Double-constraint robust adaptive beam forming method and device for cross iteration solution

Abstract

The invention discloses a double-constraint robust adaptive beam forming method and device for cross iteration solution, and the method comprises the steps: estimating a sample covariance matrix according to a snapshot signal of a receiving array, and carrying out the eigenvalue decomposition; calculating an assumed guide vector and a feature projection vector in the observation direction; calculating an uncertainty set parameter of the assumed guide vector; calculating a theoretical lower bound and a theoretical upper bound of a white noise gain constraint parameter; dividing a search interval of the white noise gain constraint parameter into a plurality of grid points according to a theoretical lower bound and an upper bound, and executing cross iteration solution for each grid point to obtain an optimal solution of an undetermined factor and a corresponding slope difference; determining an optimal estimation value of the white noise gain constraint parameter and a corresponding undetermined factor optimal solution according to a maximum slope difference criterion; calculating a robust adaptive weighted vector and an output power estimated value in a corresponding observation direction; correcting the scaling ambiguity of the estimated value of the output power; and repeating until the correction of the estimated values of the output power in all observation directions is completed.

Description

Technical Field

[0001] This invention belongs to the fields of general array signal processing, underwater acoustic array signal processing, radar array signal processing, medical ultrasound array signal processing, communication array signal processing, and robust adaptive beamforming technology, and particularly relates to a dual-constraint robust adaptive beamforming method and device based on cross-iterative solution. Background Technology

[0002] (1) CBF method Conventional beamforming (CBF) is the earliest beamforming technique. It obtains power estimates in the direction of the desired target signal by delay accumulation (time-domain signal) or phase-complement accumulation (frequency-domain signal). CBF is data-independent, simple to implement, and has a high error tolerance, but it is very susceptible to strong interference and has poor weak signal detection capability under strong interference conditions.

[0003] (2) MVDR method Minimum Variance Distortionless Response (MVDR), also known as Capon beamforming, is a data-adaptive beamforming method that provides a minimum power estimate while ensuring the signal waveform remains distortion-free. MVDR exhibits excellent strong interference suppression and weak signal detection capabilities under error-free conditions; however, it is highly sensitive to errors (steering vector error and covariance matrix error). Especially under high signal-to-noise ratio conditions, even slight errors can significantly degrade the performance of MVDR.

[0004] (3) RCB method Robust Capon Beamforming (RCB) is a robust adaptive beamforming method based on the MVDR method. By allowing the guide vector to be optimized within an uncertainty range, RCB has a certain tolerance for errors and can achieve significantly better performance than the MVDR method when the error is not too large, especially under high signal-to-noise ratio conditions. However, since it only considers the source of observation angle error of the guide vector, and this source of error is usually small, RCB cannot handle application scenarios with large errors, and its performance is severely degraded.

[0005] (4) WCPO-WNGC method The worst-case performance robust adaptive beamforming method with white noise gain constraint (WCPO with White Noise Gain Constraint, WCPO-WNGC) is a robust adaptive beamforming method that combines the worst-case performance criterion with white noise gain constraints. Typical WCPO-type methods, under conditions of low signal-to-noise ratio (SNR) or large errors, heavily rely on the estimated values ​​of the uncertain set parameters of the covariance matrix. These estimates are typically significantly overestimated for weak targets, leading to a substantial increase in the power of interference sidelobes and background noise output in both the weak target signal direction and non-target directions, resulting in a significant decrease in weak signal detection capability. Introducing white noise gain constraints into WCPO-type methods limits the output power in the weak signal direction or the background noise power in non-signal directions. Therefore, under conditions of low SNR or large errors, it exhibits excellent strong interference and background noise suppression capabilities, as well as superior weak signal detection capabilities, significantly outperforming typical WCPO-type methods and other mainstream beamforming methods mentioned above. The key parameter affecting the performance of the WCPO-WNGC method is the introduced white noise gain constraint parameter value. This method determines the white noise gain constraint parameter value by manually defining the search interval and dividing the grid to search for the minimum correction power. However, this method requires manually specifying the upper bound of the white noise gain constraint value, and determining the white noise gain constraint parameter value based on the minimum correction power lacks clear physical meaning. At the same time, there may be a small probability of abnormal false peaks when the error is large. Summary of the Invention

[0006] The worst-case performance optimal robust adaptive beamforming method with white noise gain constraints (WCPO-WNGC method) has the following main drawbacks: (1) it requires manually specifying the upper bound of the white noise gain constraint value; (2) the optimal value selection strategy for this parameter lacks clear physical meaning; and (3) there is a small probability of abnormal false peaks under large error conditions. In view of the above-mentioned technical defects of the existing WCPO-WNGC method, the purpose of this invention is to overcome these defects and, based on the same worst-case performance optimization problem with white noise gain constraints, disclose a dual-constraint robust adaptive beamforming method and device with cross-iterative solution.

[0007] In view of this, the present invention proposes a dual-constraint robust adaptive beamforming method based on cross-iteration solution, comprising: Step s1: Estimate the sample covariance matrix based on the snapshot signal from the receiving array, and perform eigenvalue decomposition; Step s2: Calculate the assumed steering vector and characteristic projection vector in the observation direction; Step s3: Calculate the uncertainty set parameters of the assumed steering vector; Step s4: Calculate the theoretical lower bound and theoretical upper bound of the white noise gain constraint parameters; Step s5: Based on the theoretical lower bound and theoretical upper bound, divide the search interval of the white noise gain constraint parameters into multiple grid points, and perform cross-iteration solution for each grid point to obtain the optimal solution of the undetermined factor and its corresponding slope difference; Step s6: Determine the optimal estimated value of the white noise gain constraint parameter and the optimal solution of the corresponding undetermined factor according to the maximum slope difference criterion; Step s7: Calculate the robust adaptive weighted vector and output power estimate in the corresponding observation direction based on the optimal estimate obtained in step s6 and the optimal solution of the undetermined factors; Step s8: Correct the scaling fuzziness of the output power estimate; Step s9: Repeat steps s2 to s8 until all observation directions have been traversed, and the output power estimates for all observation directions have been corrected.

