influence of dictionary correlation and noise, and obtain a sharper orientation spectrum and higher resolution under conditions of low signal-to-noise ratio, low snapshot, and adjacent targets. Attached Figure Description

[0028] 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. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0029] Figure 1 The diagram illustrates the steps of a tensor-enhanced orientation estimation method applicable to a high-order acoustic field sensor array according to an exemplary embodiment of the present disclosure. Figure 2 A schematic diagram of a high-order acoustic field sensor array in an exemplary embodiment of this disclosure is shown; Figure 3 This illustration shows the azimuth spectrum results of a high-order acoustic field sensor array under different methods in an exemplary embodiment of this disclosure; Figure 4 The resolution probabilities of different methods in exemplary embodiments of this disclosure are shown; Figure 5 This illustrates the trend of RMSE as a function of signal-to-noise ratio in an exemplary embodiment of this disclosure. Detailed Implementation

[0030] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0031] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0032] This example implementation provides a tensor-enhanced azimuth estimation method suitable for high-order acoustic field sensor arrays. (Reference) Figure 1 As shown, the tensor-enhanced orientation estimation method applicable to high-order acoustic field sensor arrays may include: Step S1: Acquire the received data from the high-order sound field sensor array and construct the received data as a received tensor; Step S2: Perform multilinear low-rank modeling on the received tensor to obtain the received tensor in low-rank form; Step S3: Use the HOOI method to perform low-rank decomposition on the low-rank form of the receive tensor to obtain the optimal first subspace factor matrix, the optimal second subspace factor matrix, and the optimal third subspace factor matrix. Step S4: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the received tensor onto the multilinear signal subspace to obtain the projected tensor; Step S5: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the angle domain dictionary onto the multilinear signal subspace to obtain the projection steering vector; Step S6: Construct the signal model in the projection domain of the HOOI subspace based on the projection tensor and the projection steering vector; Step S7: Based on the signal model in the HOOI subspace projection domain, construct a multi-shot sparse Bayesian learning model, use the multi-shot sparse Bayesian learning model to estimate the sparse power spectrum in the angle domain, and determine the target orientation based on the sparse power spectrum in the angle domain.

[0033] The tensor-enhanced azimuth estimation method applicable to high-order sound field sensor arrays described above first constructs a received tensor from the received data of the high-order sound field sensor array. Then, it performs multilinear low-rank modeling on the received tensor and uses the HOOI method to extract the optimal first subspace factor matrix in the array dimension and the optimal second subspace factor matrix in the channel dimension. Next, it synchronously projects the received tensor and the angle domain dictionary into a low-dimensional tensor quantum space. Finally, it estimates the sparse power spectrum in the angle domain using a multi-shot sparse Bayesian learning model, thereby obtaining the target azimuth. Furthermore, this method can suppress noise components in each dimension while preserving multidimensional coupling relationships, reducing the data dimensionality of subsequent sparse processing, and minimizing the impact of dictionary correlation and noise. This results in a sharper azimuth spectrum and higher resolution under conditions of low signal-to-noise ratio, low snapshots, and adjacent targets.

[0034] Below, we will refer to Figures 1 to 5 The steps of the tensor-enhanced orientation estimation method for high-order acoustic field sensor arrays described in this example embodiment will be explained in more detail.

[0035] In step S1, the received data from the high-order sound field sensor array is acquired, and the received data is constructed into a received tensor.

[0036] Specifically, the tensor signal model of the high-order sound field sensor array is established: Consider the existence of a high-order sound field sensor array, such as Figure 2 As shown, it includes a total of Q A high-order sound field sensor, the high-order sound field sensor with a spacing d The sensors are uniformly distributed in a linear array, and each high-order sound field sensor is composed of... MA small-scale circular array of uniformly distributed sound pressure sensors, with a radius of [missing information]. r The phase mode decomposition method is used to weight the sound pressure received by the high-order sound field sensor, which can extract up to [amount missing]. First-order modal signal, It is the highest order. n The spatial response of the first modal signal is: (1) in, i The imaginary unit, k For wave number, for n Bessel function of order 1, e This represents the natural constant, that is, the base of the natural logarithm. The horizontal azimuth angle is the direction of observation.

