Two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching

Abstract

The present invention discloses a two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching, comprising the following steps: decomposing the direction of arrival (DOA) estimation problem of a two-dimensional broadband incoherent distributed source into two one-dimensional estimation problems by decomposing an L-shaped array into two orthogonal uniform linear arrays; recovering two angular frequency spatial spectrum matrices from the array receiving covariance matrix based on the received signal in combination with a low-rank recovery method; and extracting two sets of key parameters from the two angular frequency spatial spectrum matrices for matching; proposing a spectrum matching-based method for determining the two-dimensional DOA of a broadband incoherent distributed source based on the frequency domain parameter invariance of the distributed source in space; and directly estimating the joint angle and spectrum to obtain the joint parameters. The present invention also eliminates the need for prior knowledge of the distributed source and can directly estimate the two-dimensional angle based on the angular frequency spatial spectrum.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing, and in particular relates to a two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching. Background Art

[0002] Direction-of-arrival (DOA) estimation is a hot research topic in the field of array signal processing. The problem of joint estimation of two-dimensional DOA and frequency is a key issue in various sensor array signal processing fields, such as radar, sonar, and wireless communications. Most existing research works are based on the point source model and the assumption of narrowband signals. However, in actual natural environment scenarios, broadband target sources are more common, and sometimes due to the multipath effect and spatial diffusion of the signal, the signal has an angular expansion phenomenon, which cannot meet the assumption of the point source model. Therefore, it is necessary to model the signal model as a distributed source model. Existing methods for joint estimation of two-dimensional DOA and frequency mainly focus on models based on the point source assumption and cannot be directly extended to the distributed source model.

[0003] There have been some research results on parameter estimation methods for two-dimensional distributed sources, but existing technologies still have many limitations. For example, some traditional subspace methods require the specific distribution shape of the known signal space distribution, such as uniform distribution or Gaussian distribution. When the actual signal space distribution is inconsistent with the assumed distribution function, the performance of parameter estimation will be greatly affected. Some methods use parameterized polynomial approximation to model, which is only effective when the expansion angle is small, which is unrealistic in actual scenarios. In addition, traditional subspace methods rely on multidimensional search and eigendecomposition operations to perform pairing based on the eigenvalues ​​of the rotational invariance matrix. In addition, existing two-dimensional distributed source parameter estimation methods are all based on the assumption of narrowband models and cannot be directly extended to broadband distributed source models. There is currently no two-dimensional parameter estimation method specifically for broadband incoherent distributed sources.

[0004] For two-dimensional distributed source estimation, a distributed source two-dimensional spatial spectrum estimation method based on low-rank matrix reconstruction (CN109738852B) proposed a solution. However, this method is only applicable to narrowband scenarios and cannot be directly extended to two-dimensional wideband distributed source models. Yang et al. proposed a method for joint estimation of one-dimensional angle and frequency (Yang, Lili, et al. "Joint angular-frequency distribution estimation of incoherently distributed wideband sources via low-rank matrix recovery."). IEEE Transactions on Aerospace and Electronic Systems57.6 (2021): 3563-3573.), but this method is only for one-dimensional DOA estimation and cannot be directly extended to two-dimensional DOA estimation. Currently, no method has been proposed to solve the problem of estimating two-dimensional broadband distributed sources. Liu et al. proposed a multiple signal classification (MUSIC) algorithm (Liu, Chun-Lin, and Palghat P. Vaidyanathan. "Coprime arrays and samplers for space-time adaptive processing."). 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) IEEE, 2015.) to estimate one-dimensional angle and frequency. When extended to two-dimensional distributed source scenarios, this method requires assuming a known distribution function and performing a multidimensional search, resulting in high complexity. The one-dimensional angle and frequency estimation method proposed by Wang et al., based on the rotationally invariant subspace method (ESPRIT), while not requiring prior knowledge of the distribution function for multidimensional search, still requires the establishment of multiple joint matrices for eigenvalue decomposition. This leads to high computational complexity when extended to broadband two-dimensional distributed source scenarios. Furthermore, the Taylor expansion approximation method is required for parameterized modeling, which is only effective when the extended angle is small. Summary of the Invention

[0005] The purpose of this invention is to propose a two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching. This method decomposes the two-dimensional DOA estimation problem into two one-dimensional DOA estimation problems by decomposing an L-shaped array into two orthogonal uniform linear arrays. Based on the received array signal, a low-rank recovery algorithm is used to recover the two-dimensional angular frequency spectrum of the broadband distributed source from the covariance matrix. Two sets of one-dimensional estimated parameters (including center angle, center frequency, and spectrum) are then extracted from the angular frequency spectrum. Because the estimated angular parameters of multiple target sources are randomly arranged in an irregular order, a pairing method is required to determine the paired two-dimensional angles of each target source. Finally, based on the invariance of the frequency domain parameters of the same target source, a scheme combining center frequency and spectrum similarity is designed to determine the corresponding two-dimensional angle of each target source.

[0006] The present invention is achieved through at least one of the following technical solutions.

