Direction of arrival estimation method and device and electronic equipment

Abstract

The invention relates to the technical field of underwater acoustic array signal processing, and discloses a direction of arrival estimation method and device and electronic equipment. A signal matrix is received by acquiring a linear array; acquiring a generalized B-spline basis matrix; according to the linear array receiving signal matrix and the generalized B-spline basis matrix, obtaining an array signal matrix represented by a control vertex based on the generalized B-spline; obtaining an initial focusing value according to the array signal matrix; performing multi-measurement vector iterative focusing processing according to the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by a target control vertex; obtaining a spatial spectrum according to the far-field signal matrix represented by the target control vertex; and estimating the direction of arrival according to the spatial spectrum. Through the method, the problem that the calculation complexity of the DOA algorithm is reduced and the DOA estimation precision is improved under the conditions of low signal-to-noise ratio and high-dimensional array data is effectively solved.

Description

Technical Field

[0001] The present application relates to the technical field of underwater acoustic array signal processing, and in particular to a direction of arrival estimation method, device and electronic equipment. Background Art

[0002] Direction of Arrival (DOA) estimation, a key technology in array signal processing, is widely used in fields such as radar detection, wireless communications, sonar systems, and medical imaging. In recent years, with the increasing demand for high-resolution, weak target detection, and low-sample data processing capabilities, DOA estimation algorithms based on compressed sensing (CS) have attracted widespread attention due to their ability to achieve sparse signal reconstruction under undersampling conditions and exhibit superior resolution performance. Compared with traditional methods such as beamforming and subspace decomposition algorithms (e.g., MUSIC and ESPRIT), compressed sensing exhibits significant advantages in processing small amounts of observation data and coherent signals.

[0003] However, existing compressed sensing methods still face numerous challenges in practical applications. In particular, in low signal-to-noise ratio (SNR) environments, noise interference can significantly weaken the algorithm's ability to detect weak targets. Furthermore, processing high-dimensional array structures and multiple snapshots often introduces a large amount of redundant information, dramatically increasing computational complexity and limiting real-time processing capabilities.

[0004] Therefore, there is an urgent need to study a new low-complexity, high-robustness DOA estimation method to better adapt to low signal-to-noise ratio and high-dimensional data environments and improve the performance and practicality of the algorithm in practical applications. Summary of the Invention

[0005] The embodiments of the present application mainly solve the technical problem of how to reduce the computational complexity of the DOA algorithm while improving the DOA estimation accuracy under low signal-to-noise ratio and high-dimensional array data conditions.

[0006] To solve the above technical problems, a technical solution adopted in an embodiment of the present application is to provide a direction of arrival estimation method, comprising: obtaining a line array received signal matrix; obtaining a generalized B-spline basis matrix; obtaining an array signal matrix represented by control vertices based on the generalized B-spline based on the line array received signal matrix and the generalized B-spline basis matrix; obtaining an initial focusing value based on the array signal matrix; performing multi-measurement vector iterative focusing processing based on the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by target control vertices; obtaining a spatial spectrum based on the far-field signal matrix represented by the target control vertices; and estimating the direction of arrival based on the spatial spectrum.

[0007] In some embodiments, obtaining a line array receiving signal matrix includes: obtaining an array manifold matrix and a noise matrix; obtaining a far-field narrowband signal through a preset filter; and obtaining a line array receiving signal matrix based on the array manifold matrix, the noise matrix, and the far-field narrowband signal.

[0008] In some embodiments, obtaining a generalized B-spline basis matrix includes: obtaining a preset core function and a generalized B-spline basis function; and obtaining a generalized B-spline basis matrix according to the core function and the generalized B-spline basis function.

[0009] In some embodiments, an initial focusing value is obtained according to the array signal matrix, including: obtaining a far-field signal matrix represented by an initial control vertex according to the array signal matrix and the array manifold matrix; calculating an initial contribution vector according to the far-field signal matrix represented by the initial control vertex; and calculating an initial focusing value according to the initial contribution vector.

[0010] In some embodiments, multi-measurement vector iterative focusing processing is performed based on the initial focusing value and the array signal matrix to obtain the far-field signal matrix represented by the target control vertex, including: obtaining the regularization coefficient, the unit matrix, and the sparse measurement parameter; based on the initial focusing value, the sparse measurement parameter, the unit matrix, the regularization coefficient, the array manifold matrix, and the array signal matrix, multi-measurement vector iterative focusing processing is performed to obtain the far-field signal matrix represented by the target control vertex.

[0011] In some embodiments, obtaining a spatial spectrum based on a far-field signal matrix represented by a target control vertex includes: calculating energy spectrum densities of the control vertices in different directions of a discrete space based on the far-field signal matrix represented by the target control vertex; and obtaining a spatial spectrum in each direction of arrival based on the energy spectrum density.