[0037] Consider the existence in space K A sound source, with incident direction as The k A far-field narrowband sound source, whose array spatial steering vector is expressed as: (2) in, , This represents the matrix transpose. The horizontal azimuth angle in equation (1) is ignored. θ The irrelevant amplitude term allows us to express the modal channel response of the high-order sound field sensor as follows: (3) in, . N c This represents the number of modal channels for each high-order sound field sensor. Then the joint steering vector of the higher-order acoustic field sensor array corresponding to this direction is: (4) Assume the signal has L A quick snapshot defines the received signal of the high-order sound field sensor array as... Therefore, we have: (5) in, Indicates the first l The first quick shot k A complex signal from a sound source. Let this represent the array's received mode noise matrix. Furthermore, the array's received signal can be represented in tensor form, i.e., the received tensor is: (6) in, , The outer product operation is represented by N, which represents the modal noise tensor. The received tensor preserves the multidimensional coupling relationship between the received data of the high-order sound field sensor array in the array space dimension, modal channel dimension, and snapshot dimension.

[0038] In step S2, the received tensor is modeled as a multilinear low-rank tensor to obtain a low-rank form of the received tensor.

[0039] Specifically, multilinear low-rank modeling is performed on the received tensor: The data received by the high-order sound field sensor array is contributed by a few target sound sources, exhibiting low-rank characteristics in the array space dimension, modal channel dimension, and snapshot dimension. Therefore, the received tensor is modeled as a Tucker multilinear low-rank form: (7) Where K is the core tensor, , and These are the first initial subspace factor matrix, the second initial subspace factor matrix, and the third initial subspace factor matrix, respectively, corresponding to the three dimensions. The first tensor represents the tensor. n Modular product. , , It is a multilinear rank and usually satisfies: , , By establishing this low-rank model, we can preserve the main sound source information as much as possible while suppressing noise components scattered across various dimensions.

[0040] In step S3, the low-rank form of the receive tensor is decomposed using the HOOI method to obtain the optimal first subspace factor matrix, the optimal second subspace factor matrix, and the optimal third subspace factor matrix.

[0041] Specifically, the higher-order orthogonal iteration (HOOI) method extracts the tensor signal subspace: The HOOI method is used to perform low-rank decomposition on the received signal tensor, and the optimization objective function is defined as follows: (8) The constraints are: (9) in, Describing the Frobenius norm, This represents the conjugate transpose. Given subspace factor matrices U1, U2, and U3, the optimal core tensor can be obtained by projecting the original tensor onto subspaces of each dimension: (10) Therefore, the key to the HOOI method lies in the alternating iterative update of the three-dimensional factor matrix, which gradually reduces the error of low-rank reconstruction. The specific HOOI process is shown below.

[0042] 1. Initialize the factor matrix using Higher-Order Singular Value Decomposition (HOSVD). The specific process is as follows: For receiving tensors Performing modular expansions of 1, 2, and 3 respectively, the resulting expansion matrices are the first modular expansion matrices. The second modular expansion matrix The third modular expansion matrix Then, singular value decomposition is performed on each modular expansion matrix. Taking the nth modular expansion as an example: (11) in, It is a left singular value matrix. It is a singular value matrix. It is a right singular value matrix.

[0043] Furthermore, take the former The left singular value vector is used as the th . n The initial value of the modulus factor matrix is: (12) This yields the initial factor matrix of HOOI. HOSVD initialization provides a good initial estimate of the low-rank subspace, which is beneficial for the subsequent convergence of HOOI alternating iterations.

