Decrossing term free frequency difference resolution method based on deconvolution post-processing for azimuth estimation

Abstract

The application belongs to the technical field of underwater acoustic signal processing and array signal processing, and discloses a non-cross-term frequency difference resolution ambiguity bearing estimation method based on deconvolution post-processing, which comprises the following steps: obtaining wideband time domain data received by an array and performing Fourier transform to obtain array observation data of each frequency point; constructing a receiving covariance matrix and performing eigenvalue decomposition, and pre-estimating an array manifold based on the eigenvalue decomposition result; multiplying the conjugate of the pre-estimated array manifold vector by the array observation data to construct a non-cross-term frequency difference equivalent covariance matrix; calculating a grating lobe suppression bearing spectrum by using the equivalent covariance matrix and the difference frequency array manifold vector, and constructing a convolution model of the grating lobe suppression bearing spectrum; constructing a point spread function and performing iterative deconvolution processing to obtain a deconvolution bearing spectrum. The application can effectively suppress spatial aliasing of a sparse array and cross-term interference in a multi-target scene, and simultaneously reduce a bearing spectrum sidelobe level and improve an angle resolution capability.

Description

Technical Field

[0001] This invention belongs to the technical fields of underwater acoustic signal processing, array signal processing and passive sonar target azimuth estimation, and particularly relates to a fuzzy azimuth estimation method based on non-cross term frequency difference decomposition after deconvolution post-processing. Background Technology

[0002] Sparse arrays have significant applications in passive underwater target detection due to their ability to achieve large array apertures with a limited number of elements. However, when the element spacing is greater than half the wavelength of the incident signal, traditional methods such as beamforming, minimum variance distortionless response, and multiple signal classification are prone to spatial aliasing and grating lobes, leading to ambiguity in azimuth-of-arrival estimation.

[0003] Frequency difference methods can suppress spatial aliasing caused by sparse arrays by constructing equivalent low-frequency signals. However, in multi-target scenarios, traditional frequency difference methods require conjugate product processing of array observation data at different frequencies, which can lead to cross-product terms between different targets, forming false peaks or raising the background level in the azimuth spectrum. When strong and weak targets coexist, weak targets are easily masked by the cross-product terms and sidelobe energy of strong targets.

[0004] Chinese invention patent CN120490963A proposes a frequency-differential spatial anti-aliasing azimuth estimation method based on blind array manifold estimation. This method replaces the spatial scanning in traditional frequency-differential estimation with blind estimation of the array manifold, eliminating interference from multi-target cross-terms while significantly reducing computational complexity. However, this patent directly extracts peak values ​​after obtaining the grating lobe-suppressed azimuth spectrum without further optimization. In practical processing, due to factors such as finite aperture, finite number of snapshots, noise perturbations, and array model errors, the grating lobe-suppressed azimuth spectrum still suffers from problems such as main lobe broadening, high side lobe order, and insufficient resolution of adjacent targets.

[0005] Deconvolutional beamforming treats the azimuth spectrum as the convolution result of the real target distribution and the point spread function. Through iterative post-processing, a narrower main lobe and lower side lobes can be obtained. However, existing deconvolution methods are mainly aimed at traditional beamforming and azimuth spectrum for multiple signal classification, and have not been combined with frequency differential processing mechanisms. Therefore, they cannot simultaneously solve the problems of high grating lobes, cross terms, and side lobes.