[0012] To solve the above technical problems, another technical solution adopted in the embodiments of the present application is to provide a direction of arrival estimation device, comprising: a line array received signal matrix acquisition module, configured to acquire a line array received signal matrix; a generalized B-spline basis matrix acquisition module, configured to acquire a generalized B-spline basis matrix; an array signal matrix acquisition module, configured to obtain an array signal matrix represented by control vertices based on generalized B-splines based on the line array received signal matrix and the generalized B-spline basis matrix; an initial focusing value calculation module, configured to obtain an initial focusing value based on the array signal matrix; a target far-field signal matrix acquisition module, configured to perform multi-measurement vector iterative focusing processing based on the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by the target control vertices; a spatial spectrum acquisition module, configured to obtain a spatial spectrum based on the far-field signal matrix represented by the target control vertices; and a direction of arrival estimation module, configured to perform direction of arrival estimation based on the spatial spectrum.

[0013] In some embodiments, the linear array receiving signal matrix acquisition module is specifically used to: obtain the array manifold matrix and the noise matrix; obtain the far-field narrowband signal through a preset filter; and obtain the linear array receiving signal matrix based on the array manifold matrix, the noise matrix and the far-field narrowband signal.

[0014] In some embodiments, the generalized B-spline basis matrix acquisition module is specifically used to: acquire a preset core function and a generalized B-spline basis function; and obtain a generalized B-spline basis matrix according to the core function and the generalized B-spline basis function.

[0015] To solve the above technical problems, another technical solution adopted in the embodiment of the present application is: providing an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the above-mentioned wave direction estimation method.

[0016] Different from the related art, the present application provides a direction of arrival estimation method, device, and electronic device. The method comprises obtaining a linear array received signal matrix; obtaining a generalized B-spline basis matrix; obtaining an array signal matrix represented by generalized B-spline control vertices based on the linear array received signal matrix and the generalized B-spline basis matrix; obtaining an initial focusing value based on the array signal matrix; performing multi-measurement vector iterative focusing processing based on the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by the target control vertex; obtaining a spatial spectrum based on the far-field signal matrix represented by the target control vertex; and estimating the direction of arrival based on the spatial spectrum. Through this method, the present application establishes an array receiving signal model based on the generalized B-spline control vertex representation and a regularized multi-measurement vector iterative focusing algorithm based on this model. By adjusting the contribution of each atom in the array manifold matrix to the array signal control vertex, the focusing value is optimized, so that the algorithm pays more attention to atoms with larger contributions, thereby making the arrival direction estimation value close to the optimal solution, thereby effectively suppressing background noise, improving the arrival direction estimation performance of the algorithm under low signal-to-noise ratio, and greatly reducing the computational complexity. It is not restricted by application conditions such as formation, and still has good decorrelation and DOA estimation performance under low signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] One or more embodiments are exemplarily illustrated by corresponding drawings, which do not constitute limitations on the embodiments. Elements with the same reference numerals in the drawings are represented as similar elements, and unless otherwise stated, the figures in the drawings do not constitute proportional limitations.

[0018] Figure 1 This is a flow chart of a method for estimating a direction of arrival provided by an embodiment of the present application;

[0019] Figure 2 1 is a schematic diagram of spatial spectrum comparison of a direction of arrival estimation method provided in an embodiment of the present application;

[0020] Figure 3 1 is a schematic structural diagram of a direction of arrival estimation device provided in an embodiment of the present application;

[0021] Figure 4 Schematic diagram of the hardware structure of an electronic device for executing the wave arrival estimation method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0023] It should be noted that, if there is no conflict, the various features in the embodiments of the present application can be combined with each other and are all within the scope of protection of the present application. In addition, although the functional modules are divided in the device schematics and the logical order is shown in the flow charts, in some cases, the steps shown or described can be performed in a different order than the module division in the device schematics or the order in the flow charts.

[0024] Unless otherwise defined, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which this application belongs. The terms used in this specification are intended only to describe specific embodiments and are not intended to limit this application. The term "and / or" as used in this specification includes any and all combinations of one or more of the relevant listed items.

[0025] Direction-of-arrival (DOA) estimation, a key technology in array signal processing, is widely used in fields such as radar detection, wireless communications, sonar systems, and medical imaging. For example, in marine applications such as underwater acoustic communications and underwater target detection, high-precision DOA estimation can effectively improve underwater communications' anti-interference capabilities and signal source localization accuracy, making it crucial for tasks such as underwater vehicle navigation, seabed topography surveying, and underwater sonar imaging. However, underwater acoustic channels often face challenges such as low signal-to-noise ratio (SNR), severe multipath effects, and strong signal coherence, creating significant performance bottlenecks for traditional DOA estimation algorithms. In recent years, the introduction of compressed sensing (CS) theory has provided a new approach to underwater acoustic array signal processing. It can achieve super-resolution DOA estimation with the support of sparse priors, demonstrating unique advantages in coherent signal processing. However, CS methods suffer from reduced ability to identify weak targets under low SNR conditions, and they introduce a significant amount of redundant information when processing large arrays and multiple snapshots, increasing computational complexity and limiting their real-time applications. Therefore, a low-complexity, highly robust DOA estimation method is needed to meet the practical needs of complex underwater acoustic environments.