[0007] A two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching includes the following steps:

[0008] Decompose the L-shaped array into two orthogonal uniform linear arrays, and receive the signal transmitted by the target source through the two mutually orthogonal uniform linear arrays respectively;

[0009] Based on the signals received by two mutually orthogonal uniform linear arrays, the angular frequency spatial spectrum matrices are recovered from the covariance matrices of the received signals of the two mutually orthogonal uniform linear arrays in combination with the low-rank recovery method. The key parameters are then extracted from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays for matching, and a corresponding set of two-dimensional matching angles is obtained.

[0010] Remove the target source pairs that have passed the matching and rematch the remaining target sources until all target sources are calculated.

[0011] Furthermore, the method of recovering the angular frequency spatial spectrum matrix from the covariance matrices of the received signals of two mutually orthogonal uniform linear arrays in combination with the low-rank recovery method includes the following steps:

[0012] (1) Find the covariance matrix corresponding to two mutually orthogonal uniform linear arrays and convert the covariance matrix into vector form;

[0013] (2) Constructing array manifold steering vectors corresponding to two mutually orthogonal uniform linear arrays;

[0014] (3) Construct an optimization problem for low-rank matrix recovery, and solve the angular frequency spatial spectrum matrices corresponding to two mutually orthogonal uniform linear arrays through the vector form of step (1) and the array manifold steering vector of step (2).

[0015] Furthermore, extracting key parameters from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays is respectively extracting the center angle and the corresponding center frequency from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays, including the following steps:

[0016] S1. Use image segmentation and clustering to segment the angular frequency spatial spectrum matrices corresponding to two mutually orthogonal uniform linear arrays into separate target sources;

[0017] S2. Substitute the angular frequency spatial spectrum into the following formula to calculate the central angle:

[0018] ;

[0019] ;

[0020] in 、 They represent the first The center angle of the target source is the center direction of the spatial energy distribution of the corresponding target source estimated by two mutually orthogonal uniform linear arrays. 、 Denotes the first angle domain of the target source corresponding to two mutually orthogonal uniform linear arrays. discretized grid points, Indicates the first frequency domain corresponding to the target source Discretized frequency points, 、 They represent the amplitudes of the discretized grid point coordinates in the angular frequency spatial spectrum estimated by two mutually orthogonal uniform linear arrays, and Respectively represent A uniform linear array of interest angle range and frequency range of interest in a target source; Indicates the Another uniform linear array of interest angle range in the target source;

[0021] S3. Substitute the angular frequency spatial spectrum into the following formula to calculate the center frequency:

[0022] ;

[0023] ;

[0024] in 、 They represent the first The center frequency of the target source is the weighted average frequency of the corresponding target source spectrum energy estimated by two mutually orthogonal uniform linear arrays, which reflects the main energy concentration frequency band of the target source spectrum.

[0025] Furthermore, by judging whether the center frequency distance between any two target sources in the uniform linear array is greater than a set threshold, the number of target sources with similar center frequencies is determined;

[0026] If there is a target source pair whose center frequency spacing is greater than the threshold, it is determined that the center frequencies of the target source pair do not overlap;

[0027] If there exists a target source pair whose center frequency interval is less than or equal to the threshold, it is determined that the center frequencies of the target source pair are close.

[0028] Furthermore, target source pairing is performed based on the number of target sources with similar center frequencies, specifically including:

[0029] (a) Sort the center frequencies of the target sources in the same uniform linear array from high to low, and adjust the corresponding center angle order simultaneously;

[0030] (b) Select a pairing strategy based on the number of target sources with similar center frequencies:

[0031] (b1) If there is no target source with a similar center frequency, all target sources are paired using their center frequencies;

[0032] (b2) If there are target sources with similar center frequencies, these target sources are paired based on spectral similarity, and the remaining target sources are paired based on center frequencies.

[0033] Furthermore, the pairing using the center frequency includes:

[0034] Calculate the Euclidean distance between the center frequencies of the target sources of two uniform linear arrays;

[0035] A group of target sources with the smallest Euclidean distance is determined as paired target sources.

[0036] Furthermore, the pairing by spectrum similarity is performed by the following formula:

[0037]

[0038] in For the The paired index of the target source, Indicates the number of target sources with similar center frequencies, is the correlation coefficient, which is used to measure the target source and The similarity between the target sources; is the number of target sources, Indicates the first The center frequency of the target source that needs to be frequency matched, Indicates the first The center frequency of the target source, Indicates another uniform linear array corresponding to the The target source is different The center frequency of the target source, Indicates the operation of finding the Euclidean norm; Represents the set threshold; based on the pairing index of spectrum similarity, a corresponding set of two-dimensional matching angles can be determined.

[0039] Furthermore, removing the already matched target sources and rematching the remaining target sources means removing the center angles and center frequencies of the already matched target sources, reordering the center frequencies and center angles of the remaining target sources, and selecting the pairing method according to step (b) based on the reordering result to perform pairing.

[0040] A computer device of the present invention includes a memory and a processor, wherein the memory is electrically connected to the processor and stores a computer program. When the computer program is executed by the processor, the processor implements the method described above.

[0041] A computer device of the present invention includes a memory and a processor, wherein the memory is electrically connected to the processor and stores a computer program. When the computer program is executed by the processor, the processor implements the method described above.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] (1) For the first time, we have achieved the joint estimation of two-dimensional DOA and spectrum for a wideband incoherent signal distribution source. Unlike traditional wideband problems that require converting the wideband subspace into a narrowband subspace before DOA estimation, our method directly estimates the joint angle and spectrum to obtain the joint parameters without the need for additional preprocessing such as frequency domain focusing or smoothing.