[0044] 2. HOOI employs an alternating optimization approach, meaning that when updating one modulus factor matrix, other modulus factor matrices are kept constant, and then the optimal low-rank subspace matrix of the current modulus is solved. Taking updating the array-dimensional factor matrix U1 as an example, let the factor matrices at the t-th iteration be... , and The specific update process is as follows.

[0045] By fixing the channel dimension factor matrix and the snapshot dimension factor matrix (i.e., fixing the second initial subspace factor matrix and the third initial subspace factor matrix), the received tensor is projected along the second module subspace (i.e., the channel dimension subspace) and the third module space (i.e., the snapshot dimension subspace) to obtain the projected received tensor: (13) right Performing the first modulo expansion yields the first modulo expansion matrix. Furthermore, singular value decomposition is performed on the expanded matrix: (14) Take before The left singular value vectors corresponding to the maximal singular values ​​are used as the updated first modulus factor matrix, i.e.: (15) Subsequently, following the same update process as the element space dimension factor matrix, the modal channel dimension factor matrix and the snapshot dimension factor matrix are updated sequentially. After completing one round of HOOI iteration updates for each modal factor matrix, the corresponding core tensor is calculated: (16) Then we obtain the low-rank reconstruction tensor: (17) in, This represents the reconstruction result of the received signal tensor in a multilinear low-rank subspace. The low-rank reconstructed tensor can be viewed as an enhanced version of the original received signal tensor, which preserves the main signal components while reducing noise components that are inconsistent with the low-rank signal structure.

[0046] Furthermore, during the HOOI iteration process, the reconstruction fit is used as the convergence criterion, and the fit of the t-th iteration can be defined as: (18) When the change in fit between two consecutive iterations satisfies the first convergence condition: (19) The HOOI iteration is considered convergent when the above convergence criterion is met. After HOOI iterative decomposition, we obtain... , , These represent the subspace factor matrices corresponding to the array space dimension, modal channel dimension, and snapshot dimension, respectively. Since the target orientation information is mainly contained in the joint guidance structure of the array space dimension and modal channel dimension, subsequent processing primarily utilizes... and A consistent low-dimensional subspace mapping is performed on the received signal and the array steering matrix.

[0047] In steps S4 to S6, based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, the received signal tensor and angle domain dictionary are mapped to the multilinear signal subspace estimated by HOOI, respectively, to obtain the low-dimensional projection tensor and the projection steering vector corresponding to each angle grid. Further, based on the projection tensor and projection steering vector, a low-dimensional signal model in the HOOI subspace projection domain is constructed. Specifically, the signal model in the HOOI subspace projection domain is as follows: The angular region to be scanned is divided into G discrete angular grids, defined as follows: For the first g The array guidance matrix of the angular grid is: (20) To reduce the dimensionality of subsequent processing while preserving the multidimensional structure of the received signal, the original received signal tensor is mapped along the first and second modes to the multilinear signal subspace estimated by HOOI, respectively, to obtain a low-dimensional subspace representation tensor: (twenty one) This operation divides the first and second modulus dimensions of the received signal tensor by... Q and N c Compress to r 1 and r 2. Simultaneously maintain the third module dimension L This keeps the signal tensor unchanged, thereby reducing the computational complexity of subsequent operations while preserving the multidimensional structure of the signal tensor and the main signal subspace information.

[0048] For the l Each snapshot, equation (21) can be equivalently represented in the following matrix form: (twenty two) To ensure the consistency of the low-dimensional sparse representation model, the angle domain dictionary needs to undergo the same multilinear subspace mapping as the received signal. For the g The orientation matrix of the corresponding low-dimensional subspace array of the angular grid is expressed as: (twenty three) To convert the received signal in low-dimensional matrix form into a vector form suitable for sparse representation, for the ... l The low-dimensional received signal matrix corresponding to each snapshot Column vectorization is performed to obtain a low-dimensional received signal vector. Accordingly, for the first g The low-dimensional subspace array steering matrix corresponding to each angle grid Perform the same column vectorization process to obtain the low-dimensional guided vector. ,Right now: (twenty four) This vectorization operation only changes the arrangement of matrix elements, without changing their values ​​or the signal information they contain, thus enabling the low-dimensional received signal and the angle domain dictionary to adopt a unified vector sparse representation.