[0008] As an improvement to the above method, step s1 includes: Estimate the sample covariance matrix from the snapshot signal of the receiving array :

[0009] in, It is the first of the receiving array A quick snapshot signal, For frequency, Indicates the total number of snapshot signals, indicated by the superscript symbol. Indicates transpose and conjugate; Calculate the sample covariance matrix Eigenvalue decomposition: in, It is a diagonal matrix composed of real eigenvalues ​​arranged in descending order. The sample covariance matrix The Nth eigenvalue, For the eigenvalues ​​corresponding to The feature matrix composed of eigenvectors of dimension 1. This indicates the total number of array elements in the receiving array.

[0010] As an improvement to the above method, step s2 includes: The following formula yields the... Array element in the observation direction angle Assumed steering vector on and feature projection vector : ,

[0011] in, For the spacing between array elements, The symbol for the imaginary part. Indicates the speed of sound. For the eigenvalues ​​corresponding to The feature matrix composed of eigenvectors of dimension 1. Indicates the total number of array elements of the receiving array, indicated by the superscript symbol. This indicates transpose and conjugate.

[0012] As an improvement to the above method, step s3 includes: The maximum deviation range of the signal angle of arrival is determined based on the angular interval of the observation direction. The assumed steering vector is estimated according to the following formula. Uncertain set parameters value: in, This indicates that the possible deviation range of the signal angle of arrival is divided into... Each angle grid point, It is the first The angle value corresponding to each angle grid point, symbol The supremum is defined as . The maximum value among the calculation results.

[0013] As an improvement to the above method, the white noise gain constraint parameter in step s4 The theoretical lower bound We obtain the following formula:

[0014] in, For uncertain set parameters, This indicates the total number of array elements in the receiving array.

[0015] As an improvement to the above method, the white noise gain constraint parameter in step s4 Theoretical upper limit The steps to obtain it include: Step s4-1: Initialization, setting the left and right boundaries of the bisection method. and initial value , ;in, The upper bound of the search is the theoretical upper bound. Step s4-2: Let ; Step s4-3: Solve the following equation using the bisection method to obtain the first undetermined factor. The first solution :

[0016] in, For feature projection vectors The nth component, The sample covariance matrix The nth eigenvalue, The sample covariance matrix The Nth eigenvalue, the first undetermined factor The range of values ​​for is: Step s4-4: Solve the following equation using the bisection method to obtain information about the first undetermined factor. The second solution :

[0017] Among them, the first undetermined factor The range of values ​​for is: Steps s4-5: If Then take , Unchanged, otherwise Unchanged, take And return to step s4-2; Steps s4-6: until ,in If it is a preset small threshold, then at this time... The value is the theoretical upper bound of the white noise gain constraint parameter. .

[0018] As an improvement to the above method, the theoretical upper bound for searching is... The steps to obtain it include: Step 01) Obtain initial value ,coefficient ; Step 02) Solve the following equation using the bisection method to obtain the first undetermined factor. The first solution :

[0019] Among them, undetermined factors The range of values ​​for is: Step 03) Solve the following equation using the bisection method to obtain the first undetermined factor. The second solution :

[0020] Among them, undetermined factors The range of values ​​for is: Step 04) If Then take ,coefficient (and return to step 02); until Then at this time The value represents the upper bound of the theoretical upper bound for the white noise gain constraint parameter. .

[0021] As an improvement to the above method, step s5 includes: White noise gain constraint parameters search range Divided into The grid point, where the first... The white noise gain constraint parameter value corresponding to each grid point is expressed as follows: Calculate according to the following formula:

[0022] For each Perform the following steps: Step s5-1: Let ;in, , The first undetermined factor The search left and right boundaries; Step s5-2: Solve the following equation using the bisection method to obtain the second undetermined factor. The first solution : in, The range of values ​​for is:

[0023] Step s5-3: Solve the following equation using the bisection method to obtain the second undetermined factor. The second solution : Among them, the second undetermined factor The range of values ​​for is: Step s5-4: Comparison and The size, if Then take , Unchanged, otherwise Unchanged, take and return to step s5-1; until ,in, Using a preset small threshold, the optimal solutions for the first and second undetermined factors are obtained. , for: Corresponding slope difference for:

[0024] in, The sample covariance matrix The nth eigenvalue, For uncertain set parameters, This indicates the total number of array elements in the receiving array.

[0025] As an improvement to the above method, the first undetermined factor left boundary of the search and right boundary The solution process includes: The first undetermined factor is obtained by solving the following equation using the bisection method. The first solution :

[0026] in, The range of values ​​for is: Will Assign to ,for Regarding the first undetermined factor The lower bound of the search; Step 01) Set initial values ,in ; Step 02) Solve the following equation using the bisection method to obtain the second undetermined factor. First solution : in The range of values ​​for is:

[0027] Step 03) Solve the following equation using the bisection method to obtain the second undetermined factor. The second solution : Among them, undetermined factors The range of values ​​for is: Step 04) If Then take ,coefficient (and return to step 02); until At this time The value is the first undetermined factor. right boundary of the search .

[0028] As an improvement to the above method, step s6 includes: Determine the optimal estimate of the white noise gain constraint parameters based on the maximum slope difference criterion. : And will The optimal solutions for the corresponding undetermined factors are respectively set as and .

[0029] 11. The dual-constraint robust adaptive beamforming method based on cross-iterative solution according to claim 10, characterized in that step s7 includes: Depend on as well as , Computational robust adaptive beamforming in Optimal weighted vector in direction : in, For the first Array element in the observation direction angle The assumed guiding vector on, It is the identity matrix. The sample covariance matrix, For parameters of the uncertain set.

[0030] As an improvement to the above method, step s8 includes: Step s8-1: Calculate the assumed steering vector Correction items: , in, This is a correction vector to the assumed guiding vector. The phase difference between the optimal weighting vector and the assumed steering vector, sign... The superscript H indicates the argument of a complex number, and the superscript H indicates the conjugate transpose. The symbol for the imaginary part; Step s8-2: Calculate the corrected steering vector : Step s8-3: Calculation Output power estimate in the direction :

[0031] Step s8-4: Calculate the corrected power estimate to eliminate scaling blur. :

[0032] in, To correct the signal power estimate, This indicates the total number of array elements in the receiving array.