[0044] (2) The two-dimensional DOA estimation problem of a broadband incoherent signal distribution source in the present invention is decomposed into two one-dimensional DOA estimation problems by splitting the L-shaped array into two mutually orthogonal uniform linear arrays. Based on the signals received on the X-axis and Y-axis, two joint angular frequency matrices are recovered from the covariance matrix using a low-rank recovery method. Subsequently, two sets of joint parameters are extracted from these two joint angular frequency matrices without presetting the signal distribution shape, thus avoiding the need for multi-dimensional search in traditional methods.

[0045] (3) Based on the estimated frequency characteristics, a spectrum matching method is proposed to determine the two-dimensional DOA angle of broadband distributed sources. This matching method can simultaneously use the center frequency and spectrum information to complete the matching in the presence of strong noise interference, and can achieve better matching results than traditional subspace methods and methods that only use frequency matching. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flowchart of a method for estimating two-dimensional parameters of broadband incoherent distributed sources based on spectrum matching in an embodiment of the present invention.

[0047] Figure 2 1 is a diagram of an array topology structure in an embodiment of the present invention.

[0048] Figure 3 1 and 2 are different angular frequency space spectra according to the embodiments of the present invention.

[0049] Figure 4 1 is a diagram showing the successful pairing results of 100 repeated experimental tests in the embodiment.

[0050] Figure 5 1 is a result diagram of pairing errors in 100 repeated experimental tests in the embodiment.

[0051] Figure 6 3 is a diagram of the root mean square error simulation results under different signal-to-noise ratios using 100 repeated experiments in the embodiment. DETAILED DESCRIPTION

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the technical solutions in the embodiments of the present invention will be described in detail and clearly in conjunction with the drawings in the present invention. It should be noted that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0053] like Figure 1 As shown, a method for estimating two-dimensional parameters of broadband incoherent distributed sources based on spectrum matching according to an embodiment of the present invention specifically includes the following steps:

[0054] S1. Initialization, setting the total number of array elements , the number of elements in each subarray is , angle range of interest , the frequency range of interest , discrete grid accuracy and other parameters.

[0055] As an embodiment, step S1 specifically includes the following steps:

[0056] S11, initialization, setting the total number of array elements , the number of elements in each subarray is ， The array element spacing is , Equal to half wavelength , assuming , where the number of target sources .

[0057] S12. In three-dimensional space, the angle range of interest is , the frequency range of interest , the discretization grid accuracy in the angle domain is , the frequency domain discretization grid accuracy is . Azimuth of the target source and pitch angle ,satisfy 、 The center frequency is ,satisfy The signal-to-noise ratio is SNR =10dB.

[0058] S13, using space-time sampling, the target source randomly transmits the array receiving signal, the length of the array receiving signal is , the array receives the signal and divides it into Blocks are received, each block is , the threshold is set to 5.

[0059] S2. Consider using an L-shaped array and decompose it into two mutually orthogonal uniform linear arrays. The two mutually orthogonal uniform linear arrays receive the signals transmitted by the target source respectively, thereby decomposing the two-dimensional DOA estimation problem into two one-dimensional DOA estimation problems for solution.

[0060] The step S2 specifically includes the following steps:

[0061] S21. In the three-dimensional space XYZ axis, there is A randomly generated signal is emitted by a wideband far-field independently distributed scattering target source with different distribution shapes and is incident on a two-dimensional L-shaped array. This L-shaped array is two mutually orthogonal uniform linear arrays. The L-shaped array is decomposed into a uniform sub-array on the XZ plane and a uniform sub-array on the YZ plane to process the received signal. Each sub-array has If there are array element sensors, the two-dimensional angle and frequency joint estimation signal model on the XYZ axis of the three-dimensional space is decomposed into two one-dimensional angle and frequency joint estimation signal models on the XZ plane and YZ plane respectively. This signal model is the signal model received by two orthogonal uniform linear arrays, which is used to estimate the central angle in the direction corresponding to the two orthogonal uniform linear arrays, that is, the two one-dimensional angles. 、 . Two-dimensional angle and frequency joint estimation signal model.

[0062] S22. Assuming that the target source sends a signal incident on the X-axis subarray, then the central angle on the XZ plane , Represents the center angle of the two target sources corresponding to the X-axis subarray. The center angle here refers to the center direction of the spatial energy distribution corresponding to the two target sources estimated by the X-axis subarray. The same target source signal is incident on the Y-axis subarray, so the center angle on the YZ plane is , Indicates the center angle of the two target sources corresponding to the Y-axis sub-array. The center angle here refers to the center direction of the spatial energy distribution corresponding to the two target sources estimated by the Y-axis sub-array. Then for the azimuth of the same target source and pitch angle Angle with X axis , Y-axis center angle The geometric relationship can be expressed as:

[0063] ;

[0064] ;

[0065] According to the above geometric relationship, the two-dimensional angle estimation problem can be decomposed into two one-dimensional angle estimation problems. Assume that there are two target sources in space that transmit signals incident on the array, which are received and processed by the array. The array estimates the central angle of the target source based on the received signal model. The first target source is a distributed source with Gaussian distribution in both angle and frequency domain. The center frequency of the first distributed source is set to The second distributed source is a source with uniform distribution in the angle and frequency domains and a center frequency of .