[0006] Therefore, it is urgent to propose a target azimuth estimation method that, based on the advantages of the cross-term-free frequency difference processing in CN120490963A, can suppress the interference of cross-product terms in traditional frequency difference processing in multi-target scenarios. Based on the estimation results, deconvolution post-processing is performed to reduce sidelobe level, suppress azimuth spectrum background interference, and improve angular resolution. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a fuzzy orientation estimation method based on non-crossing term frequency difference decomposition after deconvolution processing, comprising the following steps: A fuzzy orientation estimation method based on non-cross term frequency difference decomposition after deconvolution processing is characterized by the following steps: S1: Acquire the broadband time-domain data received by the array, perform Fourier transform on the broadband time-domain data, and obtain the array observation data at each frequency point; S2: Construct the receive covariance matrix for the array observation data at each frequency point; S3: Perform eigenvalue decomposition on the received covariance matrix at each frequency point, and pre-estimate the array manifold at each frequency point based on the eigenvalue decomposition result to obtain the pre-estimated array manifold matrix at each frequency point. Each column of the pre-estimated array manifold matrix is ​​a pre-estimated array manifold vector corresponding to a target. S4: For each target, multiply the conjugate of the pre-estimated array manifold vector corresponding to the current target at the target frequency point with the array observation data to construct the cross-term frequency difference equivalent covariance matrix of the target at the target frequency point; S5: Calculate the grating lobe suppression azimuth spectrum of each target at each frequency point using the non-cross term frequency difference equivalent covariance matrix and the difference frequency array manifold vector, and then construct the convolution model of the grating lobe suppression azimuth spectrum. S6: Construct a point spread function at each frequency point; use the point spread function to iteratively deconvolve the grating lobe suppression azimuth spectrum of each target at each frequency point to obtain the deconvolutioned azimuth spectrum of each target at each frequency point; S7: Accumulate the deconvolutioned azimuth spectra of all targets at all frequency points along the frequency dimension to obtain the deconvolution improved frequency difference azimuth spectrum; the method for constructing the deconvolution improved frequency difference azimuth spectrum can be applied to conventional DOA estimators such as traditional beamforming, minimum variance distortionless response, and multiple signal classification. S8: Perform peak search on the deconvolution improved frequency difference azimuth spectrum and output the angle corresponding to the peak as the target azimuth estimation result.

[0008] Furthermore, the received covariance matrix is ​​constructed according to the following formula: , in, For the first The data segment in the first Array observation data vectors at each frequency point This indicates the conjugate transpose. Represents the mathematical expectation. For the first The frequency of each frequency point.

[0009] Furthermore, the pre-estimation of the array manifold at each frequency point includes: performing eigenvalue decomposition on the received covariance matrix at each frequency point to obtain the signal subspace matrix. The signal subspace matrix With the array manifold matrix satisfy ,in It is a non-singular matrix; based on the signal subspace matrix Calculate matrix ,in For matrix eigenvector matrix, The diagonal matrix is ​​composed of eigenvalues; the pre-estimated array manifold matrix is ​​obtained according to the following formula: , in, This indicates the construction of a diagonal matrix with the elements inside the parentheses as diagonal elements. This is a column vector where the first element is 1 and the rest are 0. To select the matrix.

[0010] Furthermore, the frequency difference equivalent covariance matrix without cross terms is constructed according to the following formula: , in, To predict the array manifold matrix At frequency Upper k The pre-estimated array manifold vector of the column corresponds to the first... One goal, Indicates conjugate. For frequency point The array observation data vector above The received covariance matrix.

[0011] Furthermore, the construction of the grating lobe suppression azimuth spectrum includes the following steps: Design a spatial scanning grid for target azimuth estimation: Design orientation scanning grid Its value range is , And set initial values That is ; Calculate the array manifold vector for each azimuth scan grid: Array manifold vector under each azimuth scan grid The calculation formula is as follows: , in,c It's the speed of sound. d It is the spacing between array elements. j It is the imaginary number symbol, and exp(·) represents the natural exponential function. M It is the number of array elements; Calculate the first k The frequency difference corresponding to each target The grating lobe suppression azimuth spectrum: , in, For the first The angle corresponding to each scan grid point Differential frequency Downward scanning orientation The corresponding differential frequency array manifold vector, For the first The target is at the frequency point The above is the frequency difference equivalent covariance matrix without cross terms.

[0012] Furthermore, constructing the point spread function at each frequency point includes: Select a reference direction in angle space Based on a single reference target in the reference direction Differential frequency array manifold vectors on Construct the reference covariance matrix: in, The power of the reference target, For noise power, It is the identity matrix. For differential frequency, At differential frequency , corresponding to the reference direction The array manifold vector; the point spread function is constructed according to the following formula: , in, This is the azimuth scan variable.

[0013] Furthermore, the methods for constructing convolutional models for grating lobe suppression azimuth spectrum include: Using the impulse model Indicates the first k The true angular distribution of the target is expressed as follows: , in, For target strength, For the unit impulse function operator, For the first kThe angle corresponding to each target.