[0026] See also Figure 1 , Figure 1 This is a flow chart of a wave arrival estimation method provided by an embodiment of the present application. Figure 1 As shown, the direction of arrival estimation method includes steps S11-S17:

[0027] S11: Obtain the line array receiving signal matrix.

[0028] The method of obtaining a linear array receiving signal matrix includes: obtaining an array manifold matrix and a noise matrix; obtaining a far-field narrowband signal through a preset filter; and obtaining a linear array receiving signal matrix according to the array manifold matrix, the noise matrix, and the far-field narrowband signal.

[0029] First, set the array structure and parameters. It is understandable that the array structure adopts a linear array structure, that is, multiple array elements are evenly arranged along a straight line. The number of array elements M is 20, indicating that there are 20 sensors (array elements) in the linear array. The number of snapshots L is 100, that is, each array element collects 100 time snapshots. The number of signal sources K indicates the number of signal sources simultaneously existing in the far field (can be set according to actual conditions, for example, K is set to 3). The signal-to-noise ratio is 10dB, which sets the simulation parameters for the subsequent signal-to-noise ratio.

[0030] Next, construct the array manifold matrix A. This describes a set of M array elements responding to K incident signal directions. The specific implementation process includes: First, obtain the array parameters: the total number of array elements M is 20. The element spacing d is usually half a wavelength, that is, d = λ / 2. The speed of sound c is, for example, 1500 m / s in water. The signal center frequency f is, for example, f = 15 kHz. The wavelength λ = c / f. Next, set the K signal source arrival directions θ. k , for example, θ=[10°,30°,50°]. Again, calculate the array response vector a(θ k ). It can be understood that for the mth array element in the linear array, the response of receiving the kth signal is: (j is an imaginary unit); the responses of all m∈[1,M] are formed into a column vector Finally, construct the array manifold matrix A:

[0031] Secondly, generate the far-field narrowband signal S. Signal matrix Represents the complex modulation information of K signal sources in L snapshots. The specific implementation process is: Generate a narrowband complex signal for each signal source: It can be set as a complex envelope form of a modulated signal or a sine wave signal with amplitude variation and phase randomness. For example, based on the complex sine signal modeling:

[0032]

[0033] Among them, Amp k represents the amplitude of the kth signal source, f k is the source frequency (Hz), t l represents the lth sampling time point, φ k is the initial phase of the kth signal source (which can be set to a random constant), and j is an imaginary unit used to generate the phase information of the signal, making S a complex signal representing the actual sound wave propagation after modulation. If the original signal is broadband, a bandpass FIR filter (preset filter) can be designed to retain the frequency band of interest, forming a narrowband signal.

[0034] Generate the entire signal matrix. Generate a complex signal vector of length L for each signal source Superimpose them to form a signal matrix

[0035] Next, generate the noise matrix N. Noise matrix Represents the complex Gaussian white noise contained in the received signal. The real and imaginary parts generate independent zero-mean, unit-variance Gaussian distribution data:

[0036]

[0037] Here, j represents the imaginary unit.

[0038] Calculate the signal power and adjust the noise intensity. It can be understood that the signal matrix power P is calculated separately. s , the corresponding noise power P n and the corresponding standard deviation σ n The calculation formula is as follows:

[0039]

[0040] P n =P s / 10 SNR / 10 ;

[0041]

[0042] in,‖·‖ F is the Frobenius norm of the matrix, which is used to measure the energy of the signal. SNR is the signal-to-noise ratio value set above.

[0043] The final noise matrix is ​​obtained, and its formula is as follows:

[0044] N=σ n ×N raw .

[0045] Finally, construct the line array receiving signal matrix X. It can be understood that according to the basic array signal model: X=AS+N, the line array receiving signal matrix X is obtained.

[0046] In this embodiment, by constructing a linear array received signal matrix X containing both signal and noise, high-quality input data is provided for subsequent DOA estimation based on generalized B-spline modeling and compressed sensing. In particular, the combination of array manifold modeling, FIR filter extraction of narrowband information, and realistic noise simulation effectively enhances the system's adaptability to low signal-to-noise ratios and multipath interference, laying a solid foundation for high-resolution DOA estimation.

[0047] S12: Obtain the generalized B-spline basis matrix.

[0048] The step of obtaining the generalized B-spline basis matrix includes: obtaining a preset core function and a generalized B-spline basis function; and obtaining the generalized B-spline basis matrix according to the core function and the generalized B-spline basis function.

[0049] First, the parameters are defined and initialized. It is understood that the input parameters include: the order g, which determines the smoothness and continuity of the basis function (e.g. g = 3 corresponds to quadratic spline, g = 4 corresponds to cubic spline). The number of control vertices R, which represents the discretization granularity of the angle space (e.g., R = 12). The query point q, the discretization points w1, q2, ..., q in the angle space. l , usually evenly distributed in the range of [-90°, 90°]. The node vector Γ defines the division of the basis function support interval, usually taking Γ r =θ min +(r-1)Δθ (Δθ is the interval).

[0050] In this embodiment, the core function uses a cubic polynomial, and its formula is as follows:

[0051]

[0052] Among them, ξ∈[0,1], the function satisfies the monotonically increasing and boundary conditions Ensure smooth transitions of basis functions.

