A coherent signal near angle high-resolution direction of arrival estimation method and system
By performing stepwise repair on the covariance matrix, the problems of rank deficiency, manifold consistency violation, and Toeplitz structure deviation in the near-angle estimation of coherent signals are solved, achieving high-resolution direction-of-arrival estimation and improving estimation accuracy and stability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF ACOUSTICS CHINESE ACAD OF SCI
- Filing Date
- 2026-01-27
- Publication Date
- 2026-06-02
AI Technical Summary
Existing methods have limited performance in direction-of-arrival estimation for coherent signals in near-angular scenarios. The lack of rank in the covariance matrix, the disruption of the physical manifold consistency of the array, and the Toeplitz structural bias make high-resolution estimation difficult.
By introducing the rank recovery operator, the array manifold consistency recovery operator, and the Toeplitz structure recovery operator, the covariance matrix is repaired step by step to satisfy statistical sufficiency, physical realizability, and array structure constraints, thereby restoring the signal subspace dimension, array manifold consistency, and Toeplitz structure.
Stable high-resolution direction-of-arrival estimation of coherent near-angle signals is achieved, improving angular resolution and estimation accuracy, which is significantly better than traditional methods.
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Figure CN122131225A_ABST
Abstract
Description
Technical Field
[0001] This specification relates to the field of array direction-of-arrival estimation technology, and in particular to a method and system for high-resolution near-angle direction-of-arrival estimation of coherent signals. Background Technology
[0002] Super-resolution direction-of-arrival (DOA) estimation is a key problem in the field of array signal processing. Existing methods are typically based on models of uniform linear arrays receiving narrowband far-field signals, whose ideal covariance matrix can be expressed as... However, when dealing with coherent signals with small angular intervals, existing methods suffer from signal coherence leading to a rank deficiency in the covariance matrix and insufficient dimension of the signal subspace. This renders traditional subspace decomposition-based methods ineffective, and existing rank recovery methods often disrupt the correspondence between the covariance matrix and the array's physical manifold model. Furthermore, in uniform linear arrays, finite snapshots and processing steps introduce biases, causing the covariance matrix to deviate from its theoretically expected Toeplitz structure. Therefore, existing methods still have limitations in high-resolution estimation performance for coherent near-angular scenes.
[0003] Application content
[0004] This application describes a method and system for estimating the near-angle high-resolution direction of arrival (DOA) of coherent signals, which can solve the above-mentioned technical problems.
[0005] According to the first aspect, a method for estimating the near-angle high-resolution direction of arrival (DOA) of a coherent signal is provided, comprising the following steps:
[0006] Acquire observation data, which is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated received by the array;
[0007] A rank recovery operator is applied to the observed data to obtain a first covariance matrix. The rank recovery operator is used to remove the coherence of the signals received by the array.
[0008] An array manifold consistency recovery operator is applied to the first covariance matrix to obtain a second covariance matrix, wherein the array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix;
[0009] Applying the Toeplitz structure recovery operator to the second covariance matrix yields a third covariance matrix, wherein the Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix;
[0010] The direction of arrival (DOA) of the signal source to be estimated is determined by using the third covariance matrix.
[0011] In some embodiments, applying the rank recovery operator to the observed data to obtain the first covariance matrix includes:
[0012] A Hankel matrix is constructed for the received signal vector corresponding to each of the snapshot data, and the Hankel matrices of all the received signal vectors are stacked to obtain a third-order tensor;
[0013] The time dimension of the third-order tensor is orthogonally projected onto a basis to obtain a time-frequency slice data matrix;
[0014] The first covariance matrix is obtained by averaging the covariances of all the time-slice data matrices.
[0015] In some embodiments, applying the array manifold consistency recovery operator to the first covariance matrix to obtain the second covariance matrix includes:
[0016] Within the target angle range, G discrete scanning angles are obtained at preset angle intervals. For each scanning angle Generate the corresponding array manifold vector = a( ), and construct a dictionary matrix. , , where, in the dictionary matrix In the table, the first G columns correspond to the covariance structure of the signal sources in all potential directions, while the last column vec(I) represents the covariance structure of the spatial white noise.
[0017] The dictionary matrix is obtained by fitting the first covariance matrix. Linear model: ,in , It is the first one to be estimated Signal power in each direction, It is noise power. These are the parameters to be solved;
[0018] The optimal power estimate is obtained by solving the following constrained optimization problem. :
[0019] in, Yes / no negative constraint;
[0020] Using the optimal power estimate obtained from the solution and noise power estimation Construct the second covariance matrix ,in, yes We obtain the conjugate transpose matrix. It is an identity matrix.