[0014] Further in frequency Next, the k The grating lobe suppression azimuth spectrum corresponding to each target The approximate form of convolution is as follows: , in, This is the convolution operator. In frequency Lower lobe suppression azimuth spectrum The corresponding point spread function, In frequency Lower noise and residual error terms.

[0015] Furthermore, let the first r The target angle distribution estimate for the next iteration is: Then, based on the predicted azimuth spectrum obtained from the current estimate... for , The iterative deconvolution process employs the Richardson-Lucy iterative algorithm, with the target angle distribution estimate updated in each iteration according to the following formula: , in, For the first The target angle distribution estimation in the next iteration can be initialized to take the following values: Alternatively, a uniform non-negative distribution can be taken. The grating lobe suppression azimuth spectrum. Let be the point spread function. This is the transpose of the point spread function. This is the convolution operator. To prevent extremely small positive numbers from being divided by zero, This represents the convolution of the point spread function with the target angular distribution estimate.

[0016] Furthermore, the step of accumulating the deconvolution azimuth spectra of all targets at all frequency points along the frequency dimension includes the following steps: go through After the nth iteration, we obtain the deconvolutioned nth... k The first goal, the first q The azimuth spectrum of each frequency point: , Calculate the azimuth spectrum at each frequency point The obtained azimuth spectrum Along the incoherent superposition in the frequency dimension, we obtain the first... kThe deconvolution broadband spectrum corresponding to each target The expression is as follows: , Iterate through all target columns and deconvolve the broadband spectrum corresponding to each target. The fusion process yields the final deconvolution-improved frequency difference azimuth spectrum. The expression is as follows: .

[0017] Furthermore, the peak search of the deconvolution-improved frequency difference azimuth spectrum includes: Improved frequency difference azimuth spectrum through deconvolution The peak value is taken, and the angle corresponding to the peak value is the result of the target azimuth estimation by the proposed method, as shown in the following expression: , in, This indicates finding the deconvolution-improved frequency difference azimuth spectrum. The x-axis angle corresponding to all peaks Select the largest one. K There are several peaks, and the angles corresponding to these peaks are stored in a set. In the diagram, these angles represent the detected target's location. The total number of the stated targets. The total number of the frequency points.

[0018] Compared with the prior art, the present invention has the following technical effects: This invention effectively suppresses spatial aliasing in sparse arrays and interference from cross-product terms in multi-target scenarios through cross-term frequency difference processing; it avoids mutual contamination between different target spectra by independently constructing cross-term frequency difference equivalent covariance matrices for each target and performing deconvolution processing on each target; and it effectively reduces sidelobe level, narrows main lobe, and improves the resolution of adjacent targets by restoring the target angular distribution through point spread function modeling and Richardson-Lucy iteration. Attached Figure Description

[0019] Figure 1 This is a flowchart of the fuzzy orientation estimation method based on the non-cross term frequency difference decomposition after deconvolution processing according to the present invention. Figure 2 This is a schematic diagram of a sparse array according to an embodiment of the present invention; Figure 3 The target orientation estimation result using the traditional target orientation estimation method in the simulation embodiment; Figure 4The estimation results are obtained using the non-crossing term frequency difference decomposition fuzzy orientation estimation method based on deconvolution post-processing of the present invention in the simulation embodiment. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] Example 1 Please refer to the appendix. Figure 1 This embodiment proposes a fuzzy orientation estimation method based on the frequency difference decomposition of non-crossing terms after deconvolution, which includes the following steps: S1. Obtain array received signal S11. Obtain the array receive time domain signal Set a line by A horizontally uniform, sparse linear array of hydrophones receives... A broadband signal, the target incident angle can be expressed as: , of which The output of each array element is In the formula It is the first A broadband random signal waveform, It is a noise waveform. It is the first The signal at the first Propagation delay on each array element This refers to the signal reception time. Propagation delay. Represented as ,in, It is the speed at which sound waves travel in water. It is the spacing between array elements. It is the first The incident azimuth angle of a signal.

[0022] S12. Represent the frequency domain of the received signal. receive signal time Divided into There are data segments, each with a length of . Then perform a process on each segment. Point FFT operation. In the... In the data segment, the first The frequency domain output of each array element is denoted as ,in Is the signal at the 1st The frequencies at each frequency point. The array output is written as an array observation data vector. ,in, It is the transpose symbol.

