A method for bearing estimation of wideband signals based on bilateral correlation transform and array flow pattern interpolation

Abstract

A method for estimating the azimuth of broadband signals using bilateral correlation transformation based on array flow pattern interpolation belongs to the field of underwater acoustic target azimuth estimation. It solves the problem that the existing broadband signal azimuth estimation method only considers the information of the array flow pattern during the focusing process, and the information used is not comprehensive enough, which limits the improvement of the azimuth angle estimation accuracy. The present invention gives full play to the information acquisition advantage of the hydrophone array, while efficiently utilizing the information of multiple frequencies of the underwater acoustic broadband signal. On the basis of the idea of ​​focusing transformation processing of broadband signals, it integrates the array flow pattern interpolation and bilateral correlation transformation methods at the same time, reconstructs the signal covariance matrix of the classic bilateral correlation transformation method through the result of array flow pattern matrix decomposition, and uses the idea of ​​focusing transformation to improve the accuracy of the algorithm for broadband signal azimuth estimation. The present invention is mainly used for broadband signal azimuth estimation.

Description

Technical Field

[0001] The invention belongs to the field of underwater acoustic target azimuth estimation. Background Art

[0002] In the marine environment, target signals such as ship radiation noise can be regarded as broadband signals, and their direction of arrival is an important parameter of marine hydroacoustic targets, and is also an important parameter of concern for passive sonar equipment. As a commonly used broadband signal azimuth estimation method, the focusing transformation method of broadband signals has a azimuth estimation error that increases rapidly with the increase of angle estimation deviation, and its application in underwater environments is greatly limited. The prior art discloses that under the condition of incident broadband target signals (such as ship radiation noise, marine animal sounds, etc.), the signal data obtained by the hydrophone array is used to passively estimate the target incident azimuth. Passive focusing transformation azimuth estimation methods based on broadband signals have appeared in the prior art literature, which are summarized as follows:

[0003] Reference 1 (Zhang Jin, Ye Zhongfu, and Wang Yanlong. Wideband Signal DOA Estimation Method Based on Consistent Focusing [J]. Journal of Circuits and Systems, 2011): Leveraging the concept of consistent focusing, this approach, based on the classic bilateral correlation transform method for broadband signal direction of arrival (DOA), constructs a consistent angle set, which, to a certain extent, mitigates the influence of angle pre-estimation. This study still cannot completely mitigate the influence of angle pre-estimation, and the DOA estimation performance is comparable to that of the classic bilateral correlation transform method.

[0004] Reference 2 (Chen Hongguang. Research on a Robust Direction of Arrival Estimation Algorithm for Array Processing [D]. Doctoral Dissertation, National University of Defense Technology, 2005): Utilizing the concept of focusing transformation, based on the array flow pattern interpolation method, this paper focuses the angle-independent matrix after array flow pattern decomposition. However, this focusing process only considers the array flow pattern information, which is incomplete. This leaves significant room for improvement in direction estimation accuracy. These issues urgently need to be addressed. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that the existing broadband signal azimuth estimation method only considers the information of array flow pattern during the focusing process, the information used is not comprehensive enough, and the improvement of the azimuth angle estimation accuracy is limited. The present invention provides a broadband signal azimuth estimation method based on bilateral correlation transformation of array flow pattern interpolation.

[0006] A method for estimating the direction of a broadband signal based on bilateral correlation transformation using array flow interpolation, comprising the following steps:

[0007] Step 1: Convert the broadband signal received by the hydrophone array into a frequency domain signal. Divide the bandwidth of the broadband signal into J sub-bands. The center frequency of the frequency domain signal corresponding to each sub-band is f j′ , calculate the center frequency f under the bandwidthj′ The corresponding data covariance matrix R X (f j′ ), f j′ is the center frequency of the j′th subband, j′=1,2,3……J;

[0008] Step 2: Use the array flow interpolation method to interpolate the center frequencies f j′ The corresponding array flow matrix A θ (f j′ ) is decomposed into a matrix G(k j′ ) and the matrix W(θ) containing only the angle component; where G(k j′ ) is the wave number k j′ The corresponding array flow interpolation matrix; k j′ is the center frequency f j′ The corresponding wave number, W(θ) is the angle separation matrix corresponding to the set θ consisting of multiple real incident angles;