[0021] In some embodiments, applying the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix includes:
[0022] For the second covariance Take the arithmetic mean of all elements on each subdiagonal and assign this mean to all elements on that diagonal to generate the Toeplitz structure matrix. ;
[0023] Toeplitz structure matrix Perform eigenvalue decomposition, and transform the eigenvalue diagonal matrix... The negative eigenvalues in the matrix are set to zero, resulting in the updated matrix. ;
[0024] The output satisfies the covariance of Toeplitz and positive semidefinite PSD. The third covariance matrix is obtained.
[0025] In some more specific embodiments, the step of using the third covariance matrix to perform direction-of-arrival estimation and determine the estimated direction-of-arrival value of the signal source to be estimated includes:
[0026] For the third covariance matrix Eigenvalue decomposition is performed to obtain the noise subspace;
[0027] Using the noise subspace, a spatial spectrum is constructed for any scanning angle. Local maxima are searched for in the spatial spectrum over the entire scanning angle range to obtain the estimated direction of arrival (DOA) of the signal source to be estimated.
[0028] In some more specific embodiments, the step of orthogonally projecting the time dimension of the third-order tensor to obtain a time-slice data matrix, and averaging the covariances of all the time-slice data matrices to obtain the first covariance matrix, includes:
[0029] Expand the third-order tensor along the time dimension, multiply it by the discrete Fourier transform (DFT) basis matrix U on the right, and transform it to the frequency domain. ,in, Indicates different time slots, For a time-slice data matrix, It refers to the number of snapshots. It is a third-order tensor;
[0030] For all time slices, calculate their covariance matrices and average them to obtain the first covariance matrix. , ,in It is the coherence weight of each time slice.
[0031] According to the second aspect, a near-angle high-resolution direction-of-arrival estimation system for coherent signals is provided, comprising:
[0032] The acquisition module is used to acquire observation data, which is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated received by the array;
[0033] The first processing module is used to apply a rank recovery operator to the observation data to obtain a first covariance matrix. The rank recovery operator is used to remove the coherence of the signal received by the array.
[0034] The second processing module is used to apply an array manifold consistency recovery operator to the first covariance matrix to obtain a second covariance matrix, wherein the array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix.
[0035] The third processing module is used to apply the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix. The Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix.
[0036] The fourth processing module is used to perform direction of arrival estimation using the third covariance matrix to determine the estimated direction of arrival value of the signal source to be estimated.
[0037] In some embodiments, the first processing module is configured to construct a Hankel matrix for the received signal vector corresponding to each of the snapshot data, and stack the Hankel matrices of all the received signal vectors to obtain a third-order tensor.
[0038] The time dimension of the third-order tensor is orthogonally projected onto a basis to obtain a time-frequency slice data matrix;
[0039] The first covariance matrix is obtained by averaging the covariances of all the time-slice data matrices.
[0040] In some embodiments, the second processing module is configured to obtain G discrete scanning angles at preset angle intervals within the target angle range. For each scanning angle Generate the corresponding array manifold vector = And construct a dictionary matrix. , , where, in the dictionary matrix In the table, the first G columns correspond to the covariance structure of the signal sources in all potential directions, while the last column vec(I) represents the covariance structure of the spatial white noise.
[0041] The dictionary matrix is obtained by fitting the first covariance matrix. Linear model: The parameters to be solved , It is the first one to be estimated Signal power in each direction, It is noise power. These are the parameters to be solved;
[0042] The optimal power estimate is obtained by solving the following constrained optimization problem. :
[0043] in, Yes / no negative constraint;
[0044] Using the optimal power estimate obtained from the solution and noise power estimation Construct the second covariance matrix ,in, yes We obtain the conjugate transpose matrix. It is an identity matrix.
[0045] In some embodiments, the third processing module is used to process the second covariance. Take the arithmetic mean of all elements on each subdiagonal and assign this mean to all elements on that diagonal to generate the Toeplitz structure matrix. ;
[0046] Toeplitz structure matrix Perform eigenvalue decomposition, and transform the eigenvalue diagonal matrix... The negative eigenvalues in the matrix are set to zero, resulting in the updated matrix. ;
[0047] The output satisfies the covariance of Toeplitz and positive semidefinite PSD. The third covariance matrix is obtained.
[0048] In some embodiments, the fourth processing module is used to process the third covariance matrix. Eigenvalue decomposition is performed to obtain the noise subspace;
[0049] Using the noise subspace, a spatial spectrum is constructed for any scanning angle. Local maxima are searched for in the spatial spectrum over the entire scanning angle range to obtain the estimated direction of arrival (DOA) of the signal source to be estimated.