[0023] S13. Calculate the received covariance matrix at each frequency point of the received signal. Calculate the received covariance matrix of the received signal based on the array output described above. The details are as follows: , in, It is the conjugate transpose symbol. It is the array output form for receiving signals. It is the mathematical expectation operator.

[0024] S2. Pre-estimate the array manifold of the received signal. S21. Perform eigenvalue decomposition on the covariance matrix of the received signal to obtain the expression for the array manifold. array observation data vector at each frequency point Received covariance matrix Feature decomposition is performed as follows: , in, For one A 3D matrix, representing the signal subspace. For one A 3D matrix, representing the noise subspace. and These are diagonal matrices containing the eigenvalues ​​of the signal subspace and the noise subspace, respectively.

[0025] Considering the above matrix and array manifold matrix They can span the same signal subspace, that is... , in, For one Non-singular matrix.

[0026] S22. Using constant modulus theory to achieve array manifold pre-estimation Array manifold matrix The Middle m Individual Element k Matrix elements corresponding to each signal That is, the first of the matrix m Line number k The absolute value of a column of values ​​can be written as: , in, This represents the absolute value of the scalar within the parentheses or the element-wise absolute value of the vector within the parentheses. It is the conjugate transpose symbol. To calculate the square, For matrix The m OK, It is a matrix The k Column. For each analysis frequency The signal subspace is obtained by eigenvalue decomposition using the array receiver covariance matrix, and then the matrix elements of different array elements are used for array manifold estimation. The constant modulus theory between these parameters allows for the further derivation of the pre-estimated array manifold matrix: , Among them, the pre-estimated array manifold matrix It can be represented as This eliminates the unknown matrices used in the derivation process. The above derivation enables the pre-estimation of the array manifold, avoiding spatial mesh generation and scanning.

[0027] S3. Calculate the array manifold vector under each azimuth scan grid in practice. S31. Spatial scanning grid for target orientation estimation Design orientation scanning grid Its value range is , And set initial values That is .

[0028] S32. Calculate the array manifold vector under each azimuth scan grid. Calculate the array manifold under each azimuth scan grid. , , in, c It's the speed of sound. d It is the spacing between array elements. j It is the imaginary number symbol, and exp(·) represents the natural exponential function. M It is the number of array elements.

[0029] S4. Construct an equivalent covariance matrix without cross-term interference using the array manifold vectors estimated in step two, and calculate the grating lobe suppression azimuth spectrum. S41. Construct an equivalent covariance matrix using the array manifold estimated in step S22. Using the pre-estimated array manifold matrix The k column vector That is, to construct the first k The equivalent covariance matrix of the frequency difference without cross terms corresponding to each objective The calculation is as follows: , S42, Calculate the first k The frequency difference corresponding to each target azimuth spectrum Suppose that the two frequency points satisfy... ,in, The frequency is the differential frequency, and the equivalent element spacing of the sparse array at the differential frequency does not exceed half a wavelength. The first element calculated in step S41 is... k Frequency corresponding to each target The equivalent covariance matrix under and has a frequency difference Differential frequency array manifold vector under each azimuth scan grid Calculations are performed to obtain the first frequency at that frequency point. k The grating lobe suppression azimuth spectrum corresponding to each target The calculation is as follows: , To enhance numerical robustness during the calculation process, the equivalent covariance matrix can be adjusted. Perform diagonal loading.

[0030] S43. Calculate the frequency difference that satisfies the requirement. azimuth spectrum For all K The grating lobe suppression azimuth spectra of each target are accumulated to obtain the grating lobe suppression azimuth spectrum. The calculation is as follows: .

[0031] S5. Construct a convolution model for suppressing the azimuth spectrum of grating lobes. S51 constructs the first k Impulse model of the true angle distribution of each target Using the impulse model Indicates the first k The true angular distribution of the targets is represented as follows: , in, For target strength, It is a unit impulse function operator.

[0032] S52, Approximate representation of grating lobe suppression azimuth spectrum The frequency obtained in step S42 Next, the k The grating lobe suppression azimuth spectrum corresponding to each target Approximately represented in convolution form, the calculation is as follows: , in, This is the convolution operator. In frequency Lower lobe suppression azimuth spectrum The corresponding point spread function, In frequency Lower noise and residual error terms.

