A frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation

Abstract

A frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation includes the following steps: constructing a uniform linear array to receive a broadband signal; converting the time-domain signal into a frequency signal and dividing the broadband signal into narrowband signals; calculating the covariance matrix of each frequency point of the received signal; eigendecomposing the covariance matrix of the narrowband signal and performing array manifold blind estimation; dividing a spatial scanning grid to calculate a narrowband azimuth spectrum; calculating a narrowband grating lobe suppression azimuth spectrum by frequency differential processing; traversing all narrowbands to generate a broadband azimuth spectrum and a grating lobe suppression azimuth spectrum; extracting a peak interval from the broadband grating lobe suppression azimuth spectrum, scanning within the interval range corresponding to the broadband azimuth spectrum, and extracting the peak value as a target estimation result. The present invention avoids the problem of target azimuth estimation failure caused by the generation of cross terms due to the need for multiplication of the received signal itself in traditional frequency-differential technology, while significantly reducing the huge amount of computation caused by spatial scanning.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a frequency differential space anti-aliasing azimuth estimation method for array manifold blind estimation. Background Art

[0002] In sonar systems, direction-of-arrival (DOA) estimation is an important research area. According to the spatial Nyquist sampling theorem, the element spacing of a sonar array must be half the wavelength of the incident signal. Common signals are divided into broadband and narrowband signals. For narrowband signals, as the signal frequency increases, the wavelength decreases accordingly, resulting in periodic ambiguity in the azimuth spectrum, which is known as spatial aliasing. Similarly, for broadband signals, when the element spacing is greater than half a wavelength, spatial aliasing occurs at each frequency point. Although the superposition of these frequencies can suppress spatial aliasing to a certain extent, the performance of broadband signal azimuth estimation is still affected. In summary, when the element spacing is much greater than the wavelength of the incident signal, phase ambiguity results, and a large number of grating lobes appear in the azimuth spectrum, affecting the accuracy of target azimuth estimation.

[0003] In recent years, scholars have proposed a series of methods based on frequency difference technology to solve spatial aliasing. Frequency difference processing is to multiply the array observation value of one frequency point with the conjugate form of the array observation value of another frequency point, and the frequency difference between the two frequency points must satisfy the spatial Nyquist theorem. Frequency difference technology is equivalent to an operation that can completely solve the spatial aliasing problem through frequency reduction processing. However, when solving the multi-target spatial aliasing problem, the traditional frequency difference technology will affect the target bearing estimation result due to the existence of cross terms, and the true target bearing cannot be accurately estimated. The existing technology (Yang Long, Wang Yong and Yang Yixin, "Spatial Anti-aliasing Broadband Bearing Estimation Using Frequency Difference Technology" [J]. "American Journal of Acoustics, 2021, 150 (6): 4256-4267) proposes to introduce a new reference signal to perform conjugate multiplication with the received signal and perform frequency difference processing to avoid the interference of cross terms and achieve high-resolution bearing estimation of multi-target spatial anti-aliasing. However, although the existing technology has good estimation performance, it still requires azimuth scanning of the reference signal and the received signal, so the amount of calculation is huge.

[0004] To sum up, considering that in practical applications, we will face many array and signal relationship scenarios that do not satisfy the spatial Nyquist sampling theorem. In the face of the presence of grating lobes in target azimuth estimation in these practical application scenarios, it is urgent to propose a time-effective high-resolution azimuth estimation method that can achieve multi-target spatial anti-aliasing, so as to effectively and quickly solve the spatial aliasing problem. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide a frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation, aiming to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation specifically comprises the following steps:

[0008] S1: Construction A uniform linear array of sensors is formed to receive A broadband signal;

[0009] S2: Convert the time domain signal into a frequency signal through FFT transformation, and divide the broadband signal into narrowband signals;

[0010] S3: Calculate the covariance matrix of each frequency point of the received signal;

[0011] S4: Perform eigendecomposition on the covariance matrix of the narrowband signal and perform array manifold blind estimation;

[0012] S5: Divide the spatial scanning grid and calculate the azimuth spectrum;

[0013] S6: Construct an equivalent covariance matrix using the blindly estimated array populated matrix and the covariance matrix of the narrowband signal, and calculate the grating lobe suppression azimuth spectrum. The expression of the equivalent covariance matrix is ​​as follows:

[0014] ,

[0015] in, Indicates constructing a diagonal element as the element in the brackets, is the blind estimation array manifold, is the equivalent covariance matrix, is the frequency, is the covariance matrix;

[0016] S7: traverse all narrowbands, and superimpose azimuth spectra in the frequency dimension, and obtain a broadband azimuth spectrum and a grating lobe suppression azimuth spectrum based on each narrowband azimuth spectrum and grating lobe suppression azimuth spectrum;

[0017] S8: Post-process the broadband azimuth spectrum and grating lobe suppression azimuth spectrum to improve the accuracy of target estimation results.

[0018] Further technical solutions, S1 Array element output Expressed as:

[0019] ,

[0020] ,

[0021] In the formula It is A broadband random signal waveform, is the noise waveform, It is The signal in The propagation delay on each array element is is the signal reception time length, is the speed of sound waves in water, is the array element spacing, It is The incident azimuth angle of the signal.

[0022] Further technical solution, S2 will receive the signal time Divided into data segments, each segment is , and then for each segment Point FFT operation, in the In the data segment The frequency domain output of each array element is recorded as ,in The signal is The frequency at each frequency point, write the array output into matrix form:

[0023] ,

[0024] in, is the transpose symbol.

[0025] A further technical solution is to calculate the covariance matrix of the received signal according to the above array output in S3 , calculated as follows:

[0026] ,

[0027] in, is the conjugate transpose symbol, is the array output form of the received signal, is the mathematical expectation operator.

[0028] In a further technical solution, in S4, the covariance matrix of the received signal is subjected to eigendecomposition to obtain an expression of the array manifold;

[0029] Receive signals at each frequency point The covariance matrix of Perform eigendecomposition and calculate as follows:

[0030] ,

[0031] in, For one dimensional matrix, representing the signal subspace, For one dimensional matrix, representing the noise subspace, and are diagonal matrices containing the eigenvalues ​​of the signal subspace and the noise subspace respectively;

[0032] Considering the above matrix and array manifold matrix can be stretched into the same signal subspace, which is

[0033] ,

[0034] in, For one -dimensional non-singular matrix;

[0035] The constant modulus theory is used to realize the blind estimation of array manifold, as follows:

[0036] Array Manifold Matrix Middle Array element The matrix elements corresponding to the signal , that is, the matrix Rank The absolute value of a column value can be expressed as:

[0037] ,

[0038] in, represents the absolute value of the scalar in the brackets or the element-wise absolute value of the vector in the brackets. is the conjugate transpose symbol, Indicates calculation of square, is a matrix No. OK, is a matrix No. Column, using matrix elements of different array elements The constant modulus theory between

[0039] ,

[0040] in, is the array manifold matrix Middle Array element The matrix elements corresponding to the signals are is the array manifold matrix The first element in the The matrix elements corresponding to the signals are ;

[0041] Using the matrix straightening property, we can deduce:

[0042] ,

[0043] in, is a dimensional matrix, its OK , , It is a set with all elements set to 0. dimensional vector, is the Kronecker product operator, is the conjugate symbol, is the matrix straightening operator, is the transpose symbol;

[0044] Performing singular value decomposition on the matrix, we can get the following expression:

[0045] ,

[0046] in, is a dimensional matrix, is a dimensional matrix, and these two matrices are left and right singular matrices, is a dimensional matrix, which is a matrix with the singular values ​​on the diagonal arranged in descending order. is a matrix No. k row vector;

[0047] vector and can be stretched into the same null space, and any vector in the null space It can be expressed as:

[0048] ,

[0049] in, and They are and The coefficients of ; using the matrix straightening operator The inverse Writing the above vector in matrix form gives:

[0050] ,

[0051] in, , It means to construct a matrix with the diagonal elements in the brackets and the rest of the elements are 0;

[0052] By deduction, we can get:

[0053] ,

[0054] Among them, the matrix The columns are eigenvectors, and the matrix The diagonal elements are the eigenvalues, and the unitary matrix ,and , is any real vector, It means to construct a matrix with the diagonal elements in the brackets and the rest of the elements are 0. represents an exponential function with the natural constant e (approximately 2.71828) as the base, is one The selection matrix of dimension is Only the The first element is 1, and the rest of the elements are 0. By derivation, we can see that , therefore, we can further deduce the array manifold expression obtained by blind estimation as:

[0055] ,

[0056] Among them, the matrix It can be expressed as , which can eliminate the unknown matrix used in the derivation process Through the above derivation, blind estimation of array manifold is achieved, avoiding space grid division and scanning.