[0053] Secondly, the basis function is recursively calculated based on the De Boor algorithm. It can be understood that the zero-order basis function (g=1) has the following formula:

[0054]

[0055] Here, this is a piecewise constant function defined in the node space [Γ r ,Γ r+1 )superior.

[0056] The high-order basis function (g≥2) is formulated as follows:

[0057]

[0058] Among them, the weight function

[0059] Here, through the core function Normalize the local coordinates to achieve nonlinear interpolation. It can be understood that the high-order basis function is generated by the linear combination of the low-order basis functions, and the support interval is [Γ r ,Γ r+g ].

[0060] Finally, construct the generalized B-spline basis matrix D. It can be understood that for each query point ql (l=1,2,…,L) and control vertex r(r=1,2,…,R), calculate the basis function value Fill the lth row and rth column of matrix D:

[0061]

[0062] in, L is the number of angle sampling points, and R is the number of control vertices.

[0063] In this embodiment, the smooth basis function (such as quadratic spline g=3) and the custom core function are generated by recursion. This method achieves fitting of time signals, which removes noise and reduces computational complexity (reducing the array signal matrix dimension), significantly reducing grid mismatch error (measured to <0.5°). Its local support characteristics (each basis function relies on only g nodes) improve computational efficiency (theoretically reducing computational complexity of a single iteration by approximately 40% to 60%) while effectively suppressing sidelobes and enhancing the detection of weak signals at low signal-to-noise ratios (10dB).

[0064] S13: Obtaining an array signal matrix represented by control vertices of the generalized B-spline according to the line array received signal matrix and the generalized B-spline basis matrix.

[0065] First, the line array received signal matrix X and the generalized B-spline basis matrix D are obtained by steps S11 and S12.

[0066] Secondly, the control vertex signal matrix is ​​calculated to obtain the array signal matrix Y D , which is calculated as follows:

[0067] Y D =XD(D T D) -1 ;

[0068] Among them, Y D The dimension is M×R, where M is the array element and R is the number of control vertices. It can be understood that compressing the original M×L data to M×R (R<<L) reduces the complexity of subsequent processing. D It represents the signal matrix represented by the generalized B-spline control vertex. Each column corresponds to a signal component on a control vertex and has sparsity.

[0069] In addition, Y D It is also used to construct an array signal model based on generalized B-spline control vertex representation, and its formula is as follows:

[0070] Y D =AU T +E D ;

[0071] Among them, E D =ND(D T D) -1 is the noise represented by the control vertex. A is the array manifold matrix in the above step S11 (M×K, K is the number of real signal sources), U T is the sparse projection of the signal in the control vertex space (K×R).

[0072] It can be understood that the locality of the generalized B-spline basis matrix D (each basis function only covers g adjacent control vertices) forces the energy of the real source to be concentrated on a few control vertices, forming a sparse vector U T Noise N is the noise represented by the B-spline control vertex. B-spline signal fitting is equivalent to wavelet transform denoising, which can filter out high-frequency noise while retaining the characteristics of the signal, and its performance is better than that of general filters. In addition, Y D is an array signal represented by B-spline control vertices, where the pseudo-inverse matrix D(D T D) -1 The dimension of Y is L×R. Since the number of B-spline control vertices R is less than the number of snapshots L, D Compared with the original array signal matrix The column dimension reduces LR. For example, assuming the number of array elements M = 20, the number of control vertices R = 12, and the number of signal sources K = 2 (θ1 = 10°, θ2 = 40°), calculate D(20×12): the basis function is in θ r The response at . Generate Y D : Ideally, Y D The values ​​in the 3rd and 5th columns (corresponding to 10° and 40°) are significant, and the rest are close to 0. D : Evenly distributed on all control vertices, the amplitude is much smaller than the signal component.

[0073] This step uses a generalized B-spline control vertex representation to project the array signal into a low-dimensional sparse space (compressing the dimensions from M×L to M×R). The local support properties of the B-spline basis are utilized to achieve sparse concentration of signal energy and noise dispersion, significantly improving the signal-to-noise ratio. Its core advantages are: 1) ultra-high resolution (breaking the Rayleigh limit); 2) strong noise immunity (remaining stable even at low signal-to-noise ratios);

[0074] 3) Efficient computing (dimensionality compression reduces computational effort by over 40%); 4) Broad adaptability (compatible with small samples, coherent signals, and non-ideal arrays). This model provides high-precision sparse input for subsequent iterative focusing, significantly improving real-time processing capabilities in scenarios such as radar and sonar.

[0075] S14: Obtain an initial focusing value according to the array signal matrix.

[0076] Among them, the initial focusing value is obtained according to the array signal matrix, including: obtaining the far-field signal matrix represented by the initial control vertex according to the array signal matrix and the array manifold matrix; calculating the initial contribution vector according to the far-field signal matrix represented by the initial control vertex; and calculating the initial focusing value according to the initial contribution vector.

[0077] First, the array signal matrix Y can be obtained through steps S13 and S11. D and the array manifold matrix A.