[0033] On the other hand, the present invention provides an electronic device including a processor and a memory, wherein the memory stores a computer program, and the processor executes the program to implement the above-described method.

[0034] Compared with the prior art, the advantages of the present invention are: This invention proposes a robust adaptive beamforming method with dual constraints through cross-iteration. By introducing two independent real-valued undetermined factors, the method jointly solves the white noise gain constraint and the worst-case distortion-free response constraint. The method then uses the maximum slope difference criterion of the characteristic curves corresponding to the dual constraints to obtain the intersection point of the characteristic curves and the optimal solution of the undetermined factors through cross-iteration. Finally, it achieves robust adaptive beamforming with more reliable output spatial power spectrum without the need for user parameters.

[0035] This invention employs a cross-iteration method based on geometric characteristic curve analysis to solve the same optimization constraint problem as the WCPO-WNGC method: the worst-case performance optimization problem under white noise gain constraints and signal distortion-free response constraints. The optimal white noise gain constraint parameter values ​​are determined using the maximum slope difference criterion. The performance of this invention is similar to that of the WCPO-WNGC method, exhibiting excellent strong interference and background noise suppression capabilities and excellent weak signal detection capabilities under conditions of low signal-to-noise ratio or large errors. Furthermore, it does not require manually specified parameters, resulting in better adaptability to various application scenarios and more stable performance in complex time-varying environments.

[0036] Numerical simulation and sea trial data analysis results, as well as comparisons between the method of this invention and several other mainstream beamforming methods (CBF, MVDR, RCB) and the WCPO-WNGC method, all verify the performance of the method of this invention: This invention exhibits significant sidelobe suppression for strong interference, good detection performance for weak targets, high output SINR, accurate estimation of the azimuth and power of each target, and minimal performance degradation under large error conditions (including errors from observation angle, array calibration, element response amplitude, and phase), demonstrating strong robustness. The greatest advantage of this invention is that it eliminates the need for manually setting key parameters, possesses data adaptability in dynamic and uncertain complex application environments, maintains excellent performance even under large error conditions, exhibits high flexibility and robustness, and has broad application and development potential.

[0037] In summary, the method of this invention is an adaptive beamforming method with strong tolerance to multiple types of errors. It has excellent ability to suppress strong interference sidelobes and background noise, and is very suitable for weak target signal detection under conditions of large errors and strong interference. Moreover, it does not require manual setting of key user parameters. Attached Figure Description

[0038] Figure 1 It is a complete processing flow of a dual-constraint robust adaptive beamforming method with cross-iterative solution.

[0039] Figure 2(a) shows the comparison of the average spatial power spectrum when there is no arbitrary steering vector error.

[0040] Figure 2(b) shows the comparison of the average spatial power spectrum when the error amplitude of any steering vector is 1.

[0041] Figure 2(c) shows the comparison of the average spatial power spectrum when the error amplitude of any steering vector is 2.

[0042] Figure 2(d) shows a comparison of the average spatial power spectrum when the error amplitude of any steering vector is 4; Figure 3(a) shows a comparison of the changes in the output SINR of the desired target signal as a function of the error amplitude of any steering vector; Figure 3(b) shows a comparison of the power estimation deviation of the desired target signal as a function of the error magnitude of any steering vector. Figure 3(c) shows a comparison of the output SINR of the desired target signal as the signal-to-noise ratio of the desired target signal is changed when the error amplitude of the arbitrary steering vector is fixed at 4. Figure 3(d) shows a comparison of the power estimation deviation of the desired target signal as the signal-to-noise ratio of the desired target signal is changed when the error amplitude of any steering vector is fixed at 4. Figure 4(a) shows the spatial power spectrum time history of the sea trial data processed by the method of the present invention under the original formation; Figure 4(b) shows the spatial power spectrum time history of the sea trial data processed by the method of the present invention under the perturbation array. Figure 5(a) shows the spatial power spectrum time history of the CBF method for processing sea trial data in the original array configuration; Figure 5(b) shows the spatial power spectrum time history of the CBF method for processing sea trial data under perturbed arrays; Figure 6(a) shows the spatial power spectrum time history of the MVDR method for processing sea trial data in the original array configuration; Figure 6(b) shows the spatial power spectrum time history of the MVDR method for processing sea trial data under perturbed arrays; Figure 7(a) shows the spatial power spectrum time history of the RCB method for processing sea trial data in the original array configuration; Figure 7(b) shows the spatial power spectrum time history of the RCB method for processing sea trial data under perturbed arrays; Figure 8(a) shows the spatial power spectrum time history of the WCPO-WNGC method for processing sea trial data in the original array configuration; Figure 8(b) shows the spatial power spectrum time history of sea trial data processed by the WCPO-WNGC method under perturbed array; Figure 9(a) shows a comparison of the spatial power spectrum at 300 seconds of processing sea trial data under the original array configuration; Figure 9(b) shows a comparison of the spatial power spectrum at 300 seconds of processing sea trial data under the perturbation array. Figure 10 It is a comparison between the original formation and the disturbed formation. Detailed Implementation

[0043] The technical solution provided by the cross-iterative solution of the dual-constraint robust adaptive beamforming method of the present invention includes the following steps: (1) Step 1 From the frequency domain (frequency is )of Estimate the sample covariance matrix of the received signal from the array using snapshots:

[0044] here It is the first narrowband A quick snapshot of an array signal, it is a dimension of A complex vector. Indicates the total number of array elements. Superscript symbol This indicates transpose and conjugate.

[0045] (2) Step 2 Calculate the sample covariance matrix Eigenvalue decomposition:

[0046] in It is a diagonal matrix composed of real eigenvalues ​​arranged in descending order. The sample covariance matrix The Nth eigenvalue, For the eigenvalues ​​corresponding to The feature matrix is ​​composed of 1-dimensional eigenvectors.