[0009] Step 3: For each center frequency f j′ The corresponding data covariance matrix R X (f j′ ) denoising, and obtain the center frequency f j′ The corresponding denoised data covariance matrix P(f j′ ), and combined with the matrix G(k j′ ) Solve the signal covariance matrix R j′ ; R j′ is the center frequency f j′ The corresponding signal covariance matrix; using the denoised data covariance matrix corresponding to all center frequencies, the optimal reference frequency f0 is selected from all center frequencies to obtain the denoised data covariance matrix P(f0) corresponding to the optimal reference frequency f0;

[0010] Step 4: P(f j′ ) and P(f0) are subjected to eigenvalue decomposition to obtain the corresponding eigenvectors V(f j′ ) and V(f0), and then get the focusing transformation matrix T(f j′ )=V(f0)V H (f j′ ); T(f j′ ) is the center frequency f j′ The corresponding focusing transformation matrix;

[0011] Step 5: Use each focus transformation matrix T(f j′ ) for its corresponding R X (f j′ ) to focus, and obtain the covariance matrix R of all the center frequency focused data under the optimal reference frequency f0X (f0);

[0012] Step 6: R X (f0) Implement the narrowband signal azimuth estimation method and use the spectrum peak search to obtain the broadband signal azimuth estimation result θ MUSIC .

[0013] Preferably, in step 1,

[0014]

[0015] X(f j′ )=[X1(f j′ ),X2(f j′ ),...,X M (f j′ )] T ;

[0016] M is the number of elements in the hydrophone array, X(f j′ ) is the j′th center frequency f within the bandwidth of the broadband signal received by the hydrophone array j′ The received data vector, X H (f j′ ) is X(f j′ )'s transposed conjugate, X m (f j′ ) is the signal received by the mth element in the hydrophone array at the center frequency f j′ The corresponding frequency domain signal at , m=1,2,3……M.

[0017] Preferably, in step 2, the array flow matrix A θ (f j′ ) is in the form of a series:

[0018]

[0019] A θ (f j′ ) is the array flow matrix of size M×K, M is the number of array elements in the hydrophone array, K is the total number of broadband target signal sources, [A θ (f j′ )] mi Represents the array flow matrix A θ (f j′ ) in the mth row and ith column, k j′ =2πf j′ / c, c is the speed of sound, J u (k j′ r m ) is about the variable k j′ r mThe u-order first-kind Bessel function, N is the highest order of the first-kind Bessel function, u is an integer, r m is the distance between the mth array element and the origin in the polar coordinate system established with the geometric center of the hydrophone array as the origin, is the polar angle of the mth array element, θ=[θ1,θ2,…,θ K ], e is a natural constant, and j is an imaginary unit.

[0020] Preferably, in step 2,

[0021] A θ (f j′ )=G(k j′ )W(θ);

[0022] G(k j′ ) and W(θ) are matrices of size M×(2N+1) and (2N+1)×K, respectively, where M is the number of elements in the hydrophone array, K is the total number of broadband target signal sources, N is the highest order of the first-kind Bessel function, and

[0023]

[0024] [G(k j′ )] m(u+N+1) Denotes the matrix G(k j ), the element in row m and column u+N+1, [W(θ)] (u+N+1)i represents the element in the u+N+1th row and the ith column in the matrix W(θ); J u (k j′ r m ) is about the variable k j′ r m The u-order first-kind Bessel function, where u is an integer and r m is the distance between the mth array element and the origin in the polar coordinate system established with the geometric center of the hydrophone array as the origin, is the polar angle of the mth array element, θ i is the i-th real incident angle in θ, e is a natural constant, and j is an imaginary unit.

[0025] Preferably, in step three,

[0026] P(f j′ )=R X (f j′ )-σ j′ 2 I;

[0027] σ j′ is the center frequency f j′ The corresponding noise power, σ j′ The value of RX (f j′ ) is the average of the first K eigenvalues ​​after all eigenvalues ​​are sorted from small to large after eigendecomposition, and I is the M×M identity matrix.