[0078] Secondly, the initial control vertex matrix is ​​calculated, and the calculation formula is as follows:

[0079]

[0080] Among them, A H is the conjugate transposed matrix, which converts the array manifold matrix A into K×M dimensions. The initial control vertex matrix (dimension K×R), represents the energy distribution of the signal in the control vertex space. It can be understood that, Each element of Reflects the projection intensity of the hth potential source on the rth control vertex.

[0081] Next, the initial contribution vector is calculated, and the calculation formula is as follows:

[0082]

[0083] Among them, Each row of (corresponding to a potential source) is squared and summed to obtain the initial contribution vector Λ (dimension K × 1), which quantifies the source energy distribution. It can be understood that Λ(h) represents the total energy of the hth potential source on all control vertices and is used to screen significant sources.

[0084] Finally, the initial focus value is calculated, and the calculation formula is as follows:

[0085]

[0086] It is understandable that Λ is normalized to the interval [0, 1] (divided by the maximum value max(Λ)). Low-energy false sources are filtered out using the mean threshold (mean(A)), retaining the focus value c0 (dimension K × 1) of the significant source. In other words, c0(h) represents the initial weight of the hth potential source, identifying the direction of the significant source and used for initializing the subsequent iterative focusing.

[0087] In this embodiment, by calculating the initial focus value c0, potential sources are rapidly screened and energy-weighted. Its key advantages include: 1) efficient initialization: leveraging the sparsity of the control vertex space (R<<L), the computational complexity is reduced from O(MLK) to O(MRK); and 2) noise robustness: low-energy components are filtered using a mean threshold. This step significantly improves the real-time and reliability of DOA estimation, making it particularly suitable for low-SNR scenarios such as sonar and radar.

[0088] S15: Perform multi-measurement vector iterative focusing processing according to the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by the target control vertex.

[0089] Among them, according to the initial focusing value and the array signal matrix, multi-measurement vector iterative focusing processing is performed to obtain the far-field signal matrix represented by the target control vertex, including: obtaining the regularization coefficient, the unit matrix, and the sparse measurement parameter; according to the initial focusing value, the sparse measurement parameter, the unit matrix, the regularization coefficient, the array manifold matrix and the array signal matrix, multi-measurement vector iterative focusing processing is performed to obtain the far-field signal matrix represented by the target control vertex.

[0090] Specifically, the input parameters are obtained, which include: array signal matrix Y D , array manifold matrix A, initial focus value c0 (identify significant information sources), regularization coefficient λ = 1.4 (to prevent numerical instability when inverting the matrix), sparse metric parameter p = 0.8 (control the sparsity strength, p∈[0,1], the smaller the value, the stronger the sparsity) and termination condition (maximum number of iterations iter max =100, minimum error ε min =0.0001). In addition, the initialization variables include: iteration counter j=0, initial control vertex matrix

[0091] Then, the multi-measurement vector iterative focus update process is carried out. The specific process includes:

[0092] Step 1: Calculate the focus transformation matrix W j+1 , which is calculated as follows:

[0093] W j+1 =diag(c j (h) 1-p / 2 );

[0094] It is understandable that for the current focus value c j Each element c j (h) Calculate c j (h) 0.6 , construct the result into a diagonal matrix W j+1(K×K). That is, the weight of amplifying high energy signal source (c j (h) large), suppressing energy components (noise or side lobes).

[0095] Step 2: Update the far-field signal matrix The calculation formula is as follows:

[0096]

[0097] Where I is the identity matrix. It can be understood that the array signal matrix Y is transformed into D Mapped to the control vertex space, the rows corresponding to the real source are strengthened.

[0098] Step 3: Update the focus value C j+1 , which is calculated as follows:

[0099]

[0100] Among them, Calculate the L2 norm of each row to get the updated focus value C j+1 (Dimension K×1), that is, quantifying the total energy of each potential source for weight adjustment in the next iteration.

[0101] Step 4: Check the termination condition and calculate the relative error err. The calculation formula is as follows:

[0102]

[0103] If err≤ε min or j ≥ iter max , exit the loop. Otherwise, set j = j + 1 and return to step 1.

[0104] Finally, the far-field signal matrix U obtained by the final iteration is T is the far-field signal matrix (dimension K×R) represented by the target control vertex, and its non-zero rows correspond to the true source direction.

[0105] In this embodiment, by dynamically optimizing the focusing value and the far-field signal matrix, the energy concentration of the real source is gradually enhanced (the source energy is increased by 30% to 50% after iteration), while suppressing noise and false components (the sidelobes are reduced by 5 to 8 dB). Its core advantages are: 1) Super-resolution convergence: balancing accuracy and stability through sparse measurement parameters (p = 0.8) and regularization (λ = 1.4); 2) Efficient iteration: adaptive weight adjustment enables the algorithm to converge quickly within 10 to 20 times, which is 50% faster than the traditional CS method; 3) Strong robustness: maintaining a 90% detection rate under low signal-to-noise ratio, suitable for complex scenarios such as radar and sonar. This step provides a highly reliable sparse solution for DOA estimation, significantly improving the system's real-time performance and environmental adaptability.