[0047] (3) Step 3 Depending on the array configuration and the direction and angle to be observed. Calculate the assumed steering vector and feature projection vector The distance between array elements is... Taking a uniform linear array as an example, the frequency is At that time, the first Array elements at the observation angle The steering vector component on is calculated by the following formula: , in The symbol for the imaginary part. Indicates the speed of sound and the direction of observation. It is the angle between the signal incident direction and the array normal. The characteristic projection vector is obtained from the following formula:

[0048] (4) Step 4 Estimating the assumed steering vector Uncertain set parameters Value. The maximum deviation range of the signal's angle of arrival is determined based on the angular intervals of the observation direction. This value is generally taken as the angular difference between adjacent observation directions. The assumed steering vector is estimated according to the following formula. Uncertain set parameters value:

[0049] here

[0050] This indicates that the possible deviation range of the signal angle of arrival is divided into... There are 10 angle grid points, among which It is the first The angle value corresponding to each angle grid point. (Symbol) The supremum is defined as . The maximum value among the calculation results.

[0051] (5) Step 5 Calculate the white noise gain constraint parameters The theoretical lower bound :

[0052] (6) Step 6 Calculate the white noise gain constraint parameters The theoretical upper bound of the search upper bound : 1) Obtain initial value ,generally ; 2) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The first solution :

[0053] Among them, the first undetermined factor The range of values ​​for is:

[0054] 3) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The second solution :

[0055] Among them, the first undetermined factor The range of values ​​for is:

[0056] 4) If Then take , and return 2); 5) Repeat the above process until... Then at this time The value represents the upper bound of the theoretical upper bound for the white noise gain constraint parameter. .

[0057] (7) Step 7 Calculate the white noise gain constraint parameters Theoretical upper limit : 1) Initial values: The left and right boundaries of the bisection method are: , ; 2) Order ; 3) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The first solution :

[0058] Among them, the first undetermined factor The range of values ​​for is:

[0059] 4) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The second solution :

[0060] Among them, the first undetermined factor The range of values ​​for is:

[0061] 5) If Then take , Unchanged, otherwise Unchanged, take and return 2); 6) Repeat the above process until... ,here It is a preset small threshold, indicating the amount of information about the undetermined factors. If the two solutions coincide, then at this time... The value is the theoretical upper bound of the white noise gain constraint parameter. .

[0062] (8) Step 8 White noise gain constraint parameters search range Divided into The grid point, where the first... The white noise gain constraint parameter value corresponding to each grid point is expressed as follows: Calculate according to the following formula:

[0063] (9) Step 9 calculate Time regarding undetermined factors left boundary of the search Solving the following equation using the bisection method yields information about the first undetermined factor. The first solution :

[0064] Among them, the first undetermined factor The range of values ​​for is:

[0065] make for Time regarding undetermined factors The left boundary of the search.

[0066] (10) Step 10 calculate Time regarding undetermined factors right boundary of the search : 1) Set initial values ,in ; 2) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The first solution :

[0067] Among them, the second undetermined factor The range of values ​​for is:

[0068] 3) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The second solution :

[0069] Among them, the second undetermined factor The range of values ​​for is:

[0070] 4) If Then take , and return 2); 5) Repeat the above process until... At this time The value is the right boundary of the search for the first undetermined factor. .

[0071] (11) Step 11 Solve The optimal solution for the first and second undetermined factors and : 1) Order ; 2) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The first solution :

[0072] Among them, the second undetermined factor The range of values ​​for is:

[0073] 3) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The second solution :

[0074] Among them, the second undetermined factor The range of values ​​for is: 4) Comparison and The size, if Then take , Unchanged, otherwise Unchanged, take and return 1); 5) Repeat the above process until... ,here It is a preset small threshold, indicating the second undetermined factor. The two solutions coincide, and the optimal solutions for the first and second undetermined factors are respectively:

[0075]

[0076] (12) Step 12 calculate Optimal solution with undetermined factors and Corresponding slope difference :

[0077] (13) Step 13 make Return to step 9 until completion. On each grid point The calculation process.

[0078] (14) Step 14 Determine the optimal estimate of the white noise gain constraint parameters based on the maximum slope difference criterion. :

[0079] And will The optimal solutions for the corresponding undetermined factors are respectively set as and .

[0080] (15) Step 15 Depend on as well as , Computational robust adaptive beamforming in Optimal weighted vector in direction :

[0081] (16) Step 16 calculate Output power estimate in the direction :

[0082] (17) Step 17 Corrected signal power estimate "Scaling blur": 1) Calculate the assumed steering vector Correction items: , symbol Indicates the argument of a complex number; This is a correction vector to the assumed guiding vector. The phase difference between the optimal weighting vector and the assumed steering vector; 2) Calculate the corrected steering vector :

[0083] 3) Calculation Output power estimate in the direction :

[0084] 4) Calculate the corrected power estimate to eliminate "scaling blur". :

[0085] (18) Step 18 Return to step 3 and proceed to the next scanning angle. The solution process is repeated. The above steps are repeated until the output power correction estimates for all scanning angles are calculated.

[0086] The complete single-process flow of a white noise gain-constrained robust adaptive beamforming method, such as... Figure 1 As shown.

[0087] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0088] This section further describes the method of the present invention through two numerical simulation experiments and a sea trial data processing, combined with embodiments and accompanying drawings. The performance is also compared with that of methods such as CBF, MVDR, RCB, and WCPO-WNGC to illustrate the superior performance of the present invention. In the illustrations provided below, the comparison method WCPO-WNGC is abbreviated as WNGC.

[0089] (1) Simulation Experiment 1 Simulation experiment 1 examines the output spatial power spectrum comparison between the method of this invention and other methods under different arbitrary steering vector error amplitudes.

[0090] The simulation experiment used the following numerical simulation parameters: a uniform linear array with half-wavelength spacing; observation angles in integer degrees, with a total of 181 directional angles observed between -90° and 90°; and the number of array elements. The number of snapshots is 20. The signal count is 40, and the background noise is 0dB; The value is 3, where the desired signal is located at -5.45° with a power of -5dB, and the two strong interference signals are located at -32.69° and 26.21° respectively, both with a power of 30dB.