[0028] Preferably, in step 3, R j′ =(G(k j′ ) H G(k j′ )) -1 G(k j′ ) H P(f j′ )G(k j′ )(G(k j′ ) H G(k j′ )) -1 ;

[0029] G(k j′ ) H is G(k j′ ) is the transposed conjugate of .

[0030] Preferably, in step three

[0031] G(k0) is the array flow interpolation matrix corresponding to the wave number k0, k0 is the wave number corresponding to the optimal reference frequency f0, G H (k0) is the transposed conjugate of G(k0), k0 = 2πf0 / c, and c is the speed of sound.

[0032] Preferably, the optimal reference frequency f0 is determined as follows:

[0033]

[0034] Where σ′ i (P(f0)) is the singular value of the broadband signal corresponding to the i-th broadband target signal source in the matrix P(f0) at the optimal reference frequency f0, σ′ i (P(f j′ )) is the matrix P(f j′ ) The broadband signal corresponding to the i-th broadband target signal source is at the center frequency f j′ The corresponding singular value, μ i is the i-th intermediate variable.

[0035] Preferably, in step five T H (f j′ ) is T(f j′ ) is the transposed conjugate of .

[0036] Preferably, in step six

[0037] Among them, a θ′ (f0) is the steering vector of the search angle θ′ at the optimal reference frequency f0, for a θ′ The transposed conjugate of (f0), U N R X (f0) corresponds to the noise subspace, For U N The transposed conjugate of , e is a natural constant, j is an imaginary unit, τ m (θ′) is the time delay difference between the broadband signal received by the mth element in the hydrophone array and the optimal reference frequency f0 with respect to the search angle θ′, where m = 1, 2, ..., M.

[0038] Advantages of the present invention:

[0039] The present invention fully utilizes the information acquisition advantages of the hydrophone array, while efficiently utilizing the information of multiple frequencies of the underwater acoustic broadband signal. Based on the idea of ​​focusing transformation processing of broadband signals, it also integrates the array flow interpolation and bilateral correlation transformation methods. The signal covariance matrix of the classic bilateral correlation transformation method is reconstructed through the result of array flow matrix decomposition, and the idea of ​​focusing transformation is used to improve the accuracy of the algorithm in estimating the azimuth of broadband signals. Specifically, the array flow matrix is ​​decomposed using the array flow interpolation method, and then the signal covariance matrix is ​​reconstructed based on the decomposition result, successfully avoiding angle estimation and effectively improving the algorithm's azimuth estimation accuracy for broadband signals, making the algorithm more conducive to practical engineering applications. It can completely avoid the problem of the classic bilateral correlation transformation needing to provide an estimated angle, and still have high-precision azimuth estimation capabilities in low signal-to-noise ratio environments.

[0040] The broadband signal azimuth estimation method based on bilateral correlation transformation of array flow interpolation described in the present invention is different from Documents 1 and 2 in the background technology. While utilizing the array flow interpolation method to completely avoid the influence of angle estimation, the present invention utilizes the bilateral correlation transformation method to improve the accuracy of broadband signal azimuth estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a schematic diagram of using an 8-element uniform linear array to estimate the direction of the target signal;

[0042] Figure 2 is the spatial spectrum of the broadband signal direction estimation using the method of the present invention when the signal-to-noise ratio is -10 dB;

[0043] Figure 3 This is a graph showing how the root mean square error of broadband signal azimuth estimation changes with the signal-to-noise ratio using the method of the present invention. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0046] The method for estimating the direction of a wideband signal using bilateral correlation transform based on array flow interpolation described in this embodiment includes the following steps:

[0047] Step 1: Taking an M-element planar hydrophone array as an example, the broadband signal received by the hydrophone array is converted into a frequency domain signal. The bandwidth of the broadband signal is divided into J sub-bands. The center frequency of the frequency domain signal corresponding to each sub-band is f j′ , calculate the center frequency f under the bandwidth j′ The corresponding data covariance matrix R X (f j′ ), f j′ is the center frequency of the j′th subband, j′=1,2,3……J;