[0050] In some embodiments, the first processing module is configured to expand the third-order tensor along the time dimension, right-multiply it by the discrete Fourier transform (DFT) basis matrix U, and transform it to the frequency domain. ,in, Indicates different time slots, For a time-slice data matrix, It refers to the number of snapshots. It is a third-order tensor;
[0051] For all time slices, calculate their covariance matrices and average them to obtain the first covariance matrix. , ,in It is the coherence weight of each time slice.
[0052] According to a third aspect, a computer storage medium is provided, on which a computer program is stored, which, when executed by one or more processors, implements the coherent signal near-angle high-resolution direction-of-arrival estimation method as described in any of the above embodiments.
[0053] According to a fourth aspect, an electronic device is provided, including a memory and one or more processors, wherein the memory stores a computer program that, when executed by the one or more processors, implements coherent signal near-angle high-resolution direction-of-arrival estimation as described in any of the above embodiments.
[0054] In the methods and systems provided in the embodiments of this specification, during the direction-of-arrival (DOA) estimation process, the rank recovery operator, the array manifold consistency recovery operator, and the Toeplitz structure recovery operator are introduced sequentially to repair the covariance matrix step by step, so that it ultimately satisfies statistical sufficiency, physical realizability, and array structure limitation, thereby achieving stable DOA estimation for coherent incoming wave signals with similar angles. Attached Figure Description
[0055] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0056] Figure 1This diagram illustrates a flowchart of a near-angle high-resolution direction-of-arrival estimation method for coherent signals provided in an embodiment of this specification.
[0057] Figure 2 This diagram illustrates another flowchart of a near-angle high-resolution direction-of-arrival estimation method for coherent signals provided in an embodiment of this specification.
[0058] Figure 3 This is a schematic diagram comparing the direction estimation results of SB+FBSS, MTOEP, TDD and the present invention;
[0059] Figure 4 This diagram illustrates a module schematic of a coherent signal near-angle high-resolution direction-of-arrival estimation system provided in an embodiment of this specification. Detailed Implementation
[0060] The solution provided in this specification will now be described with reference to the accompanying drawings.
[0061] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be described below with reference to the accompanying drawings.
[0062] In the description of the embodiments of this application, the words "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the words "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a specific manner.
[0063] In the description of the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, B existing alone, and A and B existing simultaneously. Furthermore, unless otherwise stated, the term "multiple" means two or more.
[0064] 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 indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and their variations all mean "including but not limited to," unless otherwise specifically emphasized.
[0065] In the field of passive sonar detection, direction-of-arrival estimation is a core issue in array signal processing, and the accuracy of the estimation directly determines the target detection and localization performance.
[0066] Currently, it is usually considered that a... An array consisting of elements, with an element spacing of . The array receives data from... One far field, frequency is Narrowband signal. Among them, the first A signal at the angle of incidence Arrival at the array. In this model, the array's observed signal vector... It can be modeled as:
[0067]
[0068] in, For array manifold vectors; It is a signal vector; For noise, ={ ,…, } is an array manifold matrix composed of array manifold vectors.
[0069] Under ideal assumptions, the signal and noise are uncorrelated, and the noise is spatial white noise. The ideal covariance matrix of this observed signal is... It can be represented as:
[0070]
[0071] in, For the source power matrix, It is noise power.
[0072] As can be seen from the above, in coherent signal scenarios with small incident angle intervals, existing direction-of-arrival estimation methods face three fundamental challenges. These challenges are interconnected and collectively lead to a decline in the performance of high-resolution estimation.
[0073] 1. Rank degeneration of the covariance matrix
[0074] Under coherent signal conditions, due to the high coherence of multiple signal sources, their covariance matrix exhibits low rank or rank deficiency. This directly results in the effective dimension of the signal subspace in the array received signal covariance matrix being lower than the actual number of signal sources, rendering traditional direction-of-arrival estimation methods based on subspace dimension separation ineffective.
[0075] 2. Problem of array physical consistency violation
[0076] To overcome rank degradation, existing methods for restoring statistical rank often disrupt the correspondence between the covariance matrix and the array physical model, making it no longer representable as a non-negative combination of the array manifold outer product.
[0077] 3. Array structure constraint mismatch problem
[0078] Under uniform linear array conditions, the covariance of the true array should satisfy the Toeplitz structure constraint. However, finite snapshots, subarray operations, and enhancement processing introduce significant non-Toeplitz biases, causing the estimation results to deviate from the true physical array structure, thus affecting the accuracy and stability of the direction-of-arrival estimation.
[0079] In summary, existing methods still have significant limitations in addressing high-resolution direction-of-arrival estimation tasks at coherent near angles.