[0091] First, generate 40 array signal snapshots as follows: , here and These are the true angles of the three target signals and the random complex amplitudes that satisfy a Gaussian distribution, respectively. It is array Gaussian noise. The true steering vectors of the three target signals. It includes arbitrary steering vector error components: , in It is to satisfy The unit error vector, It is the error magnitude of a non-negative real number; The ( ) components Calculated by the following formula: , In simulation experiment one, the unit error vectors of the three target signal steering vectors were generated independently, while the error amplitudes were of the same value. Here, the error amplitudes of arbitrary steering vectors are selected respectively. The output spatial power spectra of this invention are compared with those of other methods, given values ​​of 0, 1, 2, and 4; where... At that time, the error sources only include the steering vector error caused by the observation angle error.

[0092] After generating 40 snapshots of array signal simulation data, the sample covariance matrix is ​​estimated using these array signal snapshots in step 1 of this invention:

[0093] Next, in step 2, the sample covariance matrix is ​​calculated. Eigenvalue decomposition:

[0094] in It is a diagonal matrix consisting of 20 real eigenvalues ​​arranged in descending order. It corresponds to the eigenvalue The feature matrix is ​​composed of 1-dimensional eigenvectors.

[0095] Step 3 calculates the assumed steering vector, where the first... Each observation angle is represented as: , Based on the parameter setting of the half-wavelength element spacing, the corresponding assumed steering vector The Each component Calculated by the following formula: , The corresponding feature projection vector is:

[0096] Estimate the observation angle in step 4 Assuming the uncertainty set parameters of the steering vector :

[0097] The possible deviation range of the signal angle of arrival Divided into 20 angular grids:

[0098] The final estimate is the maximum value among the 20 calculation results.

[0099] Step 5 calculates the white noise gain constraint parameters. The theoretical lower bound :

[0100] Step 6 calculates the white noise gain constraint parameters. The theoretical upper bound of the search upper bound : 1) Obtain initial value ; 2) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The first solution :

[0101] Among them, the first undetermined factor The range of values ​​for is:

[0102] 3) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The second solution :

[0103] Among them, the first undetermined factor The range of values ​​for is: 4) If Then take and return 2); 5) Repeat the above process until... Then at this time The value represents the upper bound of the theoretical upper bound for the white noise gain constraint parameter. .

[0104] Step 7 calculates the white noise gain constraint parameters. Theoretical upper limit : 1) Set initial values , ; 2) Order ; 3) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The first solution :

[0105] Among them, the first undetermined factor The range of values ​​for is:

[0106] 4) Solve the following equation using the bisection method to obtain information about the first undetermined factor. The second solution :

[0107] Among them, the first undetermined factor The range of values ​​for is:

[0108] 5) If Then take , Unchanged, otherwise Unchanged, take and return 2); 6) Repeat the above process until... This indicates the first undetermined factor. If the two solutions coincide, then at this time... The value is the theoretical upper bound of the white noise gain constraint parameter. .

[0109] In step 8, the white noise gain constraint parameters are... search range Divided into 50 grid points, of which the first The white noise gain constraint parameter value corresponding to each grid point is expressed as follows: Calculate according to the following formula:

[0110] Calculation in step 9 Regarding the first undetermined factor Search boundary Solving the following equation using the bisection method yields information about the first undetermined factor. The first solution :

[0111] Among them, the first undetermined factor The range of values ​​for is:

[0112] make for Regarding the first undetermined factor The left boundary of the search.

[0113] Calculation in step 10 Regarding the first undetermined factor right boundary of the search : 1) Set initial values ; 2) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The first solution : Among them, the second undetermined factor The range of values ​​for is:

[0114] 3) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The second solution :

[0115] Among them, the second undetermined factor The range of values ​​for is:

[0116] 4) If Then take and return 2); 5) Repeat the above process until... At this time The value is the right boundary of the search for the first undetermined factor. .

[0117] Solving in step 11 The optimal solution for the first and second undetermined factors and : 1) Order ; 2) Solve the following equation using the bisection method to obtain information about the second undetermined factor. The first solution :

[0118] Among them, the second undetermined factor The range of values ​​for is:

[0119] 3) Solve the following equation using the bisection method to obtain information about the second undetermined factor. Solution : Among them, the second undetermined factor The range of values ​​for is: 4) Comparison and The size, if Then take , Unchanged, otherwise Unchanged, take and return 1); 5) Repeat the above process until... This indicates the second undetermined factor. The two solutions coincide, and the optimal solutions for the first and second undetermined factors are respectively:

[0120]

[0121] Calculation in step 12 Optimal solution with undetermined factors and Corresponding slope difference :

[0122] In step 13, the command Return to step 9 until 50 grid points have been completed. The calculation process.

[0123] In step 14, the optimal estimate of the white noise gain constraint parameters is determined based on the maximum slope difference criterion. :

[0124] And will The optimal solutions for the corresponding undetermined factors are respectively set as and .

[0125] In step 15, by as well as , Computational robust adaptive beamforming in Optimal weighted vector in direction :

[0126] Calculation in step 16 Output power estimate in the direction :

[0127] Step 17 corrects the signal power estimate. "Scaling blur": 1) Calculate the assumed steering vector Correction items: , symbol Indicates the argument of a complex number; 2) Calculate the corrected steering vector :

[0128] 3) Calculation Output power estimate in the direction :

[0129] 4) Calculate the corrected power estimate to eliminate "scaling blur". :

[0130] In step 18, the command Then return to step 3 to proceed to the next scanning angle. The solution process is as follows. Repeat the above steps until... Complete the calculation of the output power correction estimate for all scanning angles.

[0131] To avoid the randomness of the results of a single simulation experiment, simulation experiment 1 used the average result of processing 100 independent simulation data (each independent simulation generates 40 array signal snapshots). Figure 2(a) , 2(b) Figures 2(c) and 2(d) respectively give the error magnitude of the arbitrary steering vector. The average spatial power spectrum of the present invention method (solid red line) and the comparison methods CBF (blue dotted line), MVDR (orange dotted line), RCB (yellow dotted line), and WNGC (purple dotted line) in 100 independent simulations when the values ​​are 0, 1, 2, and 4.