[0048] Specifically, the bandwidth range received by each array element is [f L ,f H ] is a broadband signal of X m (t)(m=1,2,…,M), broadband signal X m (t) is converted into a frequency domain signal X m (f), t and f are variables, and t is time, f is frequency, and Fast Fourier Transform FFT conversion can be performed; the bandwidth is divided into J sub-bands, and the center frequency f corresponding to each sub-band in the bandwidth can be obtained j′ The received data vector X(f j′ )=[X1(f j′ ),X2(f j′ ),...,X M (f j′ )] T , and then form the data covariance matrix X H (f j′ ) is X(f j′ )'s transposed conjugate, X m (f j′ ) is the signal received by the mth element in the hydrophone array at the center frequency f j′The corresponding frequency domain signal at , m=1,2,3……M.

[0049] Step 2: Use the array flow interpolation method to interpolate the center frequencies f j′ The corresponding array flow matrix A θ (f j′ ) is decomposed into a matrix G(k j′ ) and the matrix W(θ) containing only the angle component; where G(k j′ ) is the wave number k j′ The corresponding array flow interpolation matrix; k j′ is the center frequency f j′ The corresponding wave number, W(θ) is the angle separation matrix corresponding to the set θ consisting of multiple real incident angles;

[0050] Step 3: For each center frequency f j′ The corresponding data covariance matrix R X (f j′ ) denoising, and obtain the center frequency f j′ The corresponding denoised data covariance matrix P(f j′ ), and combined with the matrix G(k j′ ) Solve the signal covariance matrix R j′ ; R j′ is the center frequency f j′ The corresponding signal covariance matrix; using the denoised data covariance matrix corresponding to all center frequencies, the optimal reference frequency f0 is selected from all center frequencies to obtain the denoised data covariance matrix P(f0) corresponding to the optimal reference frequency f0;

[0051] Step 4: P(f j′ ) and P(f0) are subjected to eigenvalue decomposition to obtain the corresponding eigenvectors V(f j′ ) and V(f0), and then get the focusing transformation matrix T(f j′ )=V(f0)V H (f j′ ); T(f j′ ) is the center frequency f j′ The corresponding focusing transformation matrix;

[0052] Step 5: Use each focus transformation matrix T(f j′ ) for its corresponding R X (f j′ ) to focus, and obtain the covariance matrix R of all the center frequency focused data under the optimal reference frequency f0 X (f0);

[0053] Step 6: R X(f0) Implement narrowband signal azimuth estimation and obtain broadband signal azimuth estimation result θ by spectrum peak search MUSIC In specific applications, narrowband signal azimuth estimation can be achieved using the MUSIC algorithm.

[0054] Based on the idea of ​​conventional focused transform broadband signal azimuth estimation, the present invention integrates the two methods of array flow interpolation and bilateral correlation transform. While avoiding the angle estimation required by focused transform algorithms, it fully utilizes the information of broadband signals and can achieve high-precision azimuth estimation of the target broadband signal.

[0055] Furthermore, in step 2, the array flow matrix A is obtained θ (f j′ )、G(k j′ ) and W(θ) are preferably implemented as follows:

[0056] A polar coordinate system is established with the geometric center of the hydrophone array as the origin, and the polar coordinate of the mth array element is marked as (r m ,φ m ), where r m is the distance between the mth array element and the origin, φ m is the angle between the polar diameter of the mth array element and the polar axis (i.e., the polar angle of the mth array element).

[0057] In order to obtain the focusing transformation matrix T(f j′ ), assuming that there are K broadband target signal sources with the same bandwidth and all of them are located in the same plane as the array, and the matrix θ composed of multiple real incident angles is θ={θ1,θ2,...,θ K}. Now we can use the first kind of Bessel function to convert the j′th frequency f in the bandwidth j′ The corresponding array flow matrix A θ (f j′ ) can be rewritten as follows:

[0058]

[0059] Where A θ (f j′ ) is the array flow matrix of size M×K, M is the number of array elements in the hydrophone array, K is the total number of broadband target signal sources, [A θ (f j′ )] mi Represents the array flow matrix A θ (f j′ ) in the mth row and ith column, k j′ =2πf j′ / c, c is the speed of sound, J u (k j′ r m) is about the variable k j′ r m The u-order first-kind Bessel function, N is the highest order of the first-kind Bessel function, u is an integer, r m is the distance between the mth array element and the origin in the polar coordinate system established with the geometric center of the hydrophone array as the origin, is the polar angle of the mth array element, θ=[θ1,θ2,...,θ K ], e is a natural constant, and j is an imaginary unit.