[0080] Therefore, this invention proposes a high-resolution near-angle direction-of-arrival estimation method for coherent signals. By sequentially introducing the rank recovery operator, the array manifold consistency recovery operator, and the Toeplitz structure recovery operator during the array covariance estimation process, the covariance matrix is repaired step by step, so that it ultimately satisfies statistical sufficiency, physical realizability, and array structure constraints, thereby achieving high-resolution near-angle direction-of-arrival estimation for coherent signals.
[0081] This invention adopts the following reconstruction framework,
[0082]
[0083] Among them, the rank restoration operator Solving the rank deficiency problem is essential; otherwise, manifold projection cannot function. The array manifold recovery operator is required. Used to restore array manifold consistency; Toeplitz structure recovery operator Restore the Toeplitz structure.
[0084] Figure 1 This is a flowchart illustrating a near-angle high-resolution direction-of-arrival estimation method for coherent signals. (Example:) Figure 1 As shown in the figure, this application proposes a method for estimating the near-angle high-resolution direction of arrival (DOA) of coherent signals, which specifically includes the following steps:
[0085] 110: Rank recovery of covariance matrix
[0086] In this embodiment of the application, the covariance matrix under coherent signal conditions is enhanced by constructing a space-time or space-translation joint observation structure, so that it can recover sufficient signal subspace dimension in a statistical sense.
[0087] First, construct the Hankel matrix for the received signal vector corresponding to the snapshot data. The generated Hankel matrix has dimensions of ,in The number of rows in the matrix. Given the number of columns in the matrix, assign all... Stacked into a third-order tensor , It refers to the number of snapshots. It is the received signal vector;
[0088] Next, for the third-order tensor By orthogonally projecting the time dimension onto the basis, we obtain... Specifically, the tensor is expanded along the time dimension and right-multiplied by the Discrete Fourier Transform (DFT) basis matrix U to transform the data to the frequency domain. The transformed result is... ,in, Representing different frequency indices, i.e., time slices, each It is a time-slice data matrix.
[0089] Then, the average covariance of the projection is calculated. We obtain a covariance matrix with sufficient rank. .
[0090] It should be understood that, in typical methods, based on a given array manifold Construct array to receive signals in, For coherent signal matrix, For additive white noise, the signal-to-noise ratio is... Based on the observed data, calculate its sample covariance matrix. ,in This refers to the number of snapshots. Under the condition of perfect signal coherence, due to the source signal matrix... A rank of 1 results in a sample covariance matrix The rank of is approximately 1, that is... .
[0091] At this point, the dimension of the signal subspace of the matrix is severely insufficient, making it impossible to provide two independent steering vector information for algorithms such as MUSIC that are based on subspace orthogonality. Therefore, it cannot be directly used to distinguish between two incident directions.
[0092] After the above processing This effectively eliminates covariance degradation.
[0093] 120: Array manifold consistency recovery
[0094] In this embodiment, the covariance matrix after rank recovery is projected onto the covariance set that satisfies the array physical model, thereby eliminating the physical mismatch introduced by the enhancement operation.
[0095] First, construct a dictionary matrix set based on the scanning angle. Specifically, within the target angle range, G discrete scanning angles are generated at preset angle intervals. Generate the corresponding array manifold vector for each angle. = a( ), and construct the following dictionary matrix:
[0096]
[0097] The first G columns correspond to the covariance structure of the signal sources in all potential directions, while the last column vec(I) represents the covariance structure of the spatial white noise.
[0098] Next, the covariance matrix is fitted and written as a linear model. Among them, the parameters to be solved , Representing the Signal power estimation in each direction, Representative noise power estimation
[0099] Solve for nonnegative least squares (NNLS). Specifically, the optimal match is obtained by solving the following constrained optimization problem. The parameters to be solved :
[0100] Among them, nonnegativity constraint This ensures the physical interpretability of the estimation results.
[0101] Subsequently, a covariance consistent with the array manifold is constructed. .
[0102] Thus, the matrix For array manifold consistency recovery operator The output maintained complete consistency with the real array model, providing physically correct input for subsequent Toeplitz structure recovery and final high-resolution estimation.
[0103] 130: Toeplitz structural restoration
[0104] By imposing a Toeplitz constraint on the covariance matrix, the deviation from the assumption of spatial stationarity of a uniform linear array is corrected.
[0105] First, the covariance matrix is consistent with the array manifold. The Toeplitz matrix is obtained by averaging the values of each offset diagonal. Specifically, for the covariance matrix consistent with the array manifold For each diagonal, that is, the set of all elements that satisfy column index j minus row index i equals the same constant, perform the following operation:
[0106] First, calculate the arithmetic mean of all elements on the diagonal. Then, replace the value of each element on the diagonal with this mean. This will make all elements on the diagonal identical and equal to the average of their original values.