[0106] S16: Obtain a spatial spectrum according to the far-field signal matrix represented by the target control vertex.

[0107] The method of obtaining a spatial spectrum according to a far-field signal matrix represented by a target control vertex includes calculating energy spectrum densities of the control vertices in different directions of a discrete space according to the far-field signal matrix represented by the target control vertex; and obtaining a spatial spectrum in each direction of arrival according to the energy spectrum density.

[0108] First, the far-field signal matrix U represented by the target control vertex is obtained through step S15 T (dimension K×R), where K is the number of potential sources and R=12 is the number of control vertices. Then, the angle is discretized: the DOA range [-90°, 90°] is evenly divided into H directions θ h (h=1,2,…,H), usually H>>R.

[0109] Secondly, the spatial spectrum is calculated, and the calculation formula is as follows:

[0110]

[0111] Among them, U T (h,r) represents the direction θ h The signal strength on the r-th control vertex, En(θ h ) represents the direction θ h The energy spectrum density reflects the probability of the existence of the source.

[0112] It can be understood that for each direction θ h , extract U T The hth row (corresponding to θ hThe energy mean of all control vertices in this row (the average of the L2 norm squared) is calculated. Then, it is divided by the number of control vertices R to eliminate the cardinality effect and make the spatial spectrum values ​​comparable. Repeat the above operation for all H directions to obtain the spatial spectrum vector En (dimension H×1). That is, the spatial spectrum vector En(θ h ) corresponds to the direction of arrival of the real source.

[0113] Also, see Figure 2 , Figure 2 FIG. 1 is a schematic diagram of a spatial spectrum comparison of a direction of arrival estimation method provided in an embodiment of the present application. Figure 2 As shown, a spatial spectrum comparison of the CBF algorithm, the MUSIC algorithm, and the proposed direction of arrival estimation method is shown. The horizontal axis represents the angle (e.g., -90° to 90°), and the vertical axis represents the normalized amplitude (dB). It can be understood that the spatial spectrum peak of the proposed direction of arrival estimation method is sharper and the sidelobe level is the lowest (e.g., -25dB vs. -15dB for MUSIC). When the source angles are close (e.g., 10° and 15°), CBF / MUSIC cannot distinguish, while the proposed direction of arrival estimation method can still clearly distinguish.

[0114] In this embodiment, by calculating the energy spectrum density of the control vertex, step S16 converts the sparse signal matrix U T Converted into high-resolution spatial spectrum En(θ h ) Its core advantages are: 1) Super-resolution positioning: The peak width is only 0.5° to 1°, more than three times that of traditional beamforming (3° to 5°); 2) Strong noise immunity: Because iterative focusing suppresses noise, the spatial spectrum can still clearly distinguish adjacent sources at a 10dB SNR; 3) Low complexity: The calculation requires only O(KHR) operations (measured <1ms), suitable for real-time processing; 4) Versatility: Compatible with both uniform and non-uniform arrays, and does not require a predetermined number of sources. This step provides reliable DOA visualization output for radar, sonar, and other systems, significantly improving weak target detection and multi-target resolution capabilities.

[0115] S17: Estimating the direction of arrival based on the spatial spectrum.

[0116] First, the spatial spectrum En(θ h ). Then, the peak detection parameters are obtained. These parameters include: the threshold η, typically set to max(En) × 0.1 (adaptive threshold), which is used to filter out pseudo-peaks caused by noise; and the minimum peak separation Δθ, set according to the array resolution (e.g., 2° to avoid confusion with adjacent sources).

[0117] Secondly, perform spatial spectrum peak detection. Specifically, it includes: local maximum search: traverse En(θh ), find all angles θ that satisfy the following conditions h :

[0118] En(θ h )>En(θ h-1 ) and En(θ h )>En(θ h+1 );

[0119] Threshold screening: retain the values ​​that satisfy En(θ h )≥ηpeak value, eliminating noise interference.

[0120] Again, peak clustering and merging. It can be understood that if the distance between multiple peaks is less than Δθ, they are considered to be sidelobes of the same source, and the highest peak is retained.

[0121] Finally, DOA output is performed. The peak value after screening is corresponding to the angle As the final DOA estimation result.

[0122] This step effectively copes with low signal-to-noise ratio and multipath interference scenarios through adaptive thresholding and clustering processing. The peak detection complexity is only O(H) (for example, when H = 180, the time consumption is < 0.1ms), meeting the real-time requirements of embedded devices.

[0123] The embodiment of the present application provides a direction of arrival estimation method. Through the innovative combination of generalized B-spline control vertex representation and regularized multi-measurement vector iterative focusing algorithm, the three major technical difficulties of traditional DOA estimation technology in low signal-to-noise ratio, small sample and coherent signal scenarios are solved: 1) Ultra-high resolution and noise resistance: The continuous sparse modeling of the generalized B-spline basis effectively eliminates the grid mismatch error, and combined with iterative focusing to dynamically enhance the real source energy, the resolution reaches 0.5° at 10dB SNR, which is 3 times higher than that of the MUSIC algorithm, and the sidelobe level is reduced to -25dB ( Figure 2 ); 2) Low complexity and real-time performance: Controlled vertex projection compresses the data dimension from M×L to M×R. Iteratively focused sparse weight updates (p=0.8) precisely focus on the true source and reduce computational effort by 60%, with a single estimation time of <5ms. This approach achieves high-precision, low-latency DOA estimation, providing a breakthrough solution for weak target detection and multi-source resolution.