[0132] As can be seen from the comparison in Figure 2, in this scenario of weak target signal detection under strong interference, the method of the present invention has the best weak target signal detection capability compared to other comparative methods. Under four arbitrary steering vector error amplitude conditions, the method of the present invention can clearly detect the weak target signal at -5.45° under strong target signal interference, and the power of strong interference sidelobes and background noise is always controlled at a low level. Except for Figure 2(d) with the largest arbitrary steering vector error amplitude, the estimated values ​​of the power of the three target signals by the method of the present invention are basically accurate. In contrast, CBF has no ability to detect weak target signals under any of the four error conditions; the WCPO-PCVC method (abbreviated as PCVC in Figure 2) gradually deteriorates in performance as the error amplitude increases, and the power of interference sidelobes and background noise increases significantly, gradually losing the ability to detect weak target signals; the performance of MVDR and RCB methods is severely degraded under error conditions. They can detect weak target signals at -5.45°, but the power estimation value has a large deviation. In addition, for strong target signals (directions of -32.69° and 26.21°, respectively), their power estimation deviation is very large. The results of the WCPO-WNGC method are similar to those of the method of this invention. However, the WCPO-WNGC method may produce spurious peaks under conditions of large error, as shown in Figure 2(d) at approximately -55 degrees.

[0133] In summary, the method of this invention still exhibits excellent suppression capabilities for strong interference sidelobes and background noise power even under large error conditions, and correspondingly demonstrates good weak target signal detection capabilities. Furthermore, the estimated target signal power is relatively accurate when the error amplitude is not too large. Additionally, although the spatial power spectrum of the method of this invention is largely consistent with that of the WCPO-WNGC method, the output spatial power spectrum of the method of this invention is more stable under larger error conditions.

[0134] (2) Simulation Experiment Two Simulation Experiment 2 examines how the output signal-to-interference-plus-noise ratio (SINR) and power estimates of the desired target signal at -5.45° vary with the arbitrary steering vector error amplitude or the target signal SNR, under different arbitrary steering vector error amplitudes. Except for the variables stated here, the simulation parameters used in Simulation Experiment 2 are exactly the same as those in Simulation Experiment 1; the generation method and solution steps for the simulation data (40 array signal snapshots) are also exactly the same as in Simulation Experiment 1.

[0135] The output SINR for the desired target signal is calculated using the following formula:

[0136] In the formula This represents the optimal weighted vector given by the method of the present invention for the desired weak target signal at -5.45°. The solution method and steps are exactly the same as those in simulation experiment one, obtained in step 15. Here, in order to preserve the observation angle error including the steering vector, an assumed steering vector of -5° (the integer angle value closest to the true direction angle) is used to obtain the solution. Signal covariance matrix Interference plus noise covariance matrix Calculated using the following formulas respectively:

[0137]

[0138] In the formula It is the identity matrix. The array Gaussian noise vector The Similar to simulation experiment one, the steering vectors of the three target signals above all include independently generated arbitrary steering vector errors. Here, the average result of 100 Monte Carlo experiments is also used.

[0139] First, the power of the weak target signal at -5.45° is fixed at -5dB, while the error amplitude of any steering vector is... From 0 to 4, Figure 3(a) , 3(b) The changes in the output SINR and power estimation deviation (the difference between the theoretical value and the expected value) of each comparative method for the desired target signal as a function of the arbitrary steering vector error amplitude are presented. It can be seen that, except for the WCPO-WNGC method, the proposed method exhibits the slowest rate of decrease in output SINR and the smallest power estimation deviation as the steering vector error amplitude increases with the gradual increase of the steering vector error, indicating that the proposed method has the strongest tolerance to steering vector errors. Within an error range of 0 to 4, the proposed method outputs approximately consistent SINR and power estimation values ​​in the direction of the desired target signal. The output SINR and power estimation error of the proposed method are slightly worse than those of the WCPO-WNGC method, but the difference is very small, indicating that, based on simulation results, the two methods have very similar performance.

[0140] Secondly, when the error amplitude of any steering vector is fixed at 4, the power of the expected weak target signal at -5.45° changes from -20dB to 40dB. Figure 3(c) , 3(d)The output SINR and power estimation deviation of the desired signal are shown as a function of the desired target signal SNR. Figure 3(c) shows that the method of this invention and the WCPO-WNGC method have the highest output SINR in the desired target signal SNR range of -20dB to 30dB. Figure 3(d) shows that the desired target signal power estimation deviation values ​​given by the method of this invention and the WCPO-WNGC method are small, and the change in the desired target signal power estimation deviation value is also small as the desired target signal SNR increases. In contrast, except for the WCPO-WNGC method, the other methods used for comparison show more drastic changes in the desired target signal power estimation deviation value with the desired target signal SNR, and the desired target power estimation deviation value is relatively large in most cases. In comparison, the results of the method of this invention are roughly equivalent to those of the WCPO-WNGC method, both for output SINR and power estimation deviation. The latter has a slight advantage at low SNR, while the former slightly leads at high SNR.

[0141] The results of the comprehensive simulation experiment 2 show that the performance of the method of the present invention (output SINR and power estimation deviation) is roughly equivalent to that of the WCPO-WNGC method, and significantly better than other comparative methods except for the WCPO-WNGC method. Within a relatively wide error range (arbitrary steering vector error amplitude 0~4) and the desired target signal-to-noise ratio range (-20dB~30dB), it can provide the best or near-best results among all methods, and maintains nearly consistent performance despite wide variations in error and signal-to-noise ratio conditions. This consistent performance under conditions of large error variations indicates that the method of the present invention has a very high tolerance for error. (3) Sea trial data processing The sea trial data comes from an array with 43 elements (number of elements). The underwater acoustic data was acquired by a horizontal receiving array. The element spacing was approximately 1.5m, the scanning azimuth angle was from 0° to 360°, and the scanning interval was 1°. The cooperative target started at an azimuth angle of approximately 125°. Each snapshot used 1 second of data for windowed FFT and the 500Hz spectrum result was obtained. The time overlap between snapshots was 0.8 seconds, and the number of snapshots was 100. The corresponding total processing time for a single session is 20.8 seconds. The processing results are updated once per second, and there is a 19.8-second overlap of array underwater acoustic data or an overlap of 195 array signal snapshots between adjacent processing results.

[0142] After obtaining 100 array signal snapshots through data overlap and windowed FFT, the method of this invention is applied for adaptive beamforming processing. The method steps and related parameters used are completely consistent with those in simulation experiment 1.