[0107]
[0108] In this way, a matrix with an exact Toeplitz structure is directly generated. This makes it conform to the theoretical model of a uniform linear array under the assumption of spatial stability.
[0109] Next, the obtained Toeplitz matrix Perform eigenvalue decomposition, and transform the eigenvalue diagonal matrix... All negative eigenvalues are set to zero, resulting in The updated matrix is .
[0110] This eliminates numerical errors that may be introduced by finite samples or prior processing, ensuring that the matrix satisfies the positive semi-definite property required for the covariance matrix.
[0111] The matrix obtained after the above two steps This is the final estimated covariance matrix that simultaneously satisfies the Toeplitz structure and the positive semidefinite constraint. This matrix serves as an operator. The output will be directly used in subsequent high-resolution direction-of-arrival estimation algorithms.
[0112] Thus, applying the Toeplitz constraint to the covariance matrix corrects the deviation from the assumption of spatial stationarity of a uniform linear array.
[0113] 140: Direction of arrival estimation
[0114] After processing by the first three operators, the resulting covariance matrix It simultaneously satisfies the following conditions: rank sufficiency, capable of resolving multiple coherent near-angular sources; array-shaped consistency, which can be represented as a target physical model; and the Toeplitz structure conforms to the spatial stationarity assumption of ULA. Therefore, it can be expressed in the covariance matrix. The arbitrary high-resolution direction-of-arrival estimation method is applied.
[0115] In this embodiment, MUSIC is used as the output for direction-of-arrival estimation. First, the final covariance matrix is... Perform eigenvalue decomposition Select the smallest one. The eigenvectors constitute the noise subspace. Since the aforementioned three operators guarantee the integrity of the signal subspace structure, therefore The orthogonality is no longer affected by coherent sources.
[0116] Next, the MUSIC spatial spectrum is constructed for any scanning angle. Its spatial spectrum is Subsequently, peak values in the direction of arrival were detected by analyzing the spatial spectrum. Throughout the entire scanning angle range By searching for local maxima, the final estimated set of directions of arrival can be obtained. .
[0117] Therefore, based on a covariance matrix with consistent structure, spectral search or subspace analysis is performed to output high-resolution direction-of-arrival estimation results.
[0118] In summary, in this embodiment, during the direction-of-arrival estimation process, the rank recovery operator, the array manifold consistency recovery operator, and the Toeplitz structure recovery operator are introduced sequentially to repair the covariance matrix step by step, so that it ultimately satisfies statistical sufficiency, physical realizability, and array structure reduction simultaneously, thereby achieving stable partial estimation of coherent near-angle incoming waves.
[0119] Figure 2 This is another flowchart illustrating a near-angle high-resolution direction-of-arrival estimation method for coherent signals. For example... Figure 2 As shown, it includes the following steps:
[0120] 210: Acquire observation data. The observation data is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated, received by the array.
[0121] For example, in this embodiment of the application, the verification test uses a horizontal uniform linear array with 27 elements, an element spacing of 1.5m, an operating frequency of 50Hz, a data sampling interval of 1s, an azimuth scanning range set to 0°-180°, and an angular interval of 0.1°. Two completely coherent narrowband 50Hz signals are provided, with an incident angle of... The sampling frequency is 2000Hz, the number of sampling points is 10000, and the relationship between the two coherent signals is as follows: This scenario is a typical example of "near-angle + fully coherent + low-frequency signal", which traditional methods have very weak resolution capabilities.
[0122] In traditional methods, the data preprocessing and covariance estimation stages are first based on a given array manifold. Construct an array to receive signals:
[0123]
[0124] in, For coherent signal matrix, For additive white noise, the signal-to-noise ratio is... .
[0125] Based on the observed data, calculate its sample covariance matrix:
[0126]
[0127] Among them, This represents the number of snapshots.
[0128] Under the condition that the signals are completely coherent, due to the source signal matrix A rank of 1 results in a sample covariance matrix The rank of is approximately 1, that is:
[0129]
[0130] At this point, the dimension of the signal subspace of the matrix is severely insufficient, making it impossible to provide two independent steering vector information for algorithms such as MUSIC that are based on subspace orthogonality. Therefore, it cannot be directly used to distinguish between two incident directions.
[0131] 220: Apply the rank recovery operator to the observation data to obtain the first covariance matrix. The rank recovery operator is used to remove the coherence of the signal received by the array.
[0132] In this embodiment, by constructing a space-time joint observation structure and utilizing frequency domain transformation, the complete coherence between signals is eliminated, thereby restoring the rank of the covariance matrix. The steps include:
[0133] 221: Constructing the Hankel space translation embedding matrix
[0134] Construct the corresponding Hankel matrix for the array signal vector received at each snapshot time. The original array is virtually spatially shifted and expanded to introduce additional observation dimensions.