[0049] Therefore, the low-dimensional multi-shot sparse signal model obtained after HOOI multilinear subspace mapping and vectorization can be expressed as: (25) The low-dimensional received signal vectors corresponding to all L snapshots are arranged column-wise to form a low-dimensional received signal matrix. The low-dimensional steering vectors corresponding to each angle grid are arranged column-wise to form the HOOI low-dimensional projection domain angle dictionary. , Let be the sparse matrix of the angle-domain signal to be estimated. This represents the noise matrix after multilinear subspace mapping and vectorization, i.e., the projection domain noise matrix. Since the actual signal corresponds to only a few grid positions in the angle domain, the sparse matrix of the angle domain signal has row sparsity characteristics, with its non-zero row positions corresponding to the arrival direction of the signal to be estimated. Based on this, a Multiple-Snapshot Sparse Bayesian Learning (MSBL) model in the low-dimensional projection domain of HOOI is further constructed to achieve high-resolution orientation estimation.

[0050] In step S7, a multi-shot sparse Bayesian learning model is constructed based on the multi-shot signal model in the low-dimensional subspace of HOOI, and the sparse power spectrum in the angle domain is estimated using the multi-shot sparse Bayesian learning model. Then, the target orientation is determined based on the spectral peak position of the sparse power spectrum in the angle domain.

[0051] Specifically, a multi-shot sparse Bayesian learning model is constructed in the low-dimensional subspace of HOOI. Since the orientation of each target remains unchanged across different snapshots within the same observation time period, the signal sparse matrix s shares common non-zero row support across snapshots, thus exhibiting a row-sparse structure. The multi-shot sparse Bayesian learning model characterizes the joint sparsity of the row coefficients across all snapshots by setting a shared hyperparameter for each row of sparse coefficients corresponding to each angle grid in s.

[0052] Define the multi-fastshot sparse coefficient vector corresponding to the g-th angle grid as: And assume that the sparse coefficient vector follows a zero-mean, circularly symmetric, complex Gaussian prior distribution, i.e.: (26) in, express First identity matrix Let be the shared hyperparameters corresponding to the g-th angle grid. Further, the hyperparameter matrix is ​​defined as: (27) This represents the operation of constructing a diagonal matrix. Indicates the first g The non-negative shared hyperparameters corresponding to each angle grid are used to characterize the signal power of that angle grid across all snapshots. Hyperparameter matrix Let be the prior covariance matrix of the sparse coefficient vector in the angular domain, whose diagonal structure indicates that the sparse coefficients corresponding to different angular grids are independent under prior conditions. When When the value approaches zero, the sparsity coefficient of the entire row under the corresponding angle grid is suppressed; when When the values ​​are significantly greater than zero, the corresponding angle grid is preserved. Therefore, the estimated values ​​of each hyperparameter collectively constitute the sparse power spectrum in the angle domain.

[0053] For the l Let each snapshot be defined as its angular domain sparse coefficient vector. And assume that it follows a zero-mean, circularly symmetric complex Gaussian distribution: (28) Because all snapshots share the same hyperparameter matrix Therefore, it can be guaranteed that the sparse coefficient vectors corresponding to different snapshots have a common non-zero angular support. Assume that the projection domain modal noise vectors of different snapshots are mutually independent and follow a zero-mean circularly symmetric complex Gaussian distribution, i.e. ,in For projection domain noise power, This is the third identity matrix. Due to the column orthogonality of the HOOI factor matrix, the noise after multilinear subspace mapping retains its white noise covariance structure, provided the original noise is spatial white noise. Since the signal and noise components in the projection domain are independent, the marginal covariance matrix of the received signal is equal to the sum of the signal covariance matrix and the noise covariance matrix. Therefore, the third identity matrix can be obtained. l The received signal vector in the projection domain corresponding to each snapshot The marginal covariance matrix is: (29) in, The covariance matrix of the signal components in the projection domain. The covariance matrix represents the noise components in the projection domain.