[0060] The array flow matrix can be further written as follows:

[0061] A θ (f j′ )=G(k j′ )W(θ);

[0062] Where: G(k j′ ) and W(θ) are matrices of size M×(2N+1) and (2N+1)×K respectively:

[0063]

[0064] Where: [G(k j′ )] m(u+N+1) Denotes the matrix G(k j ), the element in row m and column u+N+1, [W(θ)] (u+N+1)i Represents the element in the u+N+1th row and ith column of the matrix W(θ), θ i is the i-th true incident angle in θ.

[0065] Furthermore, in step 3, the center frequencies f are obtained. j′ The corresponding denoised data covariance matrix P(f j′ ) is implemented as follows:

[0066] P(f j′ )=R X (f j′ )-σ j′ 2 I;

[0067] σ j′ is the center frequency f j′ The corresponding noise power, σ j′ The value of R X (f j′ ) is the average of the first K eigenvalues ​​after all eigenvalues ​​are sorted from small to large after eigendecomposition, and I is the M×M identity matrix.

[0068] In this preferred embodiment, the above denoising process is simple and easy to implement.

[0069] Furthermore, in step 3, the denoised data covariance matrix P(f j′ ) combined with the matrix G(k j′ ) Solve the signal covariance matrix R j′ The implementation methods include:

[0070] R j′ =(G(k j′ ) H G(k j′ )) -1 G(k j′ ) H P(f j′ )G(k j′ )(G(k j′ ) H G(k j′ )) -1 ;

[0071] G(k j′ ) H is G(k j′ ) is the transposed conjugate of .

[0072] In this preferred embodiment, the above-mentioned solution of the signal covariance matrix R j′ The method can directly use known information to solve the problem without any prior information, and the solution process is simpler and more accurate.

[0073] Furthermore, the optimal reference frequency f0 is determined in step 3 as follows:

[0074]

[0075] Where σ′ i (P(f0)) is the singular value of the broadband signal corresponding to the i-th broadband target signal source in the matrix P(f0) at the optimal reference frequency f0, σ′ i (P(f j′ )) is the matrix P(f j′ ) The broadband signal corresponding to the i-th broadband target signal source is at the center frequency f j′ The corresponding singular value, μ i In this preferred embodiment, the advantage of the above-mentioned method for determining the optimal reference frequency f0 is that it can minimize the algorithm focusing error, thereby improving the azimuth estimation accuracy of the algorithm.

[0076] Furthermore, the implementation method of obtaining the denoised data covariance matrix P(f0) corresponding to the optimal reference frequency f0 in step 3 includes:

[0077]

[0078] G(k0) is the array flow interpolation matrix corresponding to the wave number k0, k0 is the wave number corresponding to the optimal reference frequency f0, G H (k0) is the transposed conjugate of G(k0), k0 = 2πf0 / c, and c is the speed of sound.

[0079] Furthermore, in step five T H (f j′ ) is T(f j′ ) is the transposed conjugate of .

[0080] In this preferred embodiment, R is constructed by the above formula X The (f0) method focuses the data of multiple frequencies within the bandwidth to the same frequency, effectively integrating the broadband information so that the covariance matrix of the focused data remains full rank, which can be used for decorrelation and high-precision azimuth estimation.

[0081] Furthermore, in step six

[0082]

[0083] Among them, a θ′ (f0) is the steering vector of the search angle θ′ at the optimal reference frequency f0, for a θ′ The transposed conjugate of (f0) is R X (f0) corresponds to the noise subspace, For U N The transposed conjugate of , e is a natural constant, j is an imaginary unit, τ m (θ′) is the time delay difference between the broadband signal received by the mth element in the hydrophone array and the optimal reference frequency f0 with respect to the search angle θ′, where m = 1, 2, ..., M.