[0066] The parameter set for the first target source includes: , the parameter set for the second distribution source includes: .in and Indicates the central angles of the two target sources corresponding to the X-axis subarray, Indicates the expansion angle of the two target sources corresponding to the X-axis subarray, Indicates the center angles of the two target sources corresponding to the Y-axis subarray, and Indicates the expansion angle of the two target sources corresponding to the Y-axis sub-array, and represents the center frequencies of the two target sources, and Indicates the frequency bandwidth of the two target sources.

[0067] S23, the angle range of interest in the three-dimensional space The above geometric relationship is converted into the angle range of interest in the X-axis direction , satisfying the X-axis center angle , the angle range of interest in the Y-axis direction , satisfying the Y-axis center angle .

[0068] As a specific embodiment, suppose that in three-dimensional space, there is The scattering target sources with independent distribution in the wideband far field reach the two-dimensional L-shaped array, and the azimuth and elevation angles of the signals are expressed as and In order to simplify the signal model of three-dimensional parameter estimation, the L-shaped array is used to decompose the two-dimensional angle and frequency joint estimation signal model into two one-dimensional angle and frequency joint estimation signal models, that is, the L-shaped array is divided into two orthogonal uniform sub-arrays to process the received signal. The array topology results are as follows Figure 2 As shown, Figure 2 (a) is the geometric diagram of the L-shaped array and the target source. Figure 2 (b) is the decomposition sub-matrix on the XZ plane, Figure 2 (c) is the decomposition sub-array on the YZ plane. For each sub-array, there is The distance between the array elements is The DOA angle of the target source incident on the X-axis subarray is , the DOA angle incident on the Y-axis sub-array is . Then for the azimuth of the same target source and pitch angle Angle with X axis , Y-axis center angle The geometric relationship can be expressed as:

[0069] ;

[0070] ;

[0071] According to the above relationship, the two-dimensional angle estimation problem can be decomposed into two one-dimensional angle estimation problems. In order to further improve the processing capability of uniform linear array for broadband signals, the space-time sampling method is used to reduce the total length of The number of snapshots is divided into Block (segment) reception is used to compensate for frequency domain information. The length of each block is , then .

[0072] S3, X-axis array receiving signal , Y-axis array receiving signal , and find the corresponding covariance matrix and , and convert the covariance matrix into vector form and .

[0073] The step S3 specifically includes the following steps:

[0074] S31. Based on the initialization parameters set in step S1, an array receiving signal model is established for the signal received by the X-axis array according to the following formula:

[0075] In order to improve the estimation effect of the spectrum, space-time sampling is used to convert the first Block receiving signal It is represented as the following vector:

[0076] ;

[0077] in is the number of target sources, is the angle range of interest in the X-axis direction, is the frequency range of interest, is the space-time steering vector, is the X-axis center angle, is the center frequency, For vectorized operations, is the complex conjugate transpose. yes The space steering vector corresponding to the X-axis array of the dimension, Indicates the The propagation delay of an array element. yes dimensional time-oriented vector, represents the imaginary unit of a complex number, Indicates the A quick shot at a certain time. It is The target source is The impact signal at . The first Block noise vector. is the array element spacing.

[0078] S32. Similarly, the array on the Y axis receives the signal Expressed as:

[0079] ;

[0080] in is the space-time steering vector in the Y-axis direction. is the noise vector in the Y-axis direction. Indicates the The target source is The impact signal at yes The transpose of the spatial steering vector corresponding to the Y-axis matrix of the dimension.

[0081] S33, according to the obtained X-axis and Y-axis array received signals, the corresponding covariance matrix is ​​obtained. Assuming that the target source signal is uncorrelated with the noise, the covariance matrix in the X-axis direction is :

[0082] ;

[0083] in It is the expectation operation. Is the first signal in the X-axis array receiving signal The receiving signal of the block. is the conjugate transpose. is the signal covariance matrix, is the noise covariance matrix. is the noise variance. yes The unit array.

[0084] S34, the covariance matrix in the Y-axis direction is obtained as follows: :

[0085] ;

[0086] in It is the first signal in the Y-axis array receiving signal The receiving signal of the block.

[0087] S35, then vectorize the covariance matrix of the X axis and Y axis into vector form and .

[0088] ;

[0089] .

[0090] S4. Construct the array manifold steering vector of the X-axis array along the X-axis angle domain and frequency domain expansion direction , the array manifold steering vector of the Y-axis array along the Y-axis angle domain and frequency domain expansion direction .

[0091] The step S4 specifically includes the following steps:

[0092] S41, space-time guidance vector Find the expectation and the space-time steering matrix after the expectation ;make ,in is the X-axis center angle, is the center frequency, is the space-time steering vector, For vectorized operations, is the space-time steering vector, is the conjugate transpose, is the space-time steering vector after the desired value is obtained, is the space-time steering matrix after the expectation is obtained.

[0093] S42, will Expand along the X-axis angle domain and frequency domain expansion direction to obtain the expanded space-time steering matrix after the expectation .