[0135] Based on the set parameters, the dimensions of the Hankel matrix are... ,in The number of rows in the matrix. To determine the number of columns in the matrix, The Hanke matrices in the snapshot are stacked to form a third-order tensor. .
[0136] In the above verification experiment, .
[0137] 222: Generalized Frequency Domain Transform Based on DFT
[0138] Expanding the tensor along the time dimension and right-multiplying it by the Discrete Fourier Transform (DFT) basis matrix U transforms the data to the frequency domain. The transformed result is:
[0139]
[0140] in, Representing different frequency indices, i.e., time slices, each It is a time-slice data matrix.
[0141] This transformation results in the original coherent signal exhibiting differentiated weighting and phase structures on different frequency slices.
[0142] 223: Average Covariance of Multi-Frequency Chips
[0143] For all frequency slices, calculate their covariance matrix and average it:
[0144]
[0145] The final matrix It is the first covariance matrix.
[0146] After the above processing The rank is restored from approximately 1 to close to the true number of sources, K=2. This process corresponds to the rank restoration operator in this invention. Its output This provides a matrix with sufficient signal subspace dimension for subsequent physical consistency recovery steps.
[0147] 230: Apply the array manifold consistency recovery operator to the first covariance matrix to obtain the second covariance matrix. The array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix.
[0148] 231: Constructing a dictionary matrix
[0149] A complete physical model dictionary has been built.
[0150] In the scanning angle range Endogenous generation The grid has 801 directions.
[0151] Constructing a dictionary:
[0152]
[0153] 232: Solving the Non-negative Least Squares (NNLS) Problem
[0154] Find the physical parameters that best match the observed data vec(R̃) by solving the following constrained optimization problem:
[0155] Wherein, the parameter vector to be solved , Representing the Signal power estimation in the direction, This represents noise power estimation. Non-negativity constraint. This ensures the physical interpretability of the estimation results.
[0156] 233: Reconstructing the Covariance Matrix Consistent with the Manifold
[0157] Using the optimal power distribution obtained in the previous step and noise power Construct the second covariance matrix, which is strictly composed of the outer product of the array manifolds:
[0158]
[0159] The matrix Let be the second covariance matrix.
[0160] 240: Apply the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix. The Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix.
[0161] For the second covariance matrix For each diagonal, i.e., the set of all elements where column index j minus row index i equals the same constant, perform the following operation:
[0162] First, calculate the arithmetic mean of all elements on the diagonal. Then, replace the value of each element on the diagonal with this mean. This will make all elements on the diagonal identical and equal to the average of their original values.
[0163]
[0164] This step restores the spatial stationarity of the ULA and reduces noise disturbances. The final third covariance matrix of the input MUSIC is:
[0165]
[0166] 250: Use the third covariance matrix to estimate the direction of arrival (DOA) and determine the estimated DOA value of the signal source to be estimated.
[0167] exist The high-resolution direction-of-arrival estimation algorithm based on the subspace principle is directly applied.
[0168] This invention selects the classic MUSIC algorithm as the final estimator. The above-mentioned standard MUSIC is implemented. Two clearly separated spectral peaks were obtained. Corresponding to the actual direction of arrival .
[0169] To verify the effectiveness of the method of this invention, the spatial spectrum results of SB+FBSS, MTOEP, TDD (TensorHOSVD) and the algorithm proposed in this invention were compared. Figure 3 This is a schematic diagram comparing the direction-of-arrival estimation results of SB+FBSS, MTOEP, TDD, and the present invention. Figure 3 As shown, SB+FBSS, MTOEP, and TDD (TensorHOSVD) can only identify one target, while our proposed method can identify two targets, namely... , corresponding to the true direction of arrival estimation results .
[0170] In summary, the method proposed in this invention can maintain stable high-resolution characteristics even in complex marine environments, with an angular resolution better than 2°, which is significantly better than CBF, MVDR and SPICE methods, fully verifying the effectiveness and advantages of this method in practical engineering applications.
[0171] Figure 4 This is a schematic diagram of a near-angle high-resolution direction-of-arrival estimation system for coherent signals. (Example:) Figure 4 As shown, a near-angle high-resolution direction-of-arrival estimation system for coherent signals includes:
[0172] The acquisition module is used to acquire observation data, which is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated received by the array;
[0173] The first processing module is used to apply a rank recovery operator to the observation data to obtain a first covariance matrix. The rank recovery operator is used to remove the coherence of the signal received by the array.