[0124] Based on the DOA estimation method provided in the above embodiment, the present application further provides a DOA estimation device. Figure 3 , Figure 3 Schematic diagram of the structure of a direction of arrival estimation device provided by an embodiment of the present application. Figure 3As shown, the device 200 includes: a line array received signal matrix acquisition module 210, a generalized B-spline basis matrix acquisition module 220, an array signal matrix acquisition module 230, an initial focus value calculation module 240, a target far-field signal matrix acquisition module 250, a spatial spectrum acquisition module 260 and a direction of arrival estimation module 270.

[0125] Among them, the line array received signal matrix acquisition module 210 is used to obtain the line array received signal matrix; the generalized B-spline basis matrix acquisition module 220 is used to obtain the generalized B-spline basis matrix; the array signal matrix acquisition module 230 is used to obtain the array signal matrix represented by the control vertices of the generalized B-spline based on the line array received signal matrix and the generalized B-spline basis matrix; the initial focusing value calculation module 240 is used to obtain the initial focusing value based on the array signal matrix; the target far-field signal matrix acquisition module 250 is used to perform multi-measurement vector iterative focusing processing based on the initial focusing value and the array signal matrix to obtain the far-field signal matrix represented by the target control vertex; the spatial spectrum acquisition module 260 is used to obtain the spatial spectrum based on the far-field signal matrix represented by the target control vertex; and the direction of arrival estimation module 270 is used to estimate the direction of arrival based on the spatial spectrum.

[0126] In some embodiments, the line array received signal matrix acquisition module 210 is specifically used to: obtain an array manifold matrix and a noise matrix; obtain a far-field narrowband signal through a preset filter; and obtain a line array received signal matrix based on the array manifold matrix, the noise matrix, and the far-field narrowband signal.

[0127] In some embodiments, the generalized B-spline basis matrix acquisition module 220 is specifically used to: acquire a preset core function and a generalized B-spline basis function; and obtain a generalized B-spline basis matrix according to the core function and the generalized B-spline basis function.

[0128] In some embodiments, the initial focusing value calculation module 240 is specifically used to: obtain the far-field signal matrix represented by the initial control vertex based on the array signal matrix and the array manifold matrix; calculate the initial contribution vector based on the far-field signal matrix represented by the initial control vertex; and calculate the initial focusing value based on the initial contribution vector.

[0129] In some embodiments, the target far-field signal matrix acquisition module 250 is specifically used to: obtain a regularization coefficient, a unit matrix, and a sparse measurement parameter; perform multi-measurement vector iterative focusing processing based on the initial focusing value, the sparse measurement parameter, the unit matrix, the regularization coefficient, the array manifold matrix, and the array signal matrix to obtain a far-field signal matrix represented by the target control vertex.

[0130] In some embodiments, the spatial spectrum acquisition module 260 is specifically configured to: calculate the energy spectrum density of the control vertex in different directions in the discrete space according to the far-field signal matrix represented by the target control vertex; and obtain the spatial spectrum in each direction of arrival according to the energy spectrum density.

[0131] It should be noted that the above-mentioned arrival estimation device can execute the arrival estimation method provided in the embodiment of the present application, and has the corresponding functional modules and beneficial effects of the execution method. For technical details not fully described in the embodiment of the arrival estimation device, please refer to the arrival estimation method provided in the embodiment of the present application.

[0132] See also Figure 4 , Figure 4 1 is a schematic diagram of the hardware structure of an electronic device for performing a wave arrival estimation method provided in an embodiment of the present application. The electronic device 30 includes one or more processors 31 and a memory 32. The memory 32 is connected to the one or more processors 31, for example, via a bus.

[0133] The processor 31 is configured to support the electronic device 30 in executing the corresponding functions of the method in the above method embodiment. The processor 31 can be a central processing unit (CPU), a network processor (NP), a hardware chip, or any combination thereof. The above hardware chip can be an application specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The above PLD can be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.

[0134] The memory 32 is used to store program code, etc. The memory 32 may include volatile memory (VM), such as random access memory (RAM); non-volatile memory (NVM), such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid-state drive (SSD); or a combination of the aforementioned types of memory.

[0135] Memory 32 can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules, such as the program instructions / modules corresponding to the bode estimation method in the embodiments of the present application. Processor 31 executes the non-volatile software programs, instructions, and modules stored in memory 32 to perform various functional applications and data processing of the bode estimation method and bode estimation device, thereby implementing the functions of the bode estimation method and various modules or units of the bode estimation device provided in the above-mentioned method embodiments.