[0094] ;

[0095] in, is the number of grid points in the angle domain discretized along the X-axis direction, is the number of frequency domain discretization grid points, , After vectorization The form of expansion along the angle domain and frequency domain is , represents the spatial dimension, yes The simplified form of yes At the discretized grid points The space-time steering vector after single expectation at represents the discretized grid points in the angle domain of the X-axis array direction, Represents the discretized frequency points in the frequency domain.

[0096] S43, array manifold expanded in the angular and frequency domains along the Y-axis for:

[0097] ;

[0098] in yes The simplified form of yes At the discretized grid points The space-time steering vector after single expectation at Represents the discretized grid points in the angular domain of the array direction along the Y-axis.

[0099] S5. Construct the optimization problem of low-rank matrix recovery and then substitute and 、 , to solve the angular frequency spatial spectrum matrix of the X-axis and Y-axis respectively and .

[0100] The step S5 specifically includes the following steps:

[0101] S51, according to the angular frequency spatial spectrum matrix The low rank property of the matrix is ​​solved by constructing an optimization problem for low rank matrix recovery to solve the angular frequency spatial spectrum matrix to be estimated on the XZ plane. , the objective function is as follows:

[0102] ;

[0103] in is the angular frequency spatial spectrum matrix to be estimated The sum of the eigenvalues ​​of . yes No. eigenvalues, represents the nuclear norm operation, is the X-axis covariance matrix in vector form, is the noise covariance matrix in vector form, To expand along the X-axis angle domain and frequency domain expansion direction, the expanded array manifold steering vector is obtained. For vectorized operations. yes 、 The minimum value in is the number of grid points in the angle domain discretized along the X-axis direction, is the number of grid points in the frequency domain. The solution of the above equation can be transformed into a convex optimization problem using convex optimization technology.

[0104] S52, Order , we can get the following constrained optimization problem:

[0105] ;

[0106] in . is the iteration matrix, is the regularization parameter, is the angular frequency spatial spectrum matrix to be estimated, The covariance matrix of the array received signal in vector form, is the array received signal covariance matrix, is the identity matrix.

[0107] S53, transform the constrained optimization problem of step S52 into an augmented Lagrangian expression:

[0108] ;

[0109] in is the dual variable, represents the augmented Lagrangian expression. represents the square operation of the two-norm, Express request F The square operation of the norm, is a penalty item, is a vectorized operation. In order to solve this optimization problem, the alternating direction method of multipliers (ADMM) is used to minimize the augmented Lagrangian expression of each variable to obtain the solution of each equation. As the iteration stopping condition, is a smaller threshold value (e.g. ), and finally solve it by iteration The approximate value of Indicates the The angular frequency spatial spectrum matrix to be estimated under the iteration, Express request F Norm operation, Indicates the number of iterations.

[0110] S54: Repeat steps S51 to S53 using the Y axis matrix to obtain the angular frequency spatial spectrum matrix on the YZ plane. .

[0111] Then we get the angular frequency spatial spectrum matrix in the X and Y axis directions and , which contains all the parameters of the target source to be estimated, including the central angles of the two target sources corresponding to the X-axis subarray and , the two target source center angles corresponding to the Y-axis sub-array , the center frequencies of the two target sources corresponding to the X-axis subarray and , the center frequencies of the two target sources corresponding to the Y-axis sub-array and . Figure 3 (a) is the X-axis real angular frequency spatial spectrum set in an embodiment of the present invention; Figure 3 (b) is a Y-axis real angular frequency spatial spectrum diagram set in an embodiment of the present invention; Figure 3 (c) is an angular frequency space spectrum of the X-axis estimation restored in an embodiment of the present invention; Figure 3 (d) is the angular frequency spatial spectrum of the Y-axis estimated image recovered in the embodiment of the present invention. The angular frequency spatial spectrum estimate needs to be split into separate target sources so that they can be paired to form the final estimate.

[0112] It should be noted that the present invention decomposes the DOA estimation problem of a two-dimensional broadband incoherent distribution source into two one-dimensional DOA estimation problems by decomposing the L-shaped array into two orthogonal uniform linear arrays. Based on the signals received from the X-axis and Y-axis, the low-rank recovery method is combined to recover the two angular frequency spatial spectrum matrices from the covariance matrix, and two sets of key parameters are extracted from the two angular frequency spatial spectrum matrices for matching.

[0113] Compared to other methods, the method provided in this embodiment decomposes the three-dimensional parameter estimation problem into two two-dimensional parameter estimation problems. By solving the angular frequency spatial spectrum to extract key parameters, only two one-dimensional DOA estimation problems need to be solved, reducing the dimensionality and eliminating the need for additional preprocessing such as frequency domain focusing or smoothing. There is no need to pre-determine the signal distribution shape, avoiding the multi-dimensional search required by traditional methods.

[0114] Next, let’s briefly introduce the principle of the low-rank recovery algorithm here: take the estimation problem of the array along the X-axis as an example. Assuming that the target source signal is uncorrelated with the noise, the covariance matrix of the array received signal is for:

[0115] ;

[0116] in Represents the X-axis array receiving signal model, The first Block receiving signal .