[0033] S53, Calculate the first k Broadband spectrum corresponding to each target Calculate the grating lobe suppression azimuth spectrum at each frequency point according to step S52, and then obtain the azimuth spectrum. Along the incoherent superposition in the frequency dimension, we obtain the first... k Broadband spectrum corresponding to each target The calculation is as follows: , in, The summation operator represents the summation of all vectors within the parentheses. This represents the number of frequency points.

[0034] S6. Constructing the point spread function This embodiment takes the MVDR method as an example. For the improved frequency differential MVDR method, a single-target reference covariance matrix can be constructed. The calculation is as follows: in, The power of the reference target, For noise power, It is the identity matrix. For differential frequency, At differential frequency , corresponding to the reference direction The array manifold vector; construct the point spread function according to the following formula.

[0035] Constructing an improved frequency differential MVDR point spread function for: .

[0036] S7. Derivation of Richardson-Lucy deconvolution under improved frequency difference MVDR. Ignoring the noise term in step S52, we get: , The further solution objective is to start from the known and China Resumption ; Order No. r The target angle distribution estimate for the next iteration is: Then, based on the predicted azimuth spectrum obtained from the current estimate... for: , True Directional Spectrum With predicted azimuth spectrum The ratio between them is: , The error ratio is back-projected using the back convolution of the point spread function to obtain the correction factor. : , in, It is the transpose symbol.

[0037] The correction factor is directly used to update the target angle distribution estimate. In each iteration, it back-projects the "error ratio" between the true spectrum and the predicted spectrum, multiplying it by the current estimate as a multiplicative correction term. Therefore, the Richardson-Lucy iterative update formula is: , in, Point spread function The transpose of the expression, when applied to the improved frequency differential MVDR, gives the point spread function as the improved frequency differential MVDR point spread function. Replacement To prevent extremely small positive numbers from being divided by zero. Initialization is acceptable Alternatively, a uniform non-negative distribution can be adopted.

[0038] go through After the nth iteration, we obtain the deconvolutioned nth... k The first goal, the first q The azimuth spectrum of each frequency point: , Calculate the azimuth spectrum at each frequency point using the steps described above. The obtained azimuth spectrum Along the incoherent superposition in the frequency dimension, we obtain the first... k The deconvolution broadband spectrum corresponding to each target The calculation is as follows: , in, The summation operator represents the summation of all vectors within the parentheses. This represents the number of frequency points.

[0039] S8. Output of target orientation estimation results Iterate through all target columns and repeat step seven to deconvolve the wideband spectrum corresponding to all targets. The fusion process yields the final deconvolution-improved frequency difference MVDR azimuth spectrum. The calculation is as follows: , Improved Frequency Difference MVDR Azimuth Spectrum by Deconvolution The peak value is taken, and the angle corresponding to the peak value is the result of the target azimuth estimation by the proposed method, that is: , in, This indicates the identification of the deconvolution-improved frequency difference MVDR azimuth spectrum. The x-axis angle corresponding to all peaks And store these angles in a set. In this context, these angles represent the detected target's location.

[0040] This embodiment effectively suppresses spatial aliasing of sparse arrays and interference from cross-product terms in multi-target scenarios through cross-term frequency difference processing; it avoids mutual contamination between different target spectra by independently constructing cross-term frequency difference equivalent covariance matrices for each target and performing deconvolution processing on each target; and it effectively reduces sidelobe level, narrows main lobe, and improves the resolution of adjacent targets by restoring the target angular distribution through point spread function modeling and Richardson-Lucy iteration.

[0041] Example 2 This embodiment is a simulation embodiment. The applicant uses a uniform linear array as the signal receiving array, designing a 10-element uniform linear array, selecting a broadband signal frequency band of 4.5kHz-5.5kHz, and a sampling rate of 15kHz. The speed of sound is selected as 1500m / s. The frequency is 250Hz, the element spacing corresponds to half the wavelength at this frequency, i.e., 3m, the number of snapshots is 100, and the number of sampling points in each snapshot is 1500.