[0174] The second processing module is used to apply an array manifold consistency recovery operator to the first covariance matrix to obtain a second covariance matrix, wherein the array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix.
[0175] The third processing module is used to apply the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix. The Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix.
[0176] The fourth processing module is used to perform direction of arrival estimation using the third covariance matrix to determine the estimated direction of arrival value of the signal source to be estimated.
[0177] In some embodiments, the first processing module is configured to construct a Hankel matrix for the received signal vector corresponding to each of the snapshot data, and stack the Hankel matrices of all the received signal vectors to obtain a third-order tensor.
[0178] The time dimension of the third-order tensor is orthogonally projected onto a basis to obtain a time-frequency slice data matrix;
[0179] The first covariance matrix is obtained by averaging the covariances of all the time-slice data matrices.
[0180] In some embodiments, the second processing module is configured to obtain G discrete scanning angles at preset angle intervals within the target angle range. For each scanning angle Generate the corresponding array manifold vector = a( ), and construct a dictionary matrix. ,
[0181] , where, in the dictionary matrix In the table, the first G columns correspond to the covariance structure of the signal sources in all potential directions, while the last column vec(I) represents the covariance structure of the spatial white noise.
[0182] The dictionary matrix is obtained by fitting the first covariance matrix. Linear model: The parameters to be solved , It is the first one to be estimated Signal power in each direction, It is noise power. These are the parameters to be solved;
[0183] The optimal power estimate is obtained by solving the following constrained optimization problem. :
[0184] in, Yes / no negative constraint;
[0185] Using the optimal power estimate obtained from the solution and noise power estimation Construct the second covariance matrix ,in, yes We obtain the conjugate transpose matrix. It is an identity matrix.
[0186] In some embodiments, the third processing module is used to process the second covariance. Take the arithmetic mean of all elements on each subdiagonal and assign this mean to all elements on that diagonal to generate the Toeplitz structure matrix. ;
[0187] Toeplitz structure matrix Perform eigenvalue decomposition, and transform the eigenvalue diagonal matrix... The negative eigenvalues in the matrix are set to zero, resulting in the updated matrix. ;
[0188] The output satisfies the covariance of Toeplitz and positive semidefinite PSD. The third covariance matrix is obtained.
[0189] In some embodiments, the fourth processing module is used to process the third covariance matrix. Eigenvalue decomposition is performed to obtain the noise subspace;
[0190] Using the noise subspace, a spatial spectrum is constructed for any scanning angle. Local maxima are searched for in the spatial spectrum over the entire scanning angle range to obtain the estimated direction of arrival (DOA) of the signal source to be estimated.
[0191] In some embodiments, the first processing module is configured to expand the third-order tensor along the time dimension, right-multiply it by the discrete Fourier transform (DFT) basis matrix U, and transform it to the frequency domain. ,in, Indicates different time slots, For a time-slice data matrix, It refers to the number of snapshots. It is a third-order tensor;
[0192] For all time slices, calculate their covariance matrices and average them to obtain the first covariance matrix. , ,in It is the coherence weight of each time slice.
[0193] In summary, the embodiments of this application introduce the rank recovery operator, the array manifold consistency recovery operator, and the Toeplitz structure recovery operator in sequence during the direction of arrival estimation process to repair the covariance matrix step by step, so that it ultimately satisfies statistical sufficiency, physical realizability, and array structure reduction, thereby achieving stable partial estimation of coherent near-angle incoming waves.
[0194] According to another embodiment, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the program, it implements the coherent signal near-angle high-resolution direction of arrival estimation method as described in the above technical solution.
[0195] According to another embodiment, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed in a computer, causes the computer to perform a coherent signal near-angle high-resolution direction of arrival estimation method.
[0196] Those skilled in the art will recognize that, in one or more of the examples above, the functions described in this invention can be implemented using hardware, software, firmware, or any combination thereof. When implemented in software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium.
[0197] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for estimating the near-angle high-resolution direction of arrival (DOA) of a coherent signal, characterized in that, Includes the following steps: Acquire observation data, which is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated received by the array; A rank recovery operator is applied to the observed data to obtain a first covariance matrix. The rank recovery operator is used to remove the coherence of the signals received by the array. An array manifold consistency recovery operator is applied to the first covariance matrix to obtain a second covariance matrix, wherein the array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix; Applying the Toeplitz structure recovery operator to the second covariance matrix yields a third covariance matrix, wherein the Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix; The direction of arrival (DOA) of the signal source to be estimated is determined by using the third covariance matrix.