[0117] in It is the expectation operation. is the conjugate transpose. is the signal covariance matrix, is the noise covariance matrix. is the noise variance. yes The signal covariance matrix Expressed as:

[0118] ;

[0119] in , represents the joint angular frequency distribution of the target sources. is the space-time steering matrix after the expectation is obtained, represents the space-time steering vector, represents the conjugate transpose of the space-time steering vector, Indicates the The target source is The angular frequency spatial spectrum function at represents the center frequency of the target source, Indicates the central angle corresponding to the X-axis array direction, and Respectively represent The power distribution function of each target source in the angle domain and frequency domain. Similarly, the covariance matrix of the array signal in the Y-axis direction can be obtained through step S34, and then used to restore the angular frequency spatial spectrum matrix. In order to more conveniently solve the double integral, the frequency domain and angle domain are first discretized into a grid. The discretization approximation is:

[0120] ;

[0121] in and The discretized grids representing the angle and frequency domains, is the number of grid points in the angle domain discretized along the X-axis direction, is the number of frequency domain discretization grid points, is the number of target sources, Indicates the The angular frequency spatial spectrum matrix of the target source, represents the angular frequency spatial spectrum matrix containing all target sources, Represents the spatial dimension. , and They are and The discretized form of , and then approximate the vectorized formula by discretizing the integral:

[0122] ;

[0123] in Indicates The discretized angular frequency space spectrum function at , Indicates The space-time steering vector after single expectation at represents the noise covariance matrix in vector form, Find the expected space-time steering matrix, Find the desired space-time steering vector. 、 and is the matrix R, and The vectorized form of . yes After vectorization The form of expansion along the angle domain and frequency domain. The low rank of , so by solving the rank minimization problem in step S51, we can get The solution.

[0124] S6, angular frequency spatial spectrum matrix recovered from the X axis Extract the X-axis center angle , and the corresponding X-axis center frequency and spectrum .

[0125] The step S6 specifically includes the following steps:

[0126] S61, the angular frequency spatial spectrum matrix in the X-axis direction Segment the image into separate target sources, which makes pairing easier. Assuming that the target sources do not completely overlap (at least not affecting the extraction of key parameters), use image segmentation and clustering methods (for example, using the K-means clustering algorithm to achieve image segmentation [Dhanachandra, N., Manglem, K. and Chanu, YJ, 2015. Image segmentation using K-means clustering algorithm and subtractive clustering algorithm. Procedia Computer Science , 54 , pp.764-771.]) The angular frequency spatial spectrum matrix can be Split into , Represents the angular frequency spatial spectrum matrix of the first target source estimated by the X-axis array, Represents the angular frequency spatial spectrum matrix of the second target source estimated by the X-axis array.

[0127] S62, the angular frequency spatial spectrum in the X-axis direction Substituting the following formula, we can calculate a set of central angles of the X axis :

[0128] ;

[0129] in and Respectively represent The X-axis angle range of interest and the frequency range of interest of the target source can be obtained by calculating the above formula to obtain the X-axis center angle . Represents the angular frequency spatial spectrum matrix at the discretized grid points The amplitude at Indicates the first target source center angle estimated by the X-axis array, Indicates the second target source center angle estimated by the X-axis array.

[0130] S63, the angular frequency spatial spectrum in the X-axis direction Substituting the following formula, we can calculate a set of center frequencies of the X axis :

[0131] ;

[0132] Then the X-axis center frequency can be obtained , Indicates the center frequency of the first target source estimated by the X-axis array. Indicates the center frequency of the second target source estimated by the X-axis array.

[0133] In order to facilitate the calculation of similarity, the X-axis direction The angular frequency spatial spectrum of each target source is normalized into a vector, and the normalized spectrum in the X-axis direction is obtained, which is defined as:

[0134] ;

[0135] in Indicates the X-axis matrix estimation The normalized spectrum of the target source, is the center frequency, Indicates that the spectrum will be normalized Each row is added up, Indicates the number of target sources; Indicates the X-axis The grid point range of the target source distribution, yes The corresponding length, is the row index.

[0136] S7, angular frequency spatial spectrum recovered from the Y axis Extracting the Y-axis center angle and the corresponding Y-axis center frequency and spectrum includes the following steps:

[0137] S71. Split the recovered angular frequency spectrum along the Y axis into separate target sources to facilitate pairing. Assuming that the target sources do not completely overlap (at least not affecting the extraction of key parameters), use image segmentation and clustering methods, such as the K-means clustering algorithm [Dhanachandra, N., Manglem, K. and Chanu, YJ, 2015. Image segmentation using K-means clustering algorithm and subtractive clustering algorithm. Procedia Computer Science , 54 , pp.764-771.] , split into , Represents the angular frequency spatial spectrum matrix of the first target source estimated by the Y-axis array, Represents the angular frequency spatial spectrum matrix of the second target source estimated by the Y-axis array.

[0138] S72, the angular frequency spatial spectrum in the Y-axis direction Substituting the following formula, we can calculate a set of central angles of the Y axis :

[0139] ;

[0140] in represents the discretized grid points in the angle domain of the Y-axis array direction, Discrete frequency points in the frequency domain, Represents the angular frequency spatial spectrum matrix at the discretized grid points The amplitude at and Respectively represent The Y-axis angle range of interest and the frequency range of interest of the target source. Then the Y-axis center angle can be obtained , Indicates the first target source center angle estimated by the Y-axis array, Indicates the second target source center angle estimated by the Y-axis array.