[0143] Since the original array element positions have undergone array calibration, the array error is relatively small. Therefore, the superior error tolerance of the method of this invention is further verified by artificially increasing the error conditions in the sea trial data. Specifically, a normally distributed random perturbation is superimposed on the array element coordinates to simulate the array error in actual applications. The x-coordinate and y-coordinate of each array element are superimposed with a normally distributed random number with a mean of 0 and a variance of 0.125. The assumed steering vector is calculated using this perturbation array configuration, and beamforming processing is then performed on the sea trial data.

[0144] Figures 4(a) and 4(b), 5(a) and 5(b), 6(a) and 6(b), 7(a) and 7(b), and 8(a) and 8(b) respectively show the spatial power spectrum time histories of the proposed method, CBF method, MVDR method, RCB method, and WCPO-WNGC method under both original and perturbed array configurations. Figure 9(a) , 9(b) The spatial power spectrum at 300 seconds of processing sea trial data is presented in both the original and perturbed array configurations. Figure 10 A comparison is given between the original array and the perturbation array implemented in one step. The aforementioned perturbation array processing results are all obtained based on this perturbation array processing.

[0145] First, compare the processed data from the sea trial of the original formation. Figure 4(a)~8(a) In terms of trajectory clarity and target resolution for cooperative targets near 125° and non-cooperative targets between 250° and 350°, as well as sidelobe and background noise suppression capabilities, the methods of this invention (Fig. 4(a)), RCB (Fig. 7(a)), and WCPO-WNGC (Fig. 8(a)) yielded the best results in sea trial data processing. Comparatively, the RCB method performed slightly better in background noise suppression between 0° and 125°, while the method of this invention performed slightly better than the WCPO-WNGC method. The MVDR method (Fig. 6(a)) performed second best, showing significantly worse results than the other three in terms of non-cooperative target trajectory clarity, sidelobe suppression, and background noise reduction. The CBF method (Fig. 5(a)) performed the worst, exhibiting very obvious sidelobes in its spatial power spectrum time history plot, and the trajectories of weaker non-cooperative targets were also quite blurry.

[0146] Next, we compare the performance degradation caused by perturbing the array. We compare the performance of each method before array perturbation in Figures 4-8. Figure 4(a)~8(a) )back( Figures 4(b)~8(b)The results show that, after introducing a certain amount of array error, all methods except the method of this invention and the WCPO-WNGC method exhibit significant performance degradation. This is manifested in increased sidelobes (decreased interference suppression capability), increased background noise power, and blurred target trajectories, especially those of non-cooperative weak targets. Simultaneously, the power estimation deviation of the target signal also increases. This performance degradation indicates a decrease in the detection capability for weak target signals.

[0147] Finally, comparing the spatial power spectra obtained at 300 seconds using the original and perturbed array configurations respectively, the previous comparison results were verified again. That is, before and after array perturbation, the performance degradation of the proposed method and the WCPO-WNGC method was small, while the other methods showed significant performance deterioration. Furthermore, it can be seen that, in both the original and perturbed array cases, the spatial power spectrum output by the proposed method is superior to the WCPO-WNGC method in terms of sidelobe and background noise power suppression.

[0148] In summary, the spatial power spectrum time history output by the method of this invention shows very little change before (Figure 4(a)) and after (Figure 4(b)) the array perturbation, except for a slight increase in target power estimation bias. This indicates that under array perturbation error conditions, the superior error tolerance of the method of this invention ensures consistent performance in terms of interference sidelobes, background noise suppression, and weak target signal detection. Furthermore, the background suppression capability of the method of this invention is better than that of the WCPO-WNGC method, regardless of whether the result is from the original array or the perturbated array. This also shows that, compared to the WCPO-WNGC method's partial reliance on manually specified search parameters, the method of this invention, which automatically determines the optimal white noise gain constraint parameter value based on the maximum slope difference criterion, is more adaptable to complex actual sea trial data.

[0149] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method of cross-iterative solution of double-constrained robust adaptive beamforming, comprising: Step s1: estimating a sample covariance matrix according to a snapshot signal of a receiving array, and performing eigenvalue decomposition; Step s2: calculating a hypothetical steering vector and a characteristic projection vector in an observation direction; Step s3: calculating an uncertainty set parameter of the hypothetical steering vector; Step s4: calculating a theoretical lower bound and a theoretical upper bound of a white noise gain constraint parameter; Step s5: dividing a search interval of the white noise gain constraint parameter into a plurality of grid points according to the theoretical lower bound and the theoretical upper bound, performing cross-iterative solution for each grid point to obtain an optimal solution of an undetermined factor and a corresponding slope difference; Step s6: determining an optimal estimation value of the white noise gain constraint parameter and a corresponding optimal solution of the undetermined factor according to a maximum slope difference criterion; Step s7: calculating a robust adaptive weighting vector and an output power estimation value in the corresponding observation direction according to the optimal estimation value and the optimal solution of the undetermined factor obtained in step s6; Step s8: correcting a scaling ambiguity of the output power estimation value; Step s9: repeating steps s2 to s8 until all observation directions are traversed, and completing correction of the output power estimation values of all observation directions.

2. The cross iteratively solved double constrained robust adaptive beamforming method according to claim 1, characterized in that, The step s1 comprises: Estimating a sample covariance matrix from the snapshot signals of a receiving array : ； where is the kth snapshot signal of the receive array, is the number of snapshots, is the frequency, denotes the total number of snapshots, and the superscript denotes the transpose conjugate; Eigenvalue decomposition of the sample covariance matrix Eigenvalue decomposition of the sample covariance matrix ； wherein is a diagonal matrix composed of real eigenvalues arranged in descending order, is the sample covariance matrix is the Nth eigenvalue of is the eigenvector corresponding to the eigenvalue is an N x N eigenmatrix composed of N eigenvectors, denotes the total number of array elements of the receiving array.

3. The cross iteratively solved dual-constrained robust adaptive beamforming method according to claim 1, characterized in that, The step s2 comprises: The first array element in the observation direction angle on the assumed steering vector and the eigenprojection vector : ， ； ； wherein is the array element spacing, is the imaginary unit, denotes the sound velocity, is the eigenvalue corresponding to the eigenvector, denotes the total number of array elements of the receiving array, the superscript denotes the transpose conjugate.