2. The method according to claim 1, characterized in that, The step of applying the rank recovery operator to the observed data to obtain the first covariance matrix includes: A Hankel matrix is constructed for the received signal vectors corresponding to the snapshot data in the observation data, and the Hankel matrices of all the received signal vectors are stacked to obtain a third-order tensor. The time dimension of the third-order tensor is orthogonally projected onto a basis to obtain a time-frequency slice data matrix; The first covariance matrix is obtained by averaging the covariances of all the time-slice data matrices.
3. The method according to claim 1, characterized in that, The step of applying the array manifold consistency recovery operator to the first covariance matrix to obtain the second covariance matrix includes: Within the target angle range, G discrete scanning angles are obtained at preset angle intervals. For each scanning angle Generate the corresponding array manifold vector = a( ), and construct a dictionary matrix. ,in In the dictionary matrix In the table, the first G columns correspond to the covariance structure of the signal sources in all potential directions, while the last column vec(I) represents the covariance structure of the spatial white noise. The dictionary matrix is obtained by fitting the first covariance matrix. Linear model: The parameters to be solved , It is the first one to be estimated Signal power in each direction, It is noise power; By solving the following constrained optimization problem: Obtain the optimal power estimate ,in, Yes / no negative constraint; Using the optimal power estimate obtained from the solution and noise power estimation Construct the second covariance matrix ,in, yes We obtain the conjugate transpose matrix. It is an identity matrix.
4. The method according to claim 1, characterized in that, The step of applying the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix includes: For the second covariance Take the arithmetic mean of all elements on each subdiagonal and assign this mean to all elements on that diagonal to generate the Toeplitz structure matrix. ; Toeplitz structure matrix Perform eigenvalue decomposition, and transform the eigenvalue diagonal matrix... The negative eigenvalues in the matrix are set to zero, resulting in the updated matrix. ; The output satisfies the covariance of Toeplitz and positive semidefinite PSD. The third covariance matrix is obtained.
5. The method according to claim 1, characterized in that, The step of using the third covariance matrix to estimate the direction of arrival (DOA) and determine the estimated DOA value of the signal source to be estimated includes: For the third covariance matrix Eigenvalue decomposition is performed to obtain the noise subspace; Using the noise subspace, a spatial spectrum is constructed for any scanning angle. Local maxima are searched for in the spatial spectrum over the entire scanning angle range to obtain the estimated direction of arrival (DOA) of the signal source to be estimated.
6. The method according to claim 2, characterized in that, The step of projecting the time dimension of the third-order tensor onto an orthogonal basis to obtain a time-slice data matrix, and averaging the covariances of all the time-slice data matrices to obtain the first covariance matrix, includes: Expand the third-order tensor along the time dimension, multiply it by the discrete Fourier transform (DFT) basis matrix U on the right, and transform it to the frequency domain. ,in, Indicates different time slots, For a time-slice data matrix, It refers to the number of snapshots. It is a third-order tensor; For all time slices, calculate their covariance matrices and average them to obtain the first covariance matrix. , ,in It is the coherence weight of the time slice.
7. A near-angle high-resolution direction-of-arrival estimation system for coherent signals, characterized in that, include: The acquisition module is used to acquire observation data, which is a collection of snapshot data of the transmitted or reflected signals of the signal source to be estimated received by the array; The first processing module is used to apply a rank recovery operator to the observation data to obtain a first covariance matrix. The rank recovery operator is used to remove the coherence of the signal received by the array. The second processing module is used to apply an array manifold consistency recovery operator to the first covariance matrix to obtain a second covariance matrix, wherein the array manifold consistency recovery operator is used to restore the array manifold consistency of the second covariance matrix. The third processing module is used to apply the Toeplitz structure recovery operator to the second covariance matrix to obtain the third covariance matrix. The Toeplitz structure recovery operator is used to restore the Toeplitz structure of the second covariance matrix. The fourth processing module is used to perform direction of arrival estimation using the third covariance matrix to determine the estimated direction of arrival value of the signal source to be estimated.
8. The system according to claim 7, characterized in that, The first processing module is used to construct a Hankel matrix for the received signal vector corresponding to each of the snapshot data, and stack the Hankel matrices of all the received signal vectors to obtain a third-order tensor. The time dimension of the third-order tensor is orthogonally projected onto a basis to obtain a time-frequency slice data matrix; The first covariance matrix is obtained by averaging the covariances of all the time-slice data matrices.
9. An electronic device, characterized in that, The device includes a memory and one or more processors, wherein the memory stores a computer program that, when executed by the one or more processors, implements a coherent signal near-angle high-resolution direction-of-arrival estimation method as described in any one of claims 1 to 6.
10. A computer storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by one or more processors, implements a coherent signal near-angle high-resolution direction-of-arrival estimation method as described in any one of claims 1 to 6.