[0141] S73, the angular frequency spatial spectrum in the Y-axis direction Substituting the following formula, we can calculate a set of center frequencies of the Y axis :

[0142] ;

[0143] Then calculate the Y-axis center frequency using the above formula , Indicates the center frequency of the first target source estimated by the Y-axis array. Indicates the center frequency of the second target source estimated by the Y-axis array.

[0144] In order to facilitate the calculation of similarity, the angular frequency spatial spectrum of the target source in the Y-axis direction is normalized into a vector, that is, the normalized spectrum in the Y-axis direction is obtained, which is defined as:

[0145] ;

[0146] in Indicates the Y-axis matrix estimation The normalized spectrum of the target source, is the center frequency, Indicates that the spectrum will be normalized Each row is added up, Indicates the Y axis The grid point range of the target source distribution. They are The corresponding length, is the row index.

[0147] S8. Sort the center frequencies from high to low, determine whether the distance between the center frequencies of different target sources on the X-axis is greater than a threshold, and determine the number of possible target sources with close center frequencies. The purpose is to determine the number of target sources that need to be paired using center frequencies and the number of target sources that need to be paired using spectrum similarity, and perform pairing to determine a corresponding set of two-dimensional matching angles.

[0148] S81, when the distance between the center frequencies of different target sources on the X axis is greater than the threshold When , it is considered that the center frequencies of the various sources do not overlap. Pairing is performed based on the Euclidean distance between the center frequencies of the X-axis and the Y-axis. The center frequency with the smallest Euclidean distance can be determined as the corresponding set of two-dimensional matching angles, which specifically includes the following steps:

[0149] S811. First, sort the estimated X-axis center frequencies from high to low. , the corresponding central angles are also arranged in order .

[0150] S812, calculate the distance between the center frequencies of each source in the X-axis direction, and determine that the number of possible sources with close center frequencies is 2. Use the set threshold ( is the grid spacing of the frequency) to determine whether the center frequencies overlap. Since the frequency change of the X-axis is almost the same as that of the Y-axis, only the center frequency of the X-axis is needed for judgment. When , it means that the estimated center frequencies do not overlap and can be clearly distinguished, the number of possible target sources with non-similar center frequencies on the X axis is determined to be 0, and the estimated two-dimensional angle can be automatically matched according to the order of the center frequencies. The center frequency distance between the X-axis source and the Y-axis source is calculated according to the following formula, and the ones with the closest distance are a pair of paired sources:

[0151] ;

[0152] in Indicates the Y-axis uniform linear array corresponding to the estimated The center frequency of the target source that needs to be frequency matched, Indicates the first estimated value of the X-axis uniform linear array The center frequency of the target source, Indicates the first estimated value of the X-axis uniform linear array The center frequency of the target source.

[0153] S813: According to the sorting labels of the frequency matching, a corresponding set of two-dimensional matching angles can be determined. , Indicates the first value estimated by the matched X-axis uniform linear array The target source center angle. Indicates the first value estimated by the matched Y-axis uniform linear array The target source center angle.

[0154] S82, when the distance between the X-axis center frequencies is less than the threshold hour, Indicates the first estimated value of the X-axis uniform linear array The center frequency of the target source, Indicates the X-axis uniform linear array estimated and the The target source is different target source center frequencies, it is considered that there is a target source with a relatively close center frequency. By comparing the spectrum similarity of each target source on the X axis with that on the Y axis, The pairing is performed. The pair with the greatest similarity is the corresponding set of two-dimensional matching angles, which specifically includes the following steps:

[0155] S821, calculate the distance between the center frequencies of each target source in the X-axis direction, and determine that the number of target sources with similar center frequencies is 2. When , it means that the center frequencies of the target sources are close to each other. Using center frequency pairing will easily lead to errors, resulting in mismatch of the two-dimensional center angle.

[0156] S822. Pairing is performed using the spectrum according to the following formula:

[0157]

[0158] in For the The pairing index of the target source. Indicates the number of target sources with similar center frequencies. It is used to measure the target source and The specific expression of the spectrum similarity between target sources is:

[0159]

[0160]

[0161] in 、 are the normalized spectra estimated for the X-axis and Y-axis uniform linear arrays, represents the center frequency, represents the number of discretized frequency points, Representative Discrete frequency points. and represent and The amplitude corresponding to the frequency point in . is a function for calculating spectral similarity. Through the above calculation, we can get the spectrum similarity between the first source on the X axis and the first and second target sources on the Y axis respectively. and , comparing the spectrum similarity between the first target source on the X axis and the first and second target sources on the Y axis is and , Shows the spectrum of the first target source on the X-axis and the second target source of the Y axis The greatest similarity.

[0162] S823: Sorting labels based on spectrum similarity matching , so the Y axis can be determined and Y axis is a corresponding set of matching angles.

[0163] Figure 4 This is a pairing result diagram using 100 repeated experimental tests, showing the first target source and the second target source respectively. Figure 5 This is the pairing result diagram. The simulation scenario is a signal-to-noise ratio of 5dB. T =2400, M =12. Figure 6 This is the RMS error simulation result diagram using 100 repeated experiments with different signal-to-noise ratios. The simulation scenario is T =2400, M =12.

[0164] S9. Mark the matched angle index , remove the already matched angles, and reorder the remaining target sources until all target sources are calculated. Indicates the first value estimated by the matched X-axis uniform linear array The target source center angle. Indicates the first value estimated by the matched Y-axis uniform linear array The target source center angle.