[0054] Within the MSBL framework, the negative logarithmic marginal likelihood function of the signal received by the projected domain array is minimized iteratively. Jointly estimate the shared power hyperparameter vector and projection domain noise power ,have: (30) in, Represents the determinant of a matrix. This represents the trace operation of a matrix. This represents the logarithmic determinant term of the marginal covariance model. This represents the fitting term between the received signal in the projection domain and the edge covariance matrix model.

[0055] Therefore, in the first t In the next iteration, based on the current power hyperparameter matrix and noise power The calculated edge covariance matrix of the received signal vector in the HOOI projection domain is: (31) Angular domain sparse coefficient vector The posterior distribution is still a circularly symmetric complex Gaussian distribution, and its posterior covariance matrix is: (32) in, Let represent the posterior covariance matrix of the sparse coefficient vector in the angle domain. Its diagonal elements represent the posterior variance of the sparse coefficients corresponding to each angle grid, and its off-diagonal elements represent the posterior correlation between the sparse coefficients corresponding to different angle grids. The posterior mean matrix of the sparse coefficients in the angle domain corresponding to all snapshots can be represented as: (33) in, For the first t The posterior mean matrix of sparse coefficients in the angle domain corresponding to all snapshots obtained in the next iteration. Indicates the first l The posterior mean of the sparse coefficients corresponding to each snapshot. Furthermore, the power hyperparameters are updated based on the posterior second moment. Let... This represents the posterior mean matrix of the sparse coefficients in the angle domain obtained in the t-th iteration. The g Okay. Further, the power hyperparameter corresponding to the g-th angle grid is updated based on the posterior second moment of the sparse coefficients of that angle grid across all snapshots. Specifically, the g-th... t The power hyperparameter of the +1 iteration is derived from the first iteration. t The sum of the posterior mean power and posterior variance of the sparse coefficients obtained in the next iteration is determined as follows: (34) in, It is the posterior covariance matrix The g The diagonal element, i.e. the th elementg The posterior variance of the sparse coefficients corresponding to each angle grid.

[0056] The update formula for the projection domain noise power in the (t+1)th iteration is: (36) In the above equation, the first term in the numerator represents the residual energy between the projected domain received signal matrix and the posterior mean reconstructed matrix, and the second term represents the reconstruction error compensation term caused by the posterior uncertainty of the sparse coefficients. The relative change in the power hyperparameter vector obtained from two consecutive iterations is calculated. When the relative change is less than a preset convergence threshold, the multi-fast-shot sparse Bayesian learning iteration process is considered to have converged, and the iteration is terminated; otherwise, the next iteration begins. The specific convergence criterion is: (37) in, A preset convergence threshold is set. After the iteration is complete, the spatial orientation spectrum (i.e., the target orientation) can be given by the final power hyperparameter vector: (38) In one specific embodiment, the receiving array is a high-order sound field sensor linear array with 6 elements. The elements are spaced at half the wavelength of the center frequency, which is set to 1 kHz. Two uncorrelated far-field complex Gaussian sound sources of equal intensity exist in a two-dimensional planar space. The signal-to-noise ratio (SNR) is set to 3 dB, the snapshot number is 50, and the sound sources are located at 85° and 95° directions, respectively. First, the SNR of the incident signals from both complex Gaussian sound sources is set to 3 dB. Each high-order sound field sensor is a small-scale circular array composed of 8 sound pressure sensors with an array radius of 0.08 meters. The -3 to 3rd order modal signals are extracted and processed. , and . Figure 3 The results of the orientation spectrum of the high-order acoustic field sensor array under different methods are shown. It can be seen that the method proposed in this application has a narrower main lobe width and lower side lobes compared with the conventional MUSIC method, the HOOI-enhanced MUSIC method (HOOI-MUSIC), the HOOI-enhanced Tensor MUSIC method (HOOI-TMUSIC), and the MSBL method. This indicates that the method proposed in this application has better resolution of nearby multiple targets and superior orientation estimation performance.