[0042] Suppose there are three broadband incident signals, each with a bandwidth of 4.5kHz-5.5kHz, and incident angles of 60°, 75.5°, and 85°, respectively. Construct an estimation scenario for weak targets under strong interference, with the signal-to-noise ratio of the first signal being 10dB. The other two targets are weak targets, and their signal energy is 10dB lower than that of the first signal.

[0043] Appendix Figure 2 The diagram shows the array layout under the assumptions of this example.

[0044] Please refer to the attached document. Figure 3Under the simulation conditions of this embodiment, the spatial spectrum obtained by estimating the target azimuth using the MVDR method is specifically affected by spatial aliasing. In the scenario of weak target estimation under strong interference, only the strong interference at 60° can be effectively estimated, while the peak values ​​of the other two weak targets are masked by the grating lobe interference.

[0045] Please refer to the attached document. Figure 4 Under the simulation conditions of this example, the target orientation estimation results of the method proposed in this application show that the fuzzy orientation estimation method based on deconvolution post-processing without cross-term frequency difference decomposition proposed in this application can accurately estimate the true orientation of the three targets and effectively suppress the interference of spatial aliasing on the estimation results.

[0046] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A fuzzy orientation estimation method based on non-cross-term frequency difference decomposition after deconvolution post-processing, characterized in that, Includes the following steps: S1: Acquire the broadband time-domain data received by the array, perform Fourier transform on the broadband time-domain data, and obtain the array observation data at each frequency point; S2: Construct the receive covariance matrix for the array observation data at each frequency point; S3: Perform eigenvalue decomposition on the received covariance matrix at each frequency point, and pre-estimate the array manifold at each frequency point based on the eigenvalue decomposition result to obtain the pre-estimated array manifold matrix at each frequency point. Each column of the pre-estimated array manifold matrix is ​​a pre-estimated array manifold vector corresponding to a target. S4: For each target, multiply the conjugate of the pre-estimated array manifold vector corresponding to the current target at the target frequency point with the array observation data to construct the cross-term frequency difference equivalent covariance matrix of the target at the target frequency point; S5: Calculate the grating lobe suppression azimuth spectrum of each target at each frequency point using the non-cross term frequency difference equivalent covariance matrix and the difference frequency array manifold vector, and then construct the convolution model of the grating lobe suppression azimuth spectrum. S6: Construct the point spread function at each frequency point; The point spread function is used to iteratively deconvolve the grating lobe suppression azimuth spectrum of each target at each frequency point to obtain the deconvolutioned azimuth spectrum of each target at each frequency point. S7: Accumulate the deconvolutioned azimuth spectra of all targets at all frequency points along the frequency dimension to obtain the deconvolutioned improved frequency difference azimuth spectrum; S8: Perform peak search on the deconvolution improved frequency difference azimuth spectrum and output the angle corresponding to the peak as the target azimuth estimation result.

2. The fuzzy orientation estimation method based on non-cross-term frequency difference decomposition according to claim 1, characterized in that, The received covariance matrix is ​​constructed according to the following formula: ， in, For the first The data segment in the first Array observation data vectors at each frequency point This indicates the conjugate transpose. Represents the mathematical expectation. For the first The frequency of each frequency point.

3. The fuzzy orientation estimation method based on non-cross-term frequency difference decomposition according to claim 2, characterized in that, The pre-estimation of the array manifold at each frequency point includes: performing eigenvalue decomposition on the received covariance matrix at each frequency point to obtain the signal subspace matrix. The signal subspace matrix With the array manifold matrix satisfy ,in It is a non-singular matrix; based on the signal subspace matrix Calculate matrix ,in For matrix eigenvector matrix, The diagonal matrix is ​​composed of eigenvalues; the pre-estimated array manifold matrix is ​​obtained according to the following formula: ， in, This indicates the construction of a diagonal matrix with the elements inside the parentheses as diagonal elements. This is a column vector where the first element is 1 and the rest are 0. To select the matrix.

4. The fuzzy orientation estimation method based on non-cross term frequency difference decomposition according to claim 3, characterized in that, The frequency difference equivalent covariance matrix without cross terms is constructed according to the following formula: ， in, To predict the array manifold matrix At frequency Upper k The pre-estimated array manifold vector of the column corresponds to the first... One goal, Indicates conjugate. For frequency point The array observation data vector above The received covariance matrix.