[0057] Further technical solutions, S5 design azimuth scanning grid , its value range is , , and set the initial value , which is ;

[0058] Calculate the array manifold under each azimuth scanning grid , calculated as follows: ,

[0059] Using the calculated array manifold and the covariance matrix of the received signal , calculate the azimuth spectrum of the frequency point by MVDR method , calculated as follows:

[0060] .

[0061] Preferably, the calculated array manifold is used and the covariance matrix of the received signal The azimuth spectrum of the frequency point can also be calculated through various azimuth estimation methods such as MUSIC and CBF .

[0062] Further technical solution, frequency differential processing described in S6 The steps are as follows:

[0063] ,

[0064] in, is the narrowband grating lobe suppression azimuth spectrum, is the frequency difference.

[0065] A further technical solution is to traverse all narrowband frequencies and repeat steps S2-S6 to calculate all azimuth spectra. and grating lobe suppression azimuth spectrum , and the azimuth spectrum and grating lobe suppression azimuth spectrum Sum along the frequency dimension to obtain the final broadband azimuth spectrum and broadband grating lobe suppression azimuth spectrum , calculated as follows:

[0066] ,

[0067] ,

[0068] in, It means to sum all the matrices in the brackets.

[0069] A further technical solution is to select a certain range near the peak of the broadband grating lobe suppression azimuth spectrum regarded as the target as a search interval in S8, extract the maximum peak of the broadband azimuth spectrum corresponding to the search interval, and use these maximum peaks as target estimation results.

[0070] In summary, the embodiments of the present invention have the following beneficial effects compared with the prior art:

[0071] The frequency-differential spatial anti-aliasing azimuth estimation method based on blind array manifold estimation, provided in an embodiment of the present invention, is a high-precision, low-computation target azimuth estimation method that can achieve spatial anti-aliasing under various array conditions and improve the accuracy of target azimuth estimation results. The frequency-differential technique avoids the impact of grating lobe ambiguity on target azimuth estimation. The blind estimation array manifold assists in the calculation of the equivalent covariance matrix, avoiding the problem of target azimuth estimation failure caused by the cross terms of the received signal itself, while significantly reducing the huge computational complexity of the algorithm due to spatial scanning.

[0072] In order to more clearly illustrate the structural features and effects of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flow chart of the present invention;

[0074] Figure 2 A schematic diagram of the sensor arrangement in a preferred embodiment;

[0075] Figure 3 Schematic diagram of target position estimation results using the MVDR method in a preferred embodiment;

[0076] Figure 4 Schematic diagram of target azimuth estimation results of a grating lobe suppression method after constructing an equivalent covariance matrix using a blindly estimated array manifold in a preferred embodiment;

[0077] Figure 5 Schematic diagram of target direction estimation results of the frequency differential spatial anti-aliasing direction estimation method using array manifold blind estimation in a preferred embodiment. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0079] The specific implementation of the present invention is described in detail below with reference to specific embodiments. Specific embodiment 1

[0081] As attached Figure 1 As shown, an embodiment of the present invention provides a frequency differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation, which specifically includes the following steps:

[0082] S1: Construction A uniform linear array of sensors is formed to receive A broadband signal;

[0083] Specifically, consider a A horizontal uniform linear array of sensors is formed to receive broadband signal, where Array element output Expressed as:

[0084] ,

[0085] ,

[0086] In the formula It is A broadband random signal waveform, is the noise waveform, It is The signal in The propagation delay on each array element is is the signal reception time length, is the speed of sound waves in water, is the array element spacing, It is The incident azimuth angle of the signal;

[0087] S2: Convert the time domain signal into a frequency signal through FFT (Fast Fourier Transform), and divide the broadband signal into narrowband signals;

[0088] Specifically, the signal receiving time Divided into data segments, each segment is , and then for each segment Point FFT operation, in the In the data segment The frequency domain output of each array element is recorded as ,in The signal is The frequency at each frequency point, write the array output into matrix form:

[0089] ,

[0090] in, is the transpose symbol;

[0091] S3: Calculate the covariance matrix of each frequency point of the received signal;

[0092] Specifically, the covariance matrix of the received signal is calculated based on the above array output , calculated as follows:

[0093] ,

[0094] in, is the conjugate transpose symbol, is the array output form of the received signal, is the mathematical expectation operator;

[0095] S4: Perform eigendecomposition on the covariance matrix of the narrowband signal and perform array manifold blind estimation;

[0096] (1) Perform eigendecomposition on the covariance matrix of the received signal to obtain the expression of the array manifold;

[0097] Specifically, for each frequency point receiving signal The covariance matrix of Perform eigendecomposition and calculate as follows:

[0098] ,

[0099] in, For one dimensional matrix, representing the signal subspace, For one dimensional matrix, representing the noise subspace, and are diagonal matrices containing the eigenvalues ​​of the signal subspace and the noise subspace respectively;

[0100] Considering the above matrix and array manifold matrix can be stretched into the same signal subspace, which is

[0101] ,

[0102] in, For one -dimensional non-singular matrix;

[0103] (2) Using constant modulus theory to achieve blind estimation of array manifold;

[0104] Specifically, the array manifold matrix Middle Array element The matrix elements corresponding to the signal , that is, the matrix Rank The absolute value of a column value can be expressed as:

[0105] ,

[0106] in, represents the absolute value of the scalar in the brackets or the element-wise absolute value of the vector in the brackets. is the conjugate transpose symbol, Indicates calculation of square, is a matrix No. OK, is a matrix No. Column, using matrix elements of different array elements The constant modulus theory between can be derived as follows:

[0107] ,

[0108] in, is the array manifold matrix Middle Array element The matrix elements corresponding to the signals are is the array manifold matrix The first element in the The matrix elements corresponding to the signals are ;

[0109] Using the matrix straightening property, we can deduce:

[0110] ,

[0111] in, is a dimensional matrix, its OK , , It is a set with all elements set to 0. dimensional vector, is the Kronecker product operator, is the conjugate symbol, is the matrix straightening operator, is the transpose symbol;

[0112] Performing singular value decomposition on the matrix, we can get the following expression:

[0113] ,

[0114] in, is a dimensional matrix, is a dimensional matrix, and these two matrices are left and right singular matrices, is a dimensional matrix, which is a matrix with the singular values ​​on the diagonal arranged in descending order. is a matrix No. k row vector;

[0115] vector and can be stretched into the same null space, and any vector in the null space It can be expressed as:

[0116] ,

[0117] in, and They are and The coefficients of ; using the matrix straightening operator The inverse Writing the above vector in matrix form gives:

[0118] ,

[0119] in, , It means to construct a matrix with the diagonal elements in the brackets and the rest of the elements are 0;

[0120] By deduction, we can get:

[0121] ,

[0122] Among them, the matrix The columns are eigenvectors, and the matrix The diagonal elements are the eigenvalues, and the unitary matrix ,and , is any real vector, It means to construct a matrix with the diagonal elements in the brackets and the rest of the elements are 0. represents an exponential function with the natural constant e (approximately 2.71828) as the base, is one The selection matrix of dimension is Only the The first element is 1, and the rest of the elements are 0. By derivation, we can see that , therefore, we can further deduce the array manifold expression obtained by blind estimation as:

[0123] ,

[0124] Among them, the matrix It can be expressed as , which can eliminate the unknown matrix used in the derivation process Through the above derivation, blind estimation of array manifold is achieved, avoiding space grid division and scanning.

[0125] S5: Divide the spatial scanning grid and calculate the azimuth spectrum using MVDR;

[0126] (1) Design a spatial scanning grid for target orientation estimation;

[0127] Designing the Azimuth Scan Grid , its value range is , , and set the initial value , which is .

[0128] (2) Calculate the array manifold vector under each azimuth scanning grid;

[0129] Calculate the array manifold under each azimuth scanning grid , calculated as follows: ,

[0130] (3) Use array manifold to estimate target direction.

[0131] Specifically, using the calculated array manifold and the covariance matrix of the received signal , calculate the azimuth spectrum of the frequency point by MVDR method , as attached Figure 3 As shown, the calculation is as follows:

[0132] ;

[0133] S6: Use the blind estimated array populated and narrowband signal covariance matrices to construct the equivalent covariance matrix and calculate the grating lobe suppression azimuth spectrum, as shown in the attached figure. Figure 4 As shown;

[0134] (1) Constructing the equivalent covariance matrix using the blindly estimated array manifold;

[0135] Using blind estimation of array manifold Constructing the equivalent covariance matrix , calculated as follows:

[0136] ,

[0137] (2) Calculate the frequency difference The azimuth spectrum;

[0138] Specifically, use The frequency calculated by the calculation formula The equivalent covariance matrix under and has a frequency difference with it The array manifold under each azimuth scanning grid Calculate the grating lobe suppression azimuth spectrum of the frequency point , calculated as follows:

[0139] ;

[0140] S7: traverse all narrowbands, and superimpose azimuth spectra in the frequency dimension, and obtain a broadband azimuth spectrum and a grating lobe suppression azimuth spectrum based on each narrowband azimuth spectrum and grating lobe suppression azimuth spectrum;

[0141] Specifically, traverse all narrowband frequencies, repeat steps S2-S6, and calculate all azimuth spectra and grating lobe suppression azimuth spectrum , and the azimuth spectrum and grating lobe suppression azimuth spectrum Sum along the frequency dimension to obtain the final broadband azimuth spectrum and broadband grating lobe suppression azimuth spectrum , calculated as follows:

[0142] ,

[0143] ,

[0144] in, Indicates the sum of all matrices in the brackets;

[0145] S8: Select a certain range near the peak of the broadband grating lobe suppression azimuth spectrum considered as the target as a search interval, extract the maximum peak of the broadband azimuth spectrum corresponding to the search interval, and use these maximum peaks as target estimation results.

[0146] Specifically, in the grating lobe suppression azimuth spectrum Take the peak value, and take the peak value around Range as an aspect spectrum constraints and calculate the orientation spectrum within these ranges The angle corresponding to the peak value of is the result of target orientation estimation by the proposed method, as shown in the attached figure. Figure 5 shown.

[0147] Simulation Example 2

[0148] In order to further verify the effectiveness of the present invention, the present invention provides a simulation example. Figure 2 As shown, a uniform linear array is used as the signal receiving array. Consider a 10-element uniform linear array, select the broadband signal frequency band as 4.5kHz-5.5kHz, and the sampling rate as 15kHz. The sound speed is selected as 1500m / s, and the selected The frequency is 250Hz, the array element spacing corresponds to the half-wavelength length at this frequency, that is, 3m, the number of snapshots is 100, and the number of sampling points in each snapshot is 1500; assuming there are three broadband incident signals, the signal bandwidth is 4.5kHz-5.5kHz, and the incident angles are 60.3°, 75.25°, and 85.37° respectively. Construct an estimation scenario for weak targets under strong interference. Only the signal-to-noise ratio of the first signal is 10dB. The other two targets are weak targets, and the signal energy of each signal is 10dB lower than that of the first signal.

[0149] Attachment Figure 2 Shown is the array arrangement under the assumptions of this simulation example.

[0150] Attachment Figure 3The spatial spectrum of the target direction estimation using the MVDR method under the simulation conditions of this example shows that due to the influence of spatial aliasing, in the weak target estimation scenario under strong interference, only the strong interference at 60.3° can be effectively estimated, while the peaks of the other two weak targets are masked by the grating lobe interference.

[0151] Attachment Figure 4 The spatial spectrum of the target azimuth estimation is performed using the grating lobe suppression method proposed in step 4 under the simulation conditions of this example. It can be seen that the method proposed in step 4 of this application can effectively suppress the spatial aliasing problem, but due to the low accuracy of the scanning grid, the estimation accuracy in this scenario is limited, and the target resolution ability needs to be improved.

[0152] Attachment Figure 5 The target azimuth estimation results of the method proposed in this application under the simulation conditions of this example show that the frequency differential spatial anti-aliasing azimuth estimation method based on array manifold blind estimation proposed in this application can accurately estimate the true azimuth of the target without spatial aliasing.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A frequency differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation, characterized in that: The specific steps include: S1: Construction A uniform linear array of sensors is formed to receive A broadband signal; S2: Convert the time domain signal into a frequency signal through FFT transformation, and divide the broadband signal into narrowband signals; S3: Calculate the covariance matrix of each frequency point of the received signal; S4: Perform eigendecomposition on the covariance matrix of the narrowband signal and perform blind estimation of the array manifold, perform eigendecomposition on the covariance matrix of the received signal, and obtain an expression of the array manifold; Receive signals at each frequency point The covariance matrix of Perform feature decomposition as follows: ， in, For one dimensional matrix, representing the signal subspace, For one dimensional matrix, representing the noise subspace, and are diagonal matrices containing the eigenvalues ​​of the signal subspace and the noise subspace respectively; Considering the above matrix and array manifold matrix can be stretched into the same signal subspace, which is ， in, For one -dimensional non-singular matrix; The constant modulus theory is used to realize the blind estimation of array manifold, and the expression is as follows: ， Among them, the matrix It can be expressed as , where the matrix The columns of are eigenvectors, It means to construct a matrix with the diagonal elements in the brackets and the rest of the elements are 0. represents the exponential function with the natural constant e as the base, is a The selection matrix of dimension is Only the elements are 1, and the rest are 0; S5: Divide the spatial scanning grid, calculate the azimuth spectrum, and design the azimuth scanning grid , its value range is , , and set the initial value , which is ; Calculate the array manifold under each azimuth scanning grid , calculated as follows: , Using the calculated array manifold And the covariance matrix of the received signal calculated , calculate the narrowband azimuth spectrum of the frequency point , calculated as follows: ； S6: Using the blindly estimated array current and the covariance matrix of the narrowband signal, an equivalent covariance matrix is ​​constructed to implement frequency differential processing and calculate the grating lobe suppression azimuth spectrum. The expression of the equivalent covariance matrix is ​​as follows: ， in, Indicates constructing a diagonal element as the element in the brackets, is the blind estimation array manifold, is the equivalent covariance matrix, is the frequency, is the covariance matrix; S7: traverse all narrowbands, and superimpose azimuth spectra in the frequency dimension, and obtain a broadband azimuth spectrum and a grating lobe suppression azimuth spectrum based on each narrowband azimuth spectrum and grating lobe suppression azimuth spectrum; S8: Post-process the broadband azimuth spectrum and grating lobe suppression azimuth spectrum to improve the accuracy of target estimation results.

2. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 1, characterized in that: S1 Array element output Expressed as: ， ， In the formula It is A broadband random signal waveform, is the noise waveform, It is The signal in The propagation delay on each array element is is the signal reception time length, is the speed of sound waves in water, is the array element spacing, It is The incident azimuth angle of the signal.

3. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 2, characterized in that: S2 will receive the signal time Divided into data segments, each segment is , and then for each segment Point FFT operation, in the In the data segment The frequency domain output of each array element is recorded as ,in The signal is The frequency at each frequency point, write the array output into matrix form: ， in, is the transpose symbol.

4. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 3, characterized in that: In S3, the covariance matrix of the received signal is calculated based on the above array output , calculated as follows: ， in, is the conjugate transpose symbol, is the array output form of the received signal, is the mathematical expectation operator.

5. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 4, characterized in that: The frequency difference processing in S6 includes the following steps: ， in, is the narrowband grating lobe suppression azimuth spectrum, is the frequency difference.

6. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 5, characterized in that: Traverse all narrowband frequencies, repeat S2-S6, and calculate the narrowband azimuth spectrum at all frequencies and narrowband grating lobe suppression azimuth spectrum , and the narrowband azimuth spectrum and narrowband grating lobe suppression azimuth spectrum Sum along the frequency dimension to obtain the final broadband azimuth spectrum and broadband grating lobe suppression azimuth spectrum , calculated as follows: ， ， in, It means to sum all the matrices in the brackets.

7. The frequency-differential spatial anti-aliasing azimuth estimation method for array manifold blind estimation according to claim 1, characterized in that: The post-processing described in S8 is specifically as follows: A certain range near the peak of the broadband grating lobe suppression azimuth spectrum considered as the target is selected as the retrieval interval, the maximum peak of the broadband azimuth spectrum corresponding to the retrieval interval is extracted, and these maximum peaks are used as target estimation results.

Images