[0057] Further analysis was conducted on the changes in azimuth resolution probability and root mean square error (RMSE) of different methods with signal-to-noise ratio (SNR). Figure 4 The resolution probabilities of different methods are shown; Figure 5The trend of RMSE with signal-to-noise ratio (SNR) is shown. In the simulation, the received SNR was set to vary from -15dB to 5dB, while other simulation conditions remained constant. It can be observed that the method proposed in this application has the highest resolution probability across the entire observation SNR range, and the RMSE remains at a low value, indicating that the method in this application has better nearest-neighbor multi-target resolution capability.

[0058] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0059] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0060] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A tensor-enhanced azimuth estimation method suitable for high-order acoustic field sensor arrays, characterized in that, include: Step S1: Acquire the received data from the high-order sound field sensor array and construct the received data as a received tensor; Step S2: Perform multilinear low-rank modeling on the received tensor to obtain the received tensor in low-rank form; Step S3: Use the HOOI method to perform low-rank decomposition on the low-rank form of the receive tensor to obtain the optimal first subspace factor matrix, the optimal second subspace factor matrix, and the optimal third subspace factor matrix. Step S4: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the received tensor onto the multilinear signal subspace to obtain the projected tensor; Step S5: Based on the optimal first subspace factor matrix and the optimal second subspace factor matrix, project the angle domain dictionary onto the multilinear signal subspace to obtain the projection steering vector; Step S6: Construct the signal model in the projection domain of the HOOI subspace based on the projection tensor and the projection steering vector; Step S7: Based on the signal model in the HOOI subspace projection domain, construct a multi-shot sparse Bayesian learning model, use the multi-shot sparse Bayesian learning model to estimate the sparse power spectrum in the angle domain, and determine the target orientation based on the sparse power spectrum in the angle domain.

2. The tensor-enhanced azimuth estimation method for high-order acoustic field sensor arrays according to claim 1, characterized in that, High-order sound field sensor array includes Q Each high-order sound field sensor; the high-order sound field sensors are spaced apart. d A uniformly distributed linear array; each high-order sound field sensor is composed of... M A circular array consisting of several sound pressure sensors.

3. The tensor enhancement orientation estimation method for high-order acoustic field sensor arrays according to claim 1, characterized in that, The received tensor is: in, K For the number of sound sources, k For the first k One sound source, To transmit signals from a sound source, L For the number of snapshots, For joint guidance vector, This represents the outer product operation, and N represents the modal noise tensor. The low-rank form of the receive tensor is: Where K is the core tensor, The first initial subspace factor matrix, This is the second initial subspace factor matrix. This is the third initial subspace factor matrix; For the product of the nth modulus, ; It is the first multilinear rank. It is the second multilinear rank. It is the third multilinear rank and satisfies: , , ; The number of modal channels for each high-order sound field sensor.