5. The fuzzy orientation estimation method based on non-cross term frequency difference decomposition according to claim 4, characterized in that, The steps for constructing the grating lobe suppression azimuth spectrum include: Design a spatial scanning grid for target azimuth estimation: Azimuth Scan Grid Its value range is , And set initial values That is ; Calculate the array manifold vector for each azimuth scan grid: Array manifold vector under each azimuth scan grid The calculation formula is as follows: , in, c It's the speed of sound. d It is the spacing between array elements. j It is the imaginary number symbol, and exp(·) represents the natural exponential function. M It is the number of array elements; Calculate the first k The frequency difference corresponding to each target The grating lobe suppression azimuth spectrum: ， in, For the first The angle corresponding to each scan grid point Differential frequency Downward scanning orientation The corresponding differential frequency array manifold vector, For the first The target is at the frequency point The above is the frequency difference equivalent covariance matrix without cross terms.

6. The fuzzy orientation estimation method based on non-cross term frequency difference decomposition according to claim 5, characterized in that, The construction of the point spread function at each frequency point includes: Select a reference direction in angle space Based on a single reference target in the reference direction Differential frequency array manifold vectors on Construct the reference covariance matrix: ， in, The power of the reference target, For noise power, It is the identity matrix. For differential frequency, At differential frequency , corresponding to the reference direction The array manifold vector; the point spread function is constructed according to the following formula: ， in, This is the azimuth scan variable.

7. The fuzzy orientation estimation method based on non-cross term frequency difference decomposition according to claim 6, characterized in that, Methods for constructing convolutional models for grating lobe suppression of azimuth spectrum include: Using the impulse model Indicates the first k The true angular distribution of the target is expressed as follows: ， in, For target strength, For the unit impulse function operator, For the first k The angle corresponding to each target; Further in frequency Next, the k The grating lobe suppression azimuth spectrum corresponding to each target The approximate form of convolution is as follows: ， in, This is the convolution operator. In frequency Lower lobe suppression azimuth spectrum The corresponding point spread function, In frequency Lower noise and residual error terms.

8. The fuzzy orientation estimation method based on non-cross term frequency difference decomposition according to claim 7, characterized in that, Order No. r The target angle distribution estimate for the next iteration is: Then, based on the predicted azimuth spectrum obtained from the current estimate... for ， The iterative deconvolution process employs the Richardson-Lucy iterative algorithm, with the target angle distribution estimate updated in each iteration according to the following formula: ， in, For the first The target angle distribution estimation in the next iteration can be initialized to take the following values: Alternatively, a uniform non-negative distribution can be taken. The grating lobe suppression azimuth spectrum. Let be the point spread function. This is the transpose of the point spread function. This is the convolution operator. To prevent extremely small positive numbers from being divided by zero, This represents the convolution of the point spread function with the target angular distribution estimate.

9. The fuzzy orientation estimation method based on non-cross-term frequency difference decomposition according to claim 8, characterized in that, The step of accumulating the deconvolution azimuth spectrum of all targets at all frequency points along the frequency dimension includes the following steps: go through After the nth iteration, we obtain the deconvolutioned nth... k The first goal, the first q The azimuth spectrum of each frequency point: ， Calculate the azimuth spectrum at each frequency point The obtained azimuth spectrum By noncoherently superimposing along the frequency dimension, the deconvolution broadband spectrum corresponding to the k-th target is obtained. The expression is as follows: ， Iterate through all target columns and deconvolve the broadband spectrum corresponding to each target. The fusion process yields the final deconvolution-improved frequency difference azimuth spectrum. The expression is as follows: 。 10. The fuzzy orientation estimation method based on non-cross-term frequency difference decomposition according to claim 9, characterized in that, The peak search for the deconvolution-improved frequency difference azimuth spectrum includes: Improved frequency difference azimuth spectrum through deconvolution The peak value is taken, and the angle corresponding to the peak value is the result of the target azimuth estimation by the proposed method, as shown in the following expression: ， in, This indicates finding the deconvolution-improved frequency difference azimuth spectrum. The x-axis angle corresponding to all peaks Select the largest one. K There are several peaks, and the angles corresponding to these peaks are stored in a set. In the diagram, these angles represent the detected target's location. The total number of the stated targets. The total number of the frequency points.

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