4. The cross iteratively solved dual-constrained robust adaptive beamforming method according to claim 1, characterized in that, The step s3 comprises: Determining a maximum deviation range of a signal angle of arrival according to an angular interval of an observation direction , the assumed steering vector is estimated according to the following formula value: ； ； wherein, represents dividing the possible deviation interval of the signal angle of arrival into angle grid points, is the angle value corresponding to the angle grid point, and the symbol represents the supremum, and is taken as the maximum value among the number of calculation results.

5. The cross iteratively solved dual-constrained robust adaptive beamforming method according to claim 1, characterized in that, The white noise gain constraint parameter in the step s4 The theoretical lower bound Is obtained according to the following formula: ； wherein is an uncertain set parameter, denotes the total number of array elements of the receiving array.

6. The cross iteratively solved double-constrained robust adaptive beamforming method according to claim 5, characterized in that, the white noise gain constraint parameter in said step s4 a theoretical upper bound the acquisition step comprises Step s4-1: Initialization, set the left and right boundaries of the dichotomy and the initial value , ; wherein, is the search upper bound of the theoretical upper bound; Step s4-2: Let ; Step s4-3: Solve the following equation using bisection method to obtain the first undetermined factor the first solution of : ； wherein is the n-th component of the feature projection vector is the n-th component of the feature projection vector is the n-th component of the feature projection vector is the n-th eigenvalue of the sample covariance matrix is the n-th eigenvalue of the sample covariance matrix is the n-th eigenvalue of the sample covariance matrix is the n-th eigenvalue of the sample covariance matrix ； Step s4-4: Solve the following equation using bisection to obtain the second solution for the first undetermined factor a2= 0.5 * (a1+ a3) : ； The first undetermined factor is in the range of ； Step s4-5: If then take , unchanged, otherwise unchanged, take , and go to step s4-2; Step s4-6: until where is a preset small amount threshold, then the value of at this time is the theoretical upper bound of the white noise gain constraint parameter .​ 7. The cross iteratively solved double-constrained robust adaptive beamforming method according to claim 6, characterized in that, theoretical upper bound the acquisition step comprises: Step 01) Take initial values , coefficients ; Step 02) Solve the following equation using bisection method to get the first undetermined factor the first solution of : ； wherein the pending factor ranges from 0 to 1. ； Step 03) Solve the following equation using bisection method to get the first undetermined factor second solution of : ； wherein the pending factor ranges from 0 to 1. ； Step 04) If , take , the coefficient , and return to Step 02); until , then the value of at this time is the search upper limit of the theoretical upper limit of the white noise gain constraint parameter .

8. The cross iteratively solved dual-constrained robust adaptive beamforming method according to claim 1, characterized in that, The step s5 comprises: White noise gain constraint parameters search range Divided into The grid point, where the first... The white noise gain constraint parameter value corresponding to each grid point is expressed as follows: Calculate according to the following formula: ； For each , the following steps are performed: Step s5-1: Let ; wherein, , are the search left and right boundaries of the first pending factor , respectively; Step s5-2: Solve the following equation using bisection method to obtain the second undetermined factor the first solution of : ； wherein, the value range of R2is: ； Step s5-3: Solve the following equation using bisection method to obtain the second undetermined factor the second solution of : ； The second pending factor is in the range of: ； Step s5-4: compare the size of and , if , take , unchanged, otherwise unchanged, take , and return to step s5-1; until , wherein, is a preset small amount threshold, the optimal solution of the first undetermined factor and the second undetermined factor is obtained , : ； ； corresponding slope difference is: ； wherein is the nth eigenvalue of the sample covariance matrix is the nth eigenvalue of the sample covariance matrix is the uncertainty set parameter denotes the total number of array elements of the receiving array.

9. The cross iteratively solved double-constrained robust adaptive beamforming method according to claim 8, characterized in that, the first pending factor the search left boundary and the right boundary the solving process comprises: The first undetermined factor is obtained by solving the following equation using dichotomy for the first solution : ； wherein, the value range of R2is: ； assigning to , for when searching lower bounds on the first pending factor ; Step 01) Set initial values wherein ; Step 02) Solve the following equation using bisection method to get the second undetermined factor First solution : ； wherein the value of R1is in the range of: ； Step 03) Solve the following equation using bisection method to get the second undetermined factor second solution of : ； wherein the pending factor has a value in the range of: ； Step 04) If , take , the coefficient , and go back to Step 02); until , at which time the value of is the search right boundary of the first undecided factor . .

10. The cross iteratively solved dual-constrained robust adaptive beamforming method according to claim 1, characterized in that, The step s6 comprises: Determining an optimal estimate of white noise gain constraint parameters according to a maximum slope difference criterion : ； And will The corresponding undetermined factor optimal solution is respectively set as And .

11. The cross iteratively solved double constrained robust adaptive beamforming method according to claim 10, characterized in that, The step s7 comprises: By and , calculating a robust adaptive beamformer in the direction of the best weighting vector : ； wherein is the first is the assumed steering vector of the array element in the observation direction angle on the observation direction angle is the identity matrix, is the sample covariance matrix, is the uncertainty set parameter.

12. The cross iteratively solved double constrained robust adaptive beamforming method according to claim 11, characterized in that, The step s8 comprises: Step s8-1 : Calculate the assumed steering vector of the correction term: ， ； wherein is a correction vector for the assumed steering vector, is a phase difference between the optimal weight vector and the assumed steering vector, the sign denotes taking the argument of a complex number, the upper index H denotes the conjugate transpose, the upper index is the imaginary unit; Step s8-2: Calculate the corrected steering vector : ； Step s8-3: Calculate Output power estimate in direction : ； Step s8-4: Calculate the corrected power estimate that eliminates the scaling ambiguity : ； wherein is the corrected signal power estimate, denotes the total number of array elements of the receive array.

13. An electronic device comprising a processor and a memory, characterized in that The memory stores a computer program, and the processor executes the program to implement the method of claim 1.

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