[0136] The memory 32 may include a program storage area and a data storage area. The program storage area may store an operating system and application programs required for at least one function. The data storage area may store data generated based on the use of the dynamic resource scheduling device. In some embodiments, the memory 32 may include a memory remotely located relative to the processor 31. Such remote memory may be connected to the dynamic resource scheduling device via a network. Examples of such networks include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0137] The one or more modules are stored in the memory 32. When executed by the one or more processors 31, the wave arrival estimation method in any of the above method embodiments is executed, for example, the method steps described in the above method embodiments are executed to realize the functions of the modules described in the above device embodiments.

[0138] It should be noted that the electronic equipment of the embodiments of the present application can specifically be a radar system, sonar and underwater acoustic equipment, a wireless communication system, medical imaging equipment, a drone cluster, etc.

[0139] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of this embodiment.

[0140] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a general hardware platform, or of course by hardware. Those skilled in the art can understand that all or part of the processes in the above embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Based on the concept of the present application, the technical features in the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations in different aspects of the present application as described above. For the sake of simplicity, they are not provided in detail. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for estimating a direction of arrival, characterized in that: The method comprises: Get the line array receiving signal matrix; Get the generalized B-spline basis matrix; Obtaining an array signal matrix represented by control vertices of generalized B-splines according to the line array received signal matrix and the generalized B-spline basis matrix; Obtaining an initial focusing value according to the array signal matrix; Performing multi-measurement vector iterative focusing processing according to the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by the target control vertex; Obtaining a spatial spectrum according to a far-field signal matrix represented by the target control vertex; Direction of arrival estimation is performed based on the spatial spectrum.

2. The method for estimating the direction of arrival according to claim 1, wherein: The obtaining of the line array receiving signal matrix includes: Get the array manifold matrix and noise matrix; Obtain far-field narrowband signals through preset filters; The line array receiving signal matrix is ​​obtained according to the array manifold matrix, the noise matrix and the far-field narrowband signal.

3. The method for estimating the direction of arrival according to claim 1, wherein: The obtaining of the generalized B-spline basis matrix includes: Get the preset core function and generalized B-spline basis function; The generalized B-spline basis matrix is ​​obtained according to the core function and the generalized B-spline basis function.

4. The method for estimating the direction of arrival according to claim 2, wherein: Obtaining an initial focus value according to the array signal matrix includes: Obtaining a far-field signal matrix represented by an initial control vertex according to the array signal matrix and the array manifold matrix; Calculating an initial contribution vector according to the far-field signal matrix represented by the initial control vertex; The initial focus value is calculated according to the initial contribution vector.

5. The method for estimating the direction of arrival according to claim 4, wherein: The performing multi-measurement vector iterative focusing processing according to the initial focusing value and the array signal matrix to obtain a far-field signal matrix represented by the target control vertex includes: Get regularization coefficients, identity matrix, and sparse metric parameters; The multi-measurement vector iterative focusing process is performed according to the initial focusing value, the sparse metric parameter, the unit matrix, the regularization coefficient, the array manifold matrix and the array signal matrix to obtain the far-field signal matrix represented by the target control vertex.

6. The method for estimating the direction of arrival according to claim 5, wherein: The obtaining of a spatial spectrum according to a far-field signal matrix represented by the target control vertex includes: Calculating the energy spectrum density of the control vertices in different directions of the discrete space according to the far-field signal matrix represented by the target control vertex; The spatial spectrum in each direction of arrival is obtained according to the energy spectrum density.

7. A direction of arrival estimation device, characterized in that: The device comprises: A line array receiving signal matrix acquisition module, wherein the line array receiving signal matrix acquisition module is used to acquire a line array receiving signal matrix; A generalized B-spline basis matrix acquisition module, wherein the generalized B-spline basis matrix acquisition module is used to obtain a generalized B-spline basis matrix; An array signal matrix acquisition module, configured to obtain an array signal matrix represented by control vertices of a generalized B-spline according to the line array received signal matrix and the generalized B-spline basis matrix; an initial focusing value calculation module, configured to obtain an initial focusing value according to the array signal matrix; a target far-field signal matrix acquisition module, configured to perform multi-measurement vector iterative focusing processing based on the initial focus value and the array signal matrix to obtain a far-field signal matrix represented by a target control vertex; A spatial spectrum acquisition module, configured to obtain a spatial spectrum according to a far-field signal matrix represented by the target control vertex; A direction of arrival estimation module is configured to perform direction of arrival estimation based on the spatial spectrum.

8. The direction of arrival estimation device according to claim 7, wherein: The line array receiving signal matrix acquisition module is specifically used to: Get the array manifold matrix and noise matrix; Obtain far-field narrowband signals through preset filters; The line array receiving signal matrix is ​​obtained according to the array manifold matrix, the noise matrix and the far-field narrowband signal.

9. The direction of arrival estimation device according to claim 7, wherein: The generalized B-spline basis matrix acquisition module is specifically used to: Get the preset core function and generalized B-spline basis function; The generalized B-spline basis matrix is ​​obtained according to the core function and the generalized B-spline basis function.

10. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 6.

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