[0165] The step S9 specifically includes the following steps:

[0166] S91, mark the matched angle index, and convert the original two-dimensional angle Relabel the 2D angle that correctly matches the first target source as If a matching error occurs, such as Figure 5 , then the first target source of the error match is .

[0167] S92: Remove the already matched center angle and center frequency of the target source, reorder the center frequency and center angle of the remaining target source, and repeat step S8 to obtain another pair of two-dimensional angles that correctly match the second target source. Then the two-dimensional angle of the two correctly matched target sources is If a matching error occurs, such as Figure 5 , then the wrong matching second target source is , then the two-dimensional angle of the two correctly matched target sources is .

[0168] S93. Reorder the remaining target sources until all target sources are calculated.

[0169] It should be noted that the above is a specific description of the preferred embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. The above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make various equivalent modifications or substitutions without departing from the scope of protection of the present invention and the claims. These equivalent modifications or substitutions all fall within the scope of protection of the present invention.

Claims

1. A two-dimensional parameter estimation method for broadband incoherent distributed sources based on spectrum matching, characterized in that: The following steps are involved: Decompose the L-shaped array into two orthogonal uniform linear arrays, and receive the signal transmitted by the target source through the two mutually orthogonal uniform linear arrays respectively; Based on the signals respectively received by two mutually orthogonal uniform linear arrays, the angular frequency spatial spectrum matrices are respectively recovered from the covariance matrices of the received signals of the two mutually orthogonal uniform linear arrays in combination with a low-rank recovery method, and key parameters are respectively extracted from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays for matching to obtain a corresponding set of two-dimensional matching angles; the method of recovering the angular frequency spatial spectrum matrices from the covariance matrices of the received signals of the two mutually orthogonal uniform linear arrays in combination with the low-rank recovery method includes the following steps: (1) Find the covariance matrix corresponding to two mutually orthogonal uniform linear arrays and convert the covariance matrix into vector form; (2) Constructing array manifold steering vectors corresponding to two mutually orthogonal uniform linear arrays; (3) Constructing the optimization problem of low-rank matrix recovery, the angular frequency spatial spectrum matrices corresponding to two mutually orthogonal uniform linear arrays are solved respectively through the vector form of step (1) and the array manifold steering vector of step (2); Extracting key parameters from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays respectively comprises extracting the center angle and the corresponding center frequency, as well as the corresponding normalized spectrum vector, from the angular frequency spatial spectrum matrices corresponding to the two mutually orthogonal uniform linear arrays respectively; determining the number of target sources with similar center frequencies by judging whether the center frequency spacing between any two target sources in the uniform linear array is greater than a set threshold; Target source pairing is performed based on the number of target sources with similar center frequencies, specifically including: (a) Sort the center frequencies of the target sources in the same uniform linear array from high to low, and adjust the corresponding center angle order simultaneously; (b) Select the pairing method based on the number of target sources with similar center frequencies: (b1) If there is no target source with a similar center frequency, all target sources are paired using their center frequencies; (b2) If there are target sources with similar center frequencies, the target sources are paired based on spectrum similarity, and the remaining target sources are paired based on center frequencies; The pairing by spectrum similarity is performed by the following formula: in For the The paired index of the target source, Indicates the number of target sources with similar center frequencies, is the correlation coefficient, which is used to measure the target source and The degree of spectral similarity between target sources; is the number of target sources, Indicates the first The center frequency of the target source that needs to be frequency matched, Indicates the first The center frequency of the target source, Indicates another uniform linear array corresponding to the The target source is different The center frequency of the target source, Indicates the operation of finding the Euclidean norm; Indicates the set threshold; according to the pairing index of spectrum similarity, a corresponding set of two-dimensional matching angles is determined; Remove the target source pairs that have passed the matching and rematch the remaining target sources until all target sources are calculated.

2. The method for estimating two-dimensional parameters of broadband incoherent distributed sources based on spectrum matching according to claim 1, wherein: In step (3), if there is a target source pair whose center frequency spacing is greater than the threshold, it is determined that the center frequencies of the target source pair do not overlap; If there exists a target source pair whose center frequency interval is less than or equal to the threshold, it is determined that the center frequencies of the target source pair are close.

3. The method for estimating two-dimensional parameters of broadband incoherent distributed sources based on spectrum matching according to claim 1, wherein: The pairing using the center frequency includes: Calculate the Euclidean distance between the center frequencies of the target sources of two uniform linear arrays; A group of target sources with the smallest Euclidean distance is determined as paired target sources.

4. The method for estimating two-dimensional parameters of broadband incoherent distributed sources based on spectrum matching according to claim 1, wherein: The step of removing the already matched target sources and rematching the remaining target sources is as follows: removing the center angles and center frequencies of the already matched target sources, reordering the center frequencies and corresponding center angles of the remaining target sources, and selecting a pairing method according to step (b) to perform pairing based on the reordering result.

5. A computer device comprising a memory and a processor, wherein the memory is electrically connected to the processor, and the memory stores a computer program, wherein: When the computer program is executed by the processor, the processor is enabled to implement the method according to any one of claims 1 to 2.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method according to any one of claims 1 to 2.

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