4. The tensor enhancement orientation estimation method for high-order acoustic field sensor arrays according to claim 3, characterized in that, Step S3 specifically includes: Define the optimization objective function: The constraints are: in, Describing the Frobenius norm, This indicates the conjugate transpose. It is the first identity matrix; The low-rank receiving tensor is expanded using the first, second, and third modular expansions to obtain the first, second, and third modular expansion matrices, respectively. Perform singular value decomposition on the first, second, and third modular expansion matrices respectively, and take the first three terms of each modular expansion matrix. Using the left singular value vectors as initial values, we obtain the initial first modulus factor matrix, the initial second modulus factor matrix, and the initial third modulus factor matrix; where, n =1,2,3; Fixing the second and third initial subspace factor matrices, the received tensor is projected onto the channel-dimensional subspace and the snapshot-dimensional subspace. The projected received tensor undergoes a first modular expansion and singular value decomposition, and the first... The left singular vectors are used as the updated first subspace factor matrix; Using the fixed and updated first and third initial subspace factor matrices, the received tensor is projected onto the array-dimensional subspace and the snapshot-dimensional subspace. The projected received tensor undergoes a second modular expansion and singular value decomposition, and the first... The left singular vectors are used as the updated second subspace factor matrix; Using the fixed and updated first and second subspace factor matrices, the received tensor is projected onto the array-dimensional subspace and the channel-dimensional subspace. The projected received tensor undergoes a third-mode expansion and singular value decomposition, and the first-order terms are taken. The left singular vectors are used as the updated third subspace factor matrix; Based on the updated first subspace factor matrix, the updated second subspace factor matrix, and the updated third subspace factor matrix, calculate the core tensor and the low-rank reconstruction tensor. The goodness of fit is calculated based on the low-rank reconstruction tensor, and the alternating update process is repeated until the first convergence condition is met, so as to obtain the optimal first subspace factor matrix of the received tensor in the array dimension, the optimal second subspace factor matrix in the channel dimension, and the optimal third subspace factor matrix in the snapshot dimension.

5. The tensor enhancement orientation estimation method for high-order acoustic field sensor arrays according to claim 4, characterized in that, The first convergence condition is: in, The goodness of fit for the (t+1)th iteration. The fit at the t-th iteration. The preset threshold, Let be the low-rank reconstruction tensor of the t-th iteration.

6. The tensor-enhanced azimuth estimation method for high-order acoustic field sensor arrays according to claim 5, characterized in that, The projection tensor is: in, The optimal first subspace factor matrix. This is the optimal second subspace factor matrix.

7. The tensor enhancement orientation estimation method for high-order acoustic field sensor arrays according to claim 6, characterized in that, Step S5 specifically includes: The angular region to be scanned is divided into G discrete angular grids, and the original joint steering vector corresponding to each angular grid is generated. Based on the first and second subspace factor matrices, the joint steering vector of each angle grid is projected to obtain the projected steering vector of each angle grid: in, This is a conjugate operation.

8. The tensor-enhanced azimuth estimation method for high-order acoustic field sensor arrays according to claim 7, characterized in that, Step S6 specifically includes: The projection tensor and projection steering vector are vectorized separately. Based on the vectorized projection tensor and the vectorized projection steering vector, construct the projection subspace domain array received signal matrix and the projection subspace domain steering matrix; Based on the received signal matrix and the steering matrix of the projection subspace array, construct the signal model in the HOOI subspace projection domain: in, For the signal matrix received by the projection subspace domain array, The guiding matrix for the projected subspace domain. Let be the sparse matrix in the angle domain to be estimated. This is the projection domain modal noise matrix.

9. The tensor enhancement orientation estimation method for high-order acoustic field sensor arrays according to claim 8, characterized in that, Step S7 specifically includes: A shared power hyperparameter is introduced for each row of the sparse matrix in the angular domain to be estimated; Based on the signal model in the HOOI subspace projection domain and the shared power hyperparameters, a multi-shot sparse Bayesian learning model is constructed. By maximizing the marginal likelihood function of the projected received signal matrix, the power hyperparameters and projection domain noise power corresponding to each angle grid are iteratively updated. Determine whether the second convergence condition is met based on the update amount of the power hyperparameter and the noise power in the projection domain. After the iteration is completed, an angular domain sparse power spectrum is constructed based on the power hyperparameter values ​​corresponding to each angular grid.

10. The tensor-enhanced azimuth estimation method for high-order acoustic field sensor arrays according to claim 9, characterized in that, Iterative updates to the projection domain noise power include: Based on the power hyperparameters of the current iteration and the noise power in the projected domain, calculate the posterior covariance matrix and posterior mean matrix of the sparse coefficient matrix. Update the projection domain noise power based on the posterior mean matrix, posterior covariance matrix, and projected received signal matrix.

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