[0084] Verification test:

[0085] The effectiveness of the broadband signal azimuth estimation method based on bilateral correlation transformation and array flow interpolation of the present invention is verified by simulation experiments.

[0086] In the simulation, the hydrophone array is an 8-element uniform linear array with a spacing of 0.25m between adjacent elements. The target radiated signal is a broadband random signal with a bandwidth of [2.8, 3.3] kHz. The noise is Gaussian noise with the same bandwidth as the target signal. Data is collected continuously for 1 second at a 10kHz sampling rate. Frequency bins are taken every 10Hz within the bandwidth, the FFT count is 512, the Bessel series expansion has 20 terms, and the angular search step size is 0.5°.

[0087] like Figure 1 A schematic diagram of a broadband random signal incident on an 8-element uniform linear array at 30° is given. Figure 2 The spatial spectrum of the broadband random signal azimuth estimation using the present invention under -10 dB conditions is given: the solid line represents the normalized signal power in that direction, the azimuth corresponding to the maximum value is the estimated azimuth of the broadband signal; the azimuth corresponding to the “◇” represents the actual incident azimuth of the broadband signal. Figure 2 The estimated azimuth is 29.5°, which is consistent with the actual incident azimuth of the broadband signal. Figure 3 The root mean square error between the azimuth estimation result of the present invention and the true incident azimuth is given after 500 independent experiments under each signal-to-noise ratio condition when the signal-to-noise ratio is -10, -8, -6, -4, -2, 0, and 2dB. It can be found that the obtained root mean square error is very small. Even when the signal-to-noise ratio is -10dB, the root mean square error is less than 0.5°, thereby verifying the accuracy of the broadband signal azimuth estimation method based on bilateral correlation transform of array manifold interpolation of the present invention.

[0088] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A method for estimating the direction of a wideband signal using bilateral correlation transform based on array flow interpolation, characterized in that: The method comprises the following steps: Step 1: Convert the broadband signal received by the hydrophone array into a frequency domain signal. Divide the bandwidth of the broadband signal into J sub-bands. The center frequency of the frequency domain signal corresponding to each sub-band is f j′ , calculate the center frequency f under the bandwidth j′ The corresponding data covariance matrix R X (f j′ ), f j′ is the center frequency of the j′th subband, j′=1,2,3……J; Step 2: Use the array flow interpolation method to interpolate the center frequencies f j′ The corresponding array flow matrix A θ (f j′ ) is decomposed into a matrix G(k j′ ) and the matrix W(θ) containing only the angle component; where G(k j′ ) is the wave number k j′ The corresponding array flow interpolation matrix; k j′ is the center frequency f j′ The corresponding wave number, W(θ) is the angle separation matrix corresponding to the set θ consisting of multiple real incident angles; Step 3: For each center frequency f j′ The corresponding data covariance matrix R X (f j′ ) denoising, and obtain the center frequency f j′ The corresponding denoised data covariance matrix P(f j′ ), and combined with the matrix G(k j′ ) Solve the signal covariance matrix R j′ ; R j′ is the center frequency f j′ The corresponding signal covariance matrix; using the denoised data covariance matrix corresponding to all center frequencies, the optimal reference frequency f0 is selected from all center frequencies to obtain the denoised data covariance matrix P(f0) corresponding to the optimal reference frequency f0; Step 4: P(f j′ ) and P(f0) are subjected to eigenvalue decomposition to obtain the corresponding eigenvectors V(f j′ ) and V(f0), and then get the focusing transformation matrix T(f j′ )=V(f0)V H (f j′ ); T(f j′ ) is the center frequency f j′ The corresponding focusing transformation matrix; Step 5: Use each focus transformation matrix T(f j′ ) for its corresponding R X (f j′ ) to focus, and obtain the covariance matrix R of all the center frequency focused data under the optimal reference frequency f0 X (f0); Step 6: R X (f0) Implement the narrowband signal azimuth estimation method and use the spectrum peak search to obtain the broadband signal azimuth estimation result θ MUSIC .

2. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step one, X(f j′ )=[X1(f j′ ),X2(f j′ ),...,X M (f j′ )] T ; M is the number of elements in the hydrophone array, X(f j′ ) is the j′th center frequency f within the bandwidth of the broadband signal received by the hydrophone array j′ The received data vector, X H (f j′ ) is X(f j′ )'s transposed conjugate, X m (f j′ ) is the signal received by the mth element in the hydrophone array at the center frequency f j′ The corresponding frequency domain signal at , m=1,2,3……M.

3. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step 2, the array flow matrix A θ (f j′ ) is in the form of a series: A θ (f j′ ) is the array flow matrix of size M×K, M is the number of array elements in the hydrophone array, K is the total number of broadband target signal sources, [A θ (f j′ )] mi Represents the array flow matrix A θ (f j′ ) in the mth row and ith column, k j′ =2πf j′ / c, c is the speed of sound, J u (k j′ r m ) is about the variable k j′ r m The u-order first-kind Bessel function, N is the highest order of the first-kind Bessel function, u is an integer, r m is the distance between the mth array element and the origin in the polar coordinate system established with the geometric center of the hydrophone array as the origin, is the polar angle of the mth array element, θ=[θ1,θ2,...,θ K ], e is a natural constant, and j is an imaginary unit.

4. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step 2, A θ (f j′ )=G(k j′ )W(θ); G(k j′ ) and W(θ) are matrices of size M×(2N+1) and (2N+1)×K, respectively, where M is the number of elements in the hydrophone array, K is the total number of broadband target signal sources, N is the highest order of the first-kind Bessel function, and [G(k j′ )] m(u+N+1) Denotes the matrix G(k j ), the element in row m and column u+N+1, [W(θ)] (u+N+1)i represents the element in the u+N+1th row and the ith column in the matrix W(θ); J u (k j′ r m ) is about the variable k j′ r m The u-order first-kind Bessel function, where u is an integer and r m is the distance between the mth array element and the origin in the polar coordinate system established with the geometric center of the hydrophone array as the origin, is the polar angle of the mth array element, θ i is the i-th real incident angle in θ, e is a natural constant, and j is an imaginary unit.

5. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step three, P(f j′ )=R X (f j′ )-σ j′ 2 I; σ j′ is the center frequency f j′ The corresponding noise power, σ j′ The value of R X (f j′ ) is the average of the first K eigenvalues ​​after all eigenvalues ​​are sorted from small to large after eigendecomposition, and I is the M×M identity matrix.

6. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step 3, R j′ =(G(k j′ ) H G(k j′ )) -1 G(k j′ ) H P(f j′ )G(k j′ )(G(k j′ ) H G(k j′ )) -1 ; G(k j′ ) H is G(k j′ ) is the transposed conjugate of .

7. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step three G(k0) is the array flow interpolation matrix corresponding to the wave number k0, k0 is the wave number corresponding to the optimal reference frequency f0, G H (k0) is the transposed conjugate of G(k0), k0 = 2πf0 / c, and c is the speed of sound.

8. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: The optimal reference frequency f0 is determined as follows: Where σ′ i (P(f0)) is the singular value of the broadband signal corresponding to the i-th broadband target signal source in the matrix P(f0) at the optimal reference frequency f0, σ′ i (P(f j′ )) is the matrix P(f j′ ) The broadband signal corresponding to the i-th broadband target signal source is at the center frequency f j′ The corresponding singular value, μ i is the i-th intermediate variable.

9. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step five T H (f j′ ) is T(f j′ ) is the transposed conjugate of .

10. The method for azimuth estimation of wideband signals using bilateral correlation transform based on array flow interpolation according to claim 1, characterized in that: In step six Among them, a θ′ (f0) is the steering vector of the search angle θ′ at the optimal reference frequency f0, for a θ′ The transposed conjugate of (f0), U N R X (f0) corresponds to the noise subspace, For U N The transposed conjugate of , e is a natural constant, j is an imaginary unit, τ m (θ′) is the time delay difference between the broadband signal received by the mth array element in the hydrophone array and the optimal reference frequency f0 with respect to the search angle θ′, m = 1, 2